vayesta.lattmod

Submodules

vayesta.lattmod.bethe

vayesta.lattmod.bethe.hubbard1d_bethe_energy(t, u, interval=(1e-14, 96.60397409788614), **kwargs)

Exact total energy per site for the 1D Hubbard model in the thermodynamic limit.

from DOI: 10.1103/PhysRevB.77.045133.

vayesta.lattmod.bethe.hubbard1d_bethe_docc(t, u, interval=(1e-14, 96.60397409788614), **kwargs)

Exact on-site double occupancy for the 1D Hubbard model in the thermodynamic limit.

vayesta.lattmod.bethe.hubbard1d_bethe_docc_numdiff(t, u, du=1e-10, order=2, **kwargs)

Exact on-site double occupancy for the 1D Hubbard model in the thermodynamic limit.

Calculated from the numerical differentiation of the exact Bethe ansatz energy.

vayesta.lattmod.bethe.hubbard1d_bethe_gap(t, u, interval=(1, 100), **kwargs)

Exact band gap for the 1D Hubbard model at half filling in the thermodynamic limit.

from DOI: 10.1103/PhysRevB.106.045123

vayesta.lattmod.latt

class vayesta.lattmod.latt.LatticeMole(nsite, nelectron=None, spin=0, order=None, incore_anyway=True, verbose=0, output=None)

Bases: Cell

For PySCF compatibility

Needs to implement: a copy() build() intor_cross() intor_symmetric() pbc_intor() basis

? atom_coord unit

property nelectron

spin = 0

incore_anyway = False

property natm

nao_nr()

Total number of contracted GTOs for the given Mole object

ao_labels(fmt=True)

Labels of AO basis functions

Kwargs:

fmtstr or bool

if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

atom_symbol(site)

For the given atom id, return the input symbol (without striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2

atom_pure_symbol(site)

For the given atom id, return the standard symbol (striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H

search_ao_label()

Find the index of the AO basis function based on the given ao_label

Parameters:

ao_label – string or a list of strings The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

property Gv

property ao_loc

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_loc_2c()

Offset of every shell in the spinor basis function spectrum

Returns:

list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

ao_loc_nr(cart=None)

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_rotation_matrix(orientation)

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

aoslice_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

atom_charge(atm_id)

Nuclear effective charge of the given atom id Note “atom_charge /= charge(atom_symbol)” when ECP is enabled. Number of electrons screened by ECP can be obtained by charge(atom_symbol)-atom_charge

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17

atom_charges()

np.asarray([mol.atom_charge(i) for i in range(mol.natm)])

atom_coord(atm_id, unit='Bohr')

Coordinates (ndarray) of the given atom id

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0.          0.          2.07869874]

atom_coords(unit='Bohr')

np.asarray([mol.atom_coord(i) for i in range(mol.natm)])

atom_mass_list(isotope_avg=False)

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean

Whether to use the isotope average mass as the atomic mass

atom_nelec_core(atm_id)

Number of core electrons for pseudo potential.

atom_nshells(atm_id)

Number of basis/shells of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5

atom_shell_ids(atm_id)

A list of the shell-ids of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.atom_shell_ids(1)
[3, 4, 5, 6, 7]

bas_angular(bas_id)

The angular momentum associated with the given basis

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2

bas_atom(bas_id)

The atom (0-based id) that the given basis sits on

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1

bas_coord(bas_id)

Coordinates (ndarray) associated with the given basis id

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0.          0.          2.07869874]

bas_ctr_coeff(bas_id)

Contract coefficients (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.M(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_ctr_coeff(0)
[[ 10.03400444]
 [  4.1188704 ]
 [  1.53971186]]

bas_exp(bas_id)

exponents (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(0)
[ 13.01     1.962    0.4446]

bas_exps()

exponents of all basis return [mol.bas_exp(i) for i in range(self.nbas)]

bas_kappa(bas_id)

Kappa (if l < j, -l-1, else l) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0

bas_len_cart(bas_id)

The number of Cartesian function associated with given basis

bas_len_spinor(bas_id)

The number of spinor associated with given basis If kappa is 0, return 4l+2

bas_nctr(bas_id)

The number of contracted GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3

bas_nprim(bas_id)

The number of primitive GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11

bas_rcut(bas_id, precision=None)

Estimate the largest distance between the function and its image to reach the precision in overlap

precision ~ int g(r-0) g(r-Rcut)

build(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

build_lattice_symmetry(check_mesh_symmetry=True)

Build cell.lattice_symmetry object.

Kwargs:

check_mesh_symmetrybool

For nonsymmorphic symmetry groups, cell.mesh may have lower symmetry than the lattice. In this case, if check_mesh_symmetry is True, the lower symmetry group will be used. Otherwise, if check_mesh_symmetry is False, the mesh grid will be modified to satisfy the higher symmetry. Default value is True.

Note

This function modifies the attributes of cell.

cart = False

cart2sph_coeff(normalized='sp')

Transformation matrix that transforms Cartesian GTOs to spherical GTOs for all basis functions

Kwargs:

normalizedstring or boolean

How the Cartesian GTOs are normalized. Except s and p functions, Cartesian GTOs do not have the universal normalization coefficients for the different components of the same shell. The value of this argument can be one of ‘sp’, ‘all’, None. ‘sp’ means the Cartesian s and p basis are normalized. ‘all’ means all Cartesian functions are normalized. None means none of the Cartesian functions are normalized. The default value ‘sp’ is the convention used by libcint library.

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> c = mol.cart2sph_coeff()
>>> s0 = mol.intor('int1e_ovlp_sph')
>>> s1 = c.T.dot(mol.intor('int1e_ovlp_cart')).dot(c)
>>> print(abs(s1-s0).sum())
>>> 4.58676826646e-15

cart_labels(fmt=True, base=0)

Labels of Cartesian GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

charge = 0

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

condense_to_shell(mat, compressor='max')

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Parameters:

compressor – string or function if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

copy(deep=True)

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

cutoff_to_mesh(ke_cutoff)

Convert KE cutoff to FFT-mesh

Parameters:

ke_cutoff – float KE energy cutoff in a.u.

Returns:

(3,) array

Return type:

mesh

decontract_basis(atoms=None, to_cart=False, aggregate=False)

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str

Atoms on which the basis to be decontracted. By default, all basis are decontracted

to_cart: bool

Decontract basis and transfer to Cartesian basis

aggregate: bool

Whether to aggregate the transformation coefficients into a giant transformation matrix

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

property drop_exponent

dump_input()

dumps()

Serialize Cell object to a JSON formatted str.

property elements

A list of elements in the molecule

energy_nuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

property enuc

nuclear repulsion energy

static etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

property ew_cut

property ew_eta

ewald(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

exp_to_discard = None

static expand_etb(l, n, alpha, beta)

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Parameters:

• l – int Angular momentum

• n – int Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

static expand_etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

format_atom(atoms, origin=0, axes=None, unit='angstrom')

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to separate the individual terms for an atom. Blank line will be ignored.

Parameters:

atoms – list or str the same to Mole.atom

Kwargs:

originndarray

new axis origin.

axesndarray

(new_x, new_y, new_z), new coordinates

unitstr or number

If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is

atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

static format_basis(basis_tab, sort_basis=True)

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..)))], … }``

Parameters:

basis_tab – dict Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

static format_ecp(ecp_tab)

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1

(exp_2, c_2), …),

((exp_1, c_1), # for r^2

…))))),

…}

static format_pseudo(pseudo_tab)

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Parameters:

pseudo_tab – dict Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

from_ase(ase_atom)

Update cell based on given ase atom object

Examples:

>>> from ase.lattice import bulk
>>> cell.from_ase(bulk('C', 'diamond', a=LATTICE_CONST))

gen_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

get_Gv(mesh=None, **kwargs)

Calculate three-dimensional G-vectors for the cell; see MH (3.8).

Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.

Parameters:

cell – instance of Cell

Returns:

(ngrids, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_Gv_weights(mesh=None, **kwargs)

Calculate G-vectors and weights.

Returns:

(ngris, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_SI(Gv=None, mesh=None, atmlst=None)

Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).

Parameters:

• cell – instance of Cell

• Gv – (N,3) array G vectors

• atmlst – list of ints, optional Indices of atoms for which the structure factors are computed.

Returns:

(natm, ngrids) ndarray, dtype=np.complex128

The structure factor for each atom at each G-vector.

Return type:

SI

get_abs_kpts(scaled_kpts)

Get absolute k-points (in 1/Bohr), given “scaled” k-points in fractions of lattice vectors.

Parameters:

scaled_kpts – (nkpts, 3) ndarray of floats

Returns:

(nkpts, 3) ndarray of floats

Return type:

abs_kpts

get_ao_indices(bas_list, ao_loc=None)

Generate (dis-continued) AO indices for basis specified in bas_list

get_bounding_sphere(rcut)

Finds all the lattice points within a sphere of radius rcut.

Defines a parallelepiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85

Parameters:

rcut – number real space cut-off for interaction

Returns:

ndarray of 3 ints defining N_x

Return type:

cut

get_enuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

get_ewald_params(precision=None, mesh=None)

Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}

Choice is based on largest G vector and desired relative precision.

The relative error in the G-space sum is given by

precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}

which determines eta. Then, real-space cutoff is determined by (exp. factors only)

precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}

Returns:

float

The Ewald ‘eta’ and ‘cut’ parameters.

Return type:

ew_eta, ew_cut

get_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

get_lattice_Ls(nimgs=None, rcut=None, dimension=None, discard=True)

Get the (Cartesian, unitful) lattice translation vectors for nearby images. The translation vectors can be used for the lattice summation.

Kwargs:

discard:

Drop less important Ls based on AO values on grid

get_nimgs(precision=None)

Choose number of basis function images in lattice sums to include for given precision in overlap, using

precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}

where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.

get_overlap_cond(shls_slice=None)

Overlap magnitudes measured by -log(overlap) between two shells

Parameters:

mol – an instance of Mole

Returns:

2D mask array of shape (nbas,nbas)

get_scaled_atom_coords(a=None)

Get scaled atomic coordinates.

get_scaled_kpts(abs_kpts, kpts_in_ibz=True)

Get scaled k-points, given absolute k-points in 1/Bohr.

Parameters:

• abs_kpts – (nkpts, 3) ndarray of floats or KPoints object

• kpts_in_ibz – bool If True, return k-points in IBZ; otherwise, return k-points in BZ. Default value is True. This has effects only if abs_kpts is a KPoints object

Returns:

(nkpts, 3) ndarray of floats

Return type:

scaled_kpts

get_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

property gs

gto_norm(l, expnt)

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Parameters:

• l (int) – angular momentum

• expnt – exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

property h

has_ecp()

Whether pseudo potential is used in the system.

has_ecp_soc()

Whether spin-orbit coupling is enabled in ECP.

intor(intor, comp=None, hermi=0, aosym='s1', out=None, shls_slice=None, grids=None)

Integral generator.

Parameters:

intor – str Name of the 1e or 2e AO integrals. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

hermiint

Symmetry of the integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian

shls_slice4-element, 6-element or 8-element tuple

Label the start-stop shells for each index in the integral. For example, the 8-element tuple for the 2-electron integral tensor (ij|kl) = intor(‘int2e’) are specified as (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor('int1e_ipnuc_sph', comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]
>>> mol.intor('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_asymmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be anti-hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_asymmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j  0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j  0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_by_shell(intor, shells, comp=None, grids=None)

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Parameters:

• intor_name – str See also getints() for the supported intor_name

• shls – list of int The AO shell-ids of the integrals

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

intor_symmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_symmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

kernel(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

lattice_vectors()

Convert the primitive lattice vectors.

Return 3x3 array in which each row represents one direction of the lattice vectors (unit in Bohr)

classmethod loads(molstr)

Deserialize a str containing a JSON document to a Cell object.

loads_(molstr)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

make_atm_env(atom, ptr=0, nucmod=1, nucprop=None)

Convert the internal format Mole._atom to the format required by libcint integrals

make_bas_env(basis_add, atom_id=0, ptr=0)

Convert Mole.basis to the argument bas for libcint integrals

make_ecp_env(_atm, _ecp, pre_env=[])

Generate the input arguments _ecpbas for ECP integrals

make_env(atoms, basis, pre_env=[], nucmod={}, nucprop=None)

Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

make_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

max_memory = 4000

property mesh

property ms

Spin quantum number. multiplicity = ms*2+1

property multiplicity

property nao

nao_2c()

Total number of contracted spinor GTOs for the given Mole object

nao_2c_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id, 0-based

• bas_id1 – int stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

nao_cart()

Total number of contracted cartesian GTOs for the given Mole object

nao_nr_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id

• bas_id1 – int stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

property nbas

property nelec

property nimgs

npgto_nr(cart=None)

Total number of primitive spherical GTOs for the given Mole object

offset_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_ao_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

property omega

output = None

pack()

Pack the input args of Cell to a dict, which can be serialized with pickle

pbc_eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_intor(intor, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)

One-electron integrals with PBC.

\[\sum_T \int \mu(r) * [intor] * \nu (r-T) dr\]

See also Mole.intor

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

precision = 1e-08

property rcut

rcut_by_shells(precision=None, rcut=0, return_pgf_radius=False)

Compute shell and primitive gaussian function radii.

reciprocal_vectors(norm_to=6.283185307179586)

\[\begin{split}\begin{align} \mathbf{b_1} &= 2\pi \frac{\mathbf{a_2} \times \mathbf{a_3}}{\mathbf{a_1} \cdot (\mathbf{a_2} \times \mathbf{a_3})} \\ \mathbf{b_2} &= 2\pi \frac{\mathbf{a_3} \times \mathbf{a_1}}{\mathbf{a_2} \cdot (\mathbf{a_3} \times \mathbf{a_1})} \\ \mathbf{b_3} &= 2\pi \frac{\mathbf{a_1} \times \mathbf{a_2}}{\mathbf{a_3} \cdot (\mathbf{a_1} \times \mathbf{a_2})} \end{align}\end{split}\]

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

search_ao_nr(atm_id, l, m, atmshell)

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Parameters:

• atm_id – int atom id, 0-based

• l – int angular momentum

• m – int magnetic angular momentum

• atmshell – int principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

search_ao_r(atm_id, l, j, m, atmshell)

search_shell_id(atm_id, l)

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

set_common_orig(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_orig_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_f12_zeta(zeta)

Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals

set_geom_(atoms_or_coords, unit=None, symmetry=None, inplace=True)

Update geometry

set_nuc_mod(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_nuc_mod_(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_range_coulomb(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_range_coulomb_(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_rinv_orig(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_orig_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_zeta(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

set_rinv_zeta_(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

sph2spinor_coeff()

Transformation matrix that transforms real-spherical GTOs to spinor GTOs for all basis functions

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> ca, cb = mol.sph2spinor_coeff()
>>> s0 = mol.intor('int1e_ovlp_spinor')
>>> s1 = ca.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(ca)
>>> s1+= cb.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(cb)
>>> print(abs(s1-s0).max())
>>> 6.66133814775e-16

sph_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spheric_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spinor_labels(fmt=True, base=0)

Labels of spinor GTO functions

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

symmetrize_mesh(mesh=None)

symmetry = False

symmetry_subgroup = None

time_reversal_map()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

tmap()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

to_mol()

Return a Mole object using the same atoms and basis functions as the Cell object.

to_uncontracted_cartesian_basis()

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

tot_electrons(nkpts=1)

Total number of electrons

unit = 'angstrom'

classmethod unpack(moldic)

Convert the packed dict to a Cell object, to generate the input arguments for Cell object.

unpack_(moldic)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

update(chkfile)

update_from_chk(chkfile)

verbose = 3

view(cls)

New view of object with the same attributes.

property vol

with_common_orig(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_common_origin(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_integral_screen(threshold)

Return a temporary mol context which has the required integral screen threshold

with_long_range_coulomb(omega)

Return a temporary mol context for long-range part of range-separated Coulomb operator.

with_range_coulomb(omega)

Return a temporary mol context which sets the required parameter omega for range-separated Coulomb operator. If omega = None, return the context for regular Coulomb integrals. See also mol.set_range_coulomb()

Examples:

>>> with mol.with_range_coulomb(omega=1.5):
...     mol.intor('int2e')

with_rinv_as_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_at_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_orig(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_origin(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_zeta(zeta)

Return a temporary mol context which has the rquired Gaussian charge distribution placed at “rinv_origin”: rho(r) = Norm * exp(-zeta * r^2). See also mol.set_rinv_zeta()

Examples:

>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
...     mol.intor('int1e_rinv')

with_short_range_coulomb(omega)

Return a temporary mol context for short-range part of range-separated Coulomb operator.

class vayesta.lattmod.latt.Hubbard(nsite, nelectron=None, spin=0, hubbard_t=1.0, hubbard_u=0.0, v_nn=0.0, **kwargs)

Bases: LatticeMole

Abstract Hubbard model class.

aoslice_by_atom()

One basis function per site (“atom”).

ao2mo(mo_coeffs, compact=False)

property Gv

ao_labels(fmt=True)

Labels of AO basis functions

Kwargs:

fmtstr or bool

if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

property ao_loc

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_loc_2c()

Offset of every shell in the spinor basis function spectrum

Returns:

list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

ao_loc_nr(cart=None)

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_rotation_matrix(orientation)

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

aoslice_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

atom_charge(atm_id)

Nuclear effective charge of the given atom id Note “atom_charge /= charge(atom_symbol)” when ECP is enabled. Number of electrons screened by ECP can be obtained by charge(atom_symbol)-atom_charge

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17

atom_charges()

np.asarray([mol.atom_charge(i) for i in range(mol.natm)])

atom_coord(atm_id, unit='Bohr')

Coordinates (ndarray) of the given atom id

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0.          0.          2.07869874]

atom_coords(unit='Bohr')

np.asarray([mol.atom_coord(i) for i in range(mol.natm)])

atom_mass_list(isotope_avg=False)

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean

Whether to use the isotope average mass as the atomic mass

atom_nelec_core(atm_id)

Number of core electrons for pseudo potential.

atom_nshells(atm_id)

Number of basis/shells of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5

atom_pure_symbol(site)

For the given atom id, return the standard symbol (striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H

atom_shell_ids(atm_id)

A list of the shell-ids of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.atom_shell_ids(1)
[3, 4, 5, 6, 7]

atom_symbol(site)

For the given atom id, return the input symbol (without striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2

bas_angular(bas_id)

The angular momentum associated with the given basis

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2

bas_atom(bas_id)

The atom (0-based id) that the given basis sits on

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1

bas_coord(bas_id)

Coordinates (ndarray) associated with the given basis id

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0.          0.          2.07869874]

bas_ctr_coeff(bas_id)

Contract coefficients (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.M(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_ctr_coeff(0)
[[ 10.03400444]
 [  4.1188704 ]
 [  1.53971186]]

bas_exp(bas_id)

exponents (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(0)
[ 13.01     1.962    0.4446]

bas_exps()

exponents of all basis return [mol.bas_exp(i) for i in range(self.nbas)]

bas_kappa(bas_id)

Kappa (if l < j, -l-1, else l) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0

bas_len_cart(bas_id)

The number of Cartesian function associated with given basis

bas_len_spinor(bas_id)

The number of spinor associated with given basis If kappa is 0, return 4l+2

bas_nctr(bas_id)

The number of contracted GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3

bas_nprim(bas_id)

The number of primitive GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11

bas_rcut(bas_id, precision=None)

Estimate the largest distance between the function and its image to reach the precision in overlap

precision ~ int g(r-0) g(r-Rcut)

build(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

build_lattice_symmetry(check_mesh_symmetry=True)

Build cell.lattice_symmetry object.

Kwargs:

check_mesh_symmetrybool

For nonsymmorphic symmetry groups, cell.mesh may have lower symmetry than the lattice. In this case, if check_mesh_symmetry is True, the lower symmetry group will be used. Otherwise, if check_mesh_symmetry is False, the mesh grid will be modified to satisfy the higher symmetry. Default value is True.

Note

This function modifies the attributes of cell.

cart = False

cart2sph_coeff(normalized='sp')

Transformation matrix that transforms Cartesian GTOs to spherical GTOs for all basis functions

Kwargs:

normalizedstring or boolean

How the Cartesian GTOs are normalized. Except s and p functions, Cartesian GTOs do not have the universal normalization coefficients for the different components of the same shell. The value of this argument can be one of ‘sp’, ‘all’, None. ‘sp’ means the Cartesian s and p basis are normalized. ‘all’ means all Cartesian functions are normalized. None means none of the Cartesian functions are normalized. The default value ‘sp’ is the convention used by libcint library.

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> c = mol.cart2sph_coeff()
>>> s0 = mol.intor('int1e_ovlp_sph')
>>> s1 = c.T.dot(mol.intor('int1e_ovlp_cart')).dot(c)
>>> print(abs(s1-s0).sum())
>>> 4.58676826646e-15

cart_labels(fmt=True, base=0)

Labels of Cartesian GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

charge = 0

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

condense_to_shell(mat, compressor='max')

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Parameters:

compressor – string or function if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

copy(deep=True)

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

cutoff_to_mesh(ke_cutoff)

Convert KE cutoff to FFT-mesh

Parameters:

ke_cutoff – float KE energy cutoff in a.u.

Returns:

(3,) array

Return type:

mesh

decontract_basis(atoms=None, to_cart=False, aggregate=False)

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str

Atoms on which the basis to be decontracted. By default, all basis are decontracted

to_cart: bool

Decontract basis and transfer to Cartesian basis

aggregate: bool

Whether to aggregate the transformation coefficients into a giant transformation matrix

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

property drop_exponent

dump_input()

dumps()

Serialize Cell object to a JSON formatted str.

property elements

A list of elements in the molecule

energy_nuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

property enuc

nuclear repulsion energy

static etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

property ew_cut

property ew_eta

ewald(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

exp_to_discard = None

static expand_etb(l, n, alpha, beta)

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Parameters:

• l – int Angular momentum

• n – int Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

static expand_etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

format_atom(atoms, origin=0, axes=None, unit='angstrom')

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to separate the individual terms for an atom. Blank line will be ignored.

Parameters:

atoms – list or str the same to Mole.atom

Kwargs:

originndarray

new axis origin.

axesndarray

(new_x, new_y, new_z), new coordinates

unitstr or number

If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is

atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

static format_basis(basis_tab, sort_basis=True)

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..)))], … }``

Parameters:

basis_tab – dict Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

static format_ecp(ecp_tab)

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1

(exp_2, c_2), …),

((exp_1, c_1), # for r^2

…))))),

…}

static format_pseudo(pseudo_tab)

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Parameters:

pseudo_tab – dict Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

from_ase(ase_atom)

Update cell based on given ase atom object

Examples:

>>> from ase.lattice import bulk
>>> cell.from_ase(bulk('C', 'diamond', a=LATTICE_CONST))

gen_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

get_Gv(mesh=None, **kwargs)

Calculate three-dimensional G-vectors for the cell; see MH (3.8).

Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.

Parameters:

cell – instance of Cell

Returns:

(ngrids, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_Gv_weights(mesh=None, **kwargs)

Calculate G-vectors and weights.

Returns:

(ngris, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_SI(Gv=None, mesh=None, atmlst=None)

Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).

Parameters:

• cell – instance of Cell

• Gv – (N,3) array G vectors

• atmlst – list of ints, optional Indices of atoms for which the structure factors are computed.

Returns:

(natm, ngrids) ndarray, dtype=np.complex128

The structure factor for each atom at each G-vector.

Return type:

SI

get_abs_kpts(scaled_kpts)

Get absolute k-points (in 1/Bohr), given “scaled” k-points in fractions of lattice vectors.

Parameters:

scaled_kpts – (nkpts, 3) ndarray of floats

Returns:

(nkpts, 3) ndarray of floats

Return type:

abs_kpts

get_ao_indices(bas_list, ao_loc=None)

Generate (dis-continued) AO indices for basis specified in bas_list

get_bounding_sphere(rcut)

Finds all the lattice points within a sphere of radius rcut.

Defines a parallelepiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85

Parameters:

rcut – number real space cut-off for interaction

Returns:

ndarray of 3 ints defining N_x

Return type:

cut

get_enuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

get_ewald_params(precision=None, mesh=None)

Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}

Choice is based on largest G vector and desired relative precision.

The relative error in the G-space sum is given by

precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}

which determines eta. Then, real-space cutoff is determined by (exp. factors only)

precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}

Returns:

float

The Ewald ‘eta’ and ‘cut’ parameters.

Return type:

ew_eta, ew_cut

get_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

get_lattice_Ls(nimgs=None, rcut=None, dimension=None, discard=True)

Get the (Cartesian, unitful) lattice translation vectors for nearby images. The translation vectors can be used for the lattice summation.

Kwargs:

discard:

Drop less important Ls based on AO values on grid

get_nimgs(precision=None)

Choose number of basis function images in lattice sums to include for given precision in overlap, using

precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}

where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.

get_overlap_cond(shls_slice=None)

Overlap magnitudes measured by -log(overlap) between two shells

Parameters:

mol – an instance of Mole

Returns:

2D mask array of shape (nbas,nbas)

get_scaled_atom_coords(a=None)

Get scaled atomic coordinates.

get_scaled_kpts(abs_kpts, kpts_in_ibz=True)

Get scaled k-points, given absolute k-points in 1/Bohr.

Parameters:

• abs_kpts – (nkpts, 3) ndarray of floats or KPoints object

• kpts_in_ibz – bool If True, return k-points in IBZ; otherwise, return k-points in BZ. Default value is True. This has effects only if abs_kpts is a KPoints object

Returns:

(nkpts, 3) ndarray of floats

Return type:

scaled_kpts

get_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

property gs

gto_norm(l, expnt)

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Parameters:

• l (int) – angular momentum

• expnt – exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

property h

has_ecp()

Whether pseudo potential is used in the system.

has_ecp_soc()

Whether spin-orbit coupling is enabled in ECP.

incore_anyway = False

intor(intor, comp=None, hermi=0, aosym='s1', out=None, shls_slice=None, grids=None)

Integral generator.

Parameters:

intor – str Name of the 1e or 2e AO integrals. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

hermiint

Symmetry of the integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian

shls_slice4-element, 6-element or 8-element tuple

Label the start-stop shells for each index in the integral. For example, the 8-element tuple for the 2-electron integral tensor (ij|kl) = intor(‘int2e’) are specified as (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor('int1e_ipnuc_sph', comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]
>>> mol.intor('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_asymmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be anti-hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_asymmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j  0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j  0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_by_shell(intor, shells, comp=None, grids=None)

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Parameters:

• intor_name – str See also getints() for the supported intor_name

• shls – list of int The AO shell-ids of the integrals

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

intor_symmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_symmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

kernel(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

lattice_vectors()

Convert the primitive lattice vectors.

Return 3x3 array in which each row represents one direction of the lattice vectors (unit in Bohr)

classmethod loads(molstr)

Deserialize a str containing a JSON document to a Cell object.

loads_(molstr)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

make_atm_env(atom, ptr=0, nucmod=1, nucprop=None)

Convert the internal format Mole._atom to the format required by libcint integrals

make_bas_env(basis_add, atom_id=0, ptr=0)

Convert Mole.basis to the argument bas for libcint integrals

make_ecp_env(_atm, _ecp, pre_env=[])

Generate the input arguments _ecpbas for ECP integrals

make_env(atoms, basis, pre_env=[], nucmod={}, nucprop=None)

Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

make_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

max_memory = 4000

property mesh

property ms

Spin quantum number. multiplicity = ms*2+1

property multiplicity

property nao

nao_2c()

Total number of contracted spinor GTOs for the given Mole object

nao_2c_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id, 0-based

• bas_id1 – int stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

nao_cart()

Total number of contracted cartesian GTOs for the given Mole object

nao_nr()

Total number of contracted GTOs for the given Mole object

nao_nr_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id

• bas_id1 – int stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

property natm

property nbas

property nelec

property nelectron

property nimgs

npgto_nr(cart=None)

Total number of primitive spherical GTOs for the given Mole object

offset_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_ao_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

property omega

output = None

pack()

Pack the input args of Cell to a dict, which can be serialized with pickle

pbc_eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_intor(intor, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)

One-electron integrals with PBC.

\[\sum_T \int \mu(r) * [intor] * \nu (r-T) dr\]

See also Mole.intor

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

precision = 1e-08

property rcut

rcut_by_shells(precision=None, rcut=0, return_pgf_radius=False)

Compute shell and primitive gaussian function radii.

reciprocal_vectors(norm_to=6.283185307179586)

\[\begin{split}\begin{align} \mathbf{b_1} &= 2\pi \frac{\mathbf{a_2} \times \mathbf{a_3}}{\mathbf{a_1} \cdot (\mathbf{a_2} \times \mathbf{a_3})} \\ \mathbf{b_2} &= 2\pi \frac{\mathbf{a_3} \times \mathbf{a_1}}{\mathbf{a_2} \cdot (\mathbf{a_3} \times \mathbf{a_1})} \\ \mathbf{b_3} &= 2\pi \frac{\mathbf{a_1} \times \mathbf{a_2}}{\mathbf{a_3} \cdot (\mathbf{a_1} \times \mathbf{a_2})} \end{align}\end{split}\]

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

search_ao_label()

Find the index of the AO basis function based on the given ao_label

Parameters:

ao_label – string or a list of strings The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

search_ao_nr(atm_id, l, m, atmshell)

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Parameters:

• atm_id – int atom id, 0-based

• l – int angular momentum

• m – int magnetic angular momentum

• atmshell – int principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

search_ao_r(atm_id, l, j, m, atmshell)

search_shell_id(atm_id, l)

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

set_common_orig(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_orig_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_f12_zeta(zeta)

Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals

set_geom_(atoms_or_coords, unit=None, symmetry=None, inplace=True)

Update geometry

set_nuc_mod(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_nuc_mod_(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_range_coulomb(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_range_coulomb_(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_rinv_orig(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_orig_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_zeta(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

set_rinv_zeta_(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

sph2spinor_coeff()

Transformation matrix that transforms real-spherical GTOs to spinor GTOs for all basis functions

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> ca, cb = mol.sph2spinor_coeff()
>>> s0 = mol.intor('int1e_ovlp_spinor')
>>> s1 = ca.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(ca)
>>> s1+= cb.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(cb)
>>> print(abs(s1-s0).max())
>>> 6.66133814775e-16

sph_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spheric_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spin = 0

spinor_labels(fmt=True, base=0)

Labels of spinor GTO functions

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

symmetrize_mesh(mesh=None)

symmetry = False

symmetry_subgroup = None

time_reversal_map()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

tmap()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

to_mol()

Return a Mole object using the same atoms and basis functions as the Cell object.

to_uncontracted_cartesian_basis()

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

tot_electrons(nkpts=1)

Total number of electrons

unit = 'angstrom'

classmethod unpack(moldic)

Convert the packed dict to a Cell object, to generate the input arguments for Cell object.

unpack_(moldic)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

update(chkfile)

update_from_chk(chkfile)

verbose = 3

view(cls)

New view of object with the same attributes.

property vol

with_common_orig(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_common_origin(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_integral_screen(threshold)

Return a temporary mol context which has the required integral screen threshold

with_long_range_coulomb(omega)

Return a temporary mol context for long-range part of range-separated Coulomb operator.

with_range_coulomb(omega)

Return a temporary mol context which sets the required parameter omega for range-separated Coulomb operator. If omega = None, return the context for regular Coulomb integrals. See also mol.set_range_coulomb()

Examples:

>>> with mol.with_range_coulomb(omega=1.5):
...     mol.intor('int2e')

with_rinv_as_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_at_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_orig(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_origin(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_zeta(zeta)

Return a temporary mol context which has the rquired Gaussian charge distribution placed at “rinv_origin”: rho(r) = Norm * exp(-zeta * r^2). See also mol.set_rinv_zeta()

Examples:

>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
...     mol.intor('int1e_rinv')

with_short_range_coulomb(omega)

Return a temporary mol context for short-range part of range-separated Coulomb operator.

class vayesta.lattmod.latt.Hubbard1D(nsite, nelectron=None, spin=0, hubbard_t=1.0, hubbard_u=0.0, v_nn=0.0, boundary='auto', **kwargs)

Bases: Hubbard

Hubbard model in 1D.

get_eri(hubbard_u=None, v_nn=None)

lattice_vectors()

Lattice vectors of 1D Hubbard model.

An arbitrary value of 1 A is assumed between sites. The lattice vectors, however, are saved in units of Bohr.

atom_coords()

np.asarray([mol.atom_coord(i) for i in range(mol.natm)])

get_index(i)

property Gv

ao2mo(mo_coeffs, compact=False)

ao_labels(fmt=True)

Labels of AO basis functions

Kwargs:

fmtstr or bool

if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

property ao_loc

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_loc_2c()

Offset of every shell in the spinor basis function spectrum

Returns:

list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

ao_loc_nr(cart=None)

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_rotation_matrix(orientation)

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

aoslice_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_by_atom()

One basis function per site (“atom”).

aoslice_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

atom_charge(atm_id)

Nuclear effective charge of the given atom id Note “atom_charge /= charge(atom_symbol)” when ECP is enabled. Number of electrons screened by ECP can be obtained by charge(atom_symbol)-atom_charge

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17

atom_charges()

np.asarray([mol.atom_charge(i) for i in range(mol.natm)])

atom_coord(atm_id, unit='Bohr')

Coordinates (ndarray) of the given atom id

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0.          0.          2.07869874]

atom_mass_list(isotope_avg=False)

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean

Whether to use the isotope average mass as the atomic mass

atom_nelec_core(atm_id)

Number of core electrons for pseudo potential.

atom_nshells(atm_id)

Number of basis/shells of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5

atom_pure_symbol(site)

For the given atom id, return the standard symbol (striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H

atom_shell_ids(atm_id)

A list of the shell-ids of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.atom_shell_ids(1)
[3, 4, 5, 6, 7]

atom_symbol(site)

For the given atom id, return the input symbol (without striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2

bas_angular(bas_id)

The angular momentum associated with the given basis

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2

bas_atom(bas_id)

The atom (0-based id) that the given basis sits on

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1

bas_coord(bas_id)

Coordinates (ndarray) associated with the given basis id

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0.          0.          2.07869874]

bas_ctr_coeff(bas_id)

Contract coefficients (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.M(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_ctr_coeff(0)
[[ 10.03400444]
 [  4.1188704 ]
 [  1.53971186]]

bas_exp(bas_id)

exponents (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(0)
[ 13.01     1.962    0.4446]

bas_exps()

exponents of all basis return [mol.bas_exp(i) for i in range(self.nbas)]

bas_kappa(bas_id)

Kappa (if l < j, -l-1, else l) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0

bas_len_cart(bas_id)

The number of Cartesian function associated with given basis

bas_len_spinor(bas_id)

The number of spinor associated with given basis If kappa is 0, return 4l+2

bas_nctr(bas_id)

The number of contracted GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3

bas_nprim(bas_id)

The number of primitive GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11

bas_rcut(bas_id, precision=None)

Estimate the largest distance between the function and its image to reach the precision in overlap

precision ~ int g(r-0) g(r-Rcut)

build(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

build_lattice_symmetry(check_mesh_symmetry=True)

Build cell.lattice_symmetry object.

Kwargs:

check_mesh_symmetrybool

For nonsymmorphic symmetry groups, cell.mesh may have lower symmetry than the lattice. In this case, if check_mesh_symmetry is True, the lower symmetry group will be used. Otherwise, if check_mesh_symmetry is False, the mesh grid will be modified to satisfy the higher symmetry. Default value is True.

Note

This function modifies the attributes of cell.

cart = False

cart2sph_coeff(normalized='sp')

Transformation matrix that transforms Cartesian GTOs to spherical GTOs for all basis functions

Kwargs:

normalizedstring or boolean

How the Cartesian GTOs are normalized. Except s and p functions, Cartesian GTOs do not have the universal normalization coefficients for the different components of the same shell. The value of this argument can be one of ‘sp’, ‘all’, None. ‘sp’ means the Cartesian s and p basis are normalized. ‘all’ means all Cartesian functions are normalized. None means none of the Cartesian functions are normalized. The default value ‘sp’ is the convention used by libcint library.

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> c = mol.cart2sph_coeff()
>>> s0 = mol.intor('int1e_ovlp_sph')
>>> s1 = c.T.dot(mol.intor('int1e_ovlp_cart')).dot(c)
>>> print(abs(s1-s0).sum())
>>> 4.58676826646e-15

cart_labels(fmt=True, base=0)

Labels of Cartesian GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

charge = 0

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

condense_to_shell(mat, compressor='max')

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Parameters:

compressor – string or function if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

copy(deep=True)

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

cutoff_to_mesh(ke_cutoff)

Convert KE cutoff to FFT-mesh

Parameters:

ke_cutoff – float KE energy cutoff in a.u.

Returns:

(3,) array

Return type:

mesh

decontract_basis(atoms=None, to_cart=False, aggregate=False)

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str

Atoms on which the basis to be decontracted. By default, all basis are decontracted

to_cart: bool

Decontract basis and transfer to Cartesian basis

aggregate: bool

Whether to aggregate the transformation coefficients into a giant transformation matrix

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

property drop_exponent

dump_input()

dumps()

Serialize Cell object to a JSON formatted str.

property elements

A list of elements in the molecule

energy_nuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

property enuc

nuclear repulsion energy

static etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

property ew_cut

property ew_eta

ewald(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

exp_to_discard = None

static expand_etb(l, n, alpha, beta)

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Parameters:

• l – int Angular momentum

• n – int Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

static expand_etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

format_atom(atoms, origin=0, axes=None, unit='angstrom')

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to separate the individual terms for an atom. Blank line will be ignored.

Parameters:

atoms – list or str the same to Mole.atom

Kwargs:

originndarray

new axis origin.

axesndarray

(new_x, new_y, new_z), new coordinates

unitstr or number

If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is

atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

static format_basis(basis_tab, sort_basis=True)

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..)))], … }``

Parameters:

basis_tab – dict Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

static format_ecp(ecp_tab)

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1

(exp_2, c_2), …),

((exp_1, c_1), # for r^2

…))))),

…}

static format_pseudo(pseudo_tab)

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Parameters:

pseudo_tab – dict Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

from_ase(ase_atom)

Update cell based on given ase atom object

Examples:

>>> from ase.lattice import bulk
>>> cell.from_ase(bulk('C', 'diamond', a=LATTICE_CONST))

gen_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

get_Gv(mesh=None, **kwargs)

Calculate three-dimensional G-vectors for the cell; see MH (3.8).

Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.

Parameters:

cell – instance of Cell

Returns:

(ngrids, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_Gv_weights(mesh=None, **kwargs)

Calculate G-vectors and weights.

Returns:

(ngris, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_SI(Gv=None, mesh=None, atmlst=None)

Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).

Parameters:

• cell – instance of Cell

• Gv – (N,3) array G vectors

• atmlst – list of ints, optional Indices of atoms for which the structure factors are computed.

Returns:

(natm, ngrids) ndarray, dtype=np.complex128

The structure factor for each atom at each G-vector.

Return type:

SI

get_abs_kpts(scaled_kpts)

Get absolute k-points (in 1/Bohr), given “scaled” k-points in fractions of lattice vectors.

Parameters:

scaled_kpts – (nkpts, 3) ndarray of floats

Returns:

(nkpts, 3) ndarray of floats

Return type:

abs_kpts

get_ao_indices(bas_list, ao_loc=None)

Generate (dis-continued) AO indices for basis specified in bas_list

get_bounding_sphere(rcut)

Finds all the lattice points within a sphere of radius rcut.

Defines a parallelepiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85

Parameters:

rcut – number real space cut-off for interaction

Returns:

ndarray of 3 ints defining N_x

Return type:

cut

get_enuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

get_ewald_params(precision=None, mesh=None)

Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}

Choice is based on largest G vector and desired relative precision.

The relative error in the G-space sum is given by

precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}

which determines eta. Then, real-space cutoff is determined by (exp. factors only)

precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}

Returns:

float

The Ewald ‘eta’ and ‘cut’ parameters.

Return type:

ew_eta, ew_cut

get_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

get_lattice_Ls(nimgs=None, rcut=None, dimension=None, discard=True)

Get the (Cartesian, unitful) lattice translation vectors for nearby images. The translation vectors can be used for the lattice summation.

Kwargs:

discard:

Drop less important Ls based on AO values on grid

get_nimgs(precision=None)

Choose number of basis function images in lattice sums to include for given precision in overlap, using

precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}

where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.

get_overlap_cond(shls_slice=None)

Overlap magnitudes measured by -log(overlap) between two shells

Parameters:

mol – an instance of Mole

Returns:

2D mask array of shape (nbas,nbas)

get_scaled_atom_coords(a=None)

Get scaled atomic coordinates.

get_scaled_kpts(abs_kpts, kpts_in_ibz=True)

Get scaled k-points, given absolute k-points in 1/Bohr.

Parameters:

• abs_kpts – (nkpts, 3) ndarray of floats or KPoints object

• kpts_in_ibz – bool If True, return k-points in IBZ; otherwise, return k-points in BZ. Default value is True. This has effects only if abs_kpts is a KPoints object

Returns:

(nkpts, 3) ndarray of floats

Return type:

scaled_kpts

get_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

property gs

gto_norm(l, expnt)

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Parameters:

• l (int) – angular momentum

• expnt – exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

property h

has_ecp()

Whether pseudo potential is used in the system.

has_ecp_soc()

Whether spin-orbit coupling is enabled in ECP.

incore_anyway = False

intor(intor, comp=None, hermi=0, aosym='s1', out=None, shls_slice=None, grids=None)

Integral generator.

Parameters:

intor – str Name of the 1e or 2e AO integrals. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

hermiint

Symmetry of the integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian

shls_slice4-element, 6-element or 8-element tuple

Label the start-stop shells for each index in the integral. For example, the 8-element tuple for the 2-electron integral tensor (ij|kl) = intor(‘int2e’) are specified as (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor('int1e_ipnuc_sph', comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]
>>> mol.intor('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_asymmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be anti-hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_asymmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j  0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j  0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_by_shell(intor, shells, comp=None, grids=None)

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Parameters:

• intor_name – str See also getints() for the supported intor_name

• shls – list of int The AO shell-ids of the integrals

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

intor_symmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_symmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

kernel(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

classmethod loads(molstr)

Deserialize a str containing a JSON document to a Cell object.

loads_(molstr)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

make_atm_env(atom, ptr=0, nucmod=1, nucprop=None)

Convert the internal format Mole._atom to the format required by libcint integrals

make_bas_env(basis_add, atom_id=0, ptr=0)

Convert Mole.basis to the argument bas for libcint integrals

make_ecp_env(_atm, _ecp, pre_env=[])

Generate the input arguments _ecpbas for ECP integrals

make_env(atoms, basis, pre_env=[], nucmod={}, nucprop=None)

Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

make_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

max_memory = 4000

property mesh

property ms

Spin quantum number. multiplicity = ms*2+1

property multiplicity

property nao

nao_2c()

Total number of contracted spinor GTOs for the given Mole object

nao_2c_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id, 0-based

• bas_id1 – int stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

nao_cart()

Total number of contracted cartesian GTOs for the given Mole object

nao_nr()

Total number of contracted GTOs for the given Mole object

nao_nr_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id

• bas_id1 – int stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

property natm

property nbas

property nelec

property nelectron

property nimgs

npgto_nr(cart=None)

Total number of primitive spherical GTOs for the given Mole object

offset_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_ao_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

property omega

output = None

pack()

Pack the input args of Cell to a dict, which can be serialized with pickle

pbc_eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_intor(intor, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)

One-electron integrals with PBC.

\[\sum_T \int \mu(r) * [intor] * \nu (r-T) dr\]

See also Mole.intor

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

precision = 1e-08

property rcut

rcut_by_shells(precision=None, rcut=0, return_pgf_radius=False)

Compute shell and primitive gaussian function radii.

reciprocal_vectors(norm_to=6.283185307179586)

\[\begin{split}\begin{align} \mathbf{b_1} &= 2\pi \frac{\mathbf{a_2} \times \mathbf{a_3}}{\mathbf{a_1} \cdot (\mathbf{a_2} \times \mathbf{a_3})} \\ \mathbf{b_2} &= 2\pi \frac{\mathbf{a_3} \times \mathbf{a_1}}{\mathbf{a_2} \cdot (\mathbf{a_3} \times \mathbf{a_1})} \\ \mathbf{b_3} &= 2\pi \frac{\mathbf{a_1} \times \mathbf{a_2}}{\mathbf{a_3} \cdot (\mathbf{a_1} \times \mathbf{a_2})} \end{align}\end{split}\]

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

search_ao_label()

Find the index of the AO basis function based on the given ao_label

Parameters:

ao_label – string or a list of strings The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

search_ao_nr(atm_id, l, m, atmshell)

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Parameters:

• atm_id – int atom id, 0-based

• l – int angular momentum

• m – int magnetic angular momentum

• atmshell – int principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

search_ao_r(atm_id, l, j, m, atmshell)

search_shell_id(atm_id, l)

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

set_common_orig(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_orig_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_f12_zeta(zeta)

Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals

set_geom_(atoms_or_coords, unit=None, symmetry=None, inplace=True)

Update geometry

set_nuc_mod(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_nuc_mod_(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_range_coulomb(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_range_coulomb_(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_rinv_orig(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_orig_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_zeta(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

set_rinv_zeta_(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

sph2spinor_coeff()

Transformation matrix that transforms real-spherical GTOs to spinor GTOs for all basis functions

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> ca, cb = mol.sph2spinor_coeff()
>>> s0 = mol.intor('int1e_ovlp_spinor')
>>> s1 = ca.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(ca)
>>> s1+= cb.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(cb)
>>> print(abs(s1-s0).max())
>>> 6.66133814775e-16

sph_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spheric_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spin = 0

spinor_labels(fmt=True, base=0)

Labels of spinor GTO functions

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

symmetrize_mesh(mesh=None)

symmetry = False

symmetry_subgroup = None

time_reversal_map()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

tmap()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

to_mol()

Return a Mole object using the same atoms and basis functions as the Cell object.

to_uncontracted_cartesian_basis()

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

tot_electrons(nkpts=1)

Total number of electrons

unit = 'angstrom'

classmethod unpack(moldic)

Convert the packed dict to a Cell object, to generate the input arguments for Cell object.

unpack_(moldic)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

update(chkfile)

update_from_chk(chkfile)

verbose = 3

view(cls)

New view of object with the same attributes.

property vol

with_common_orig(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_common_origin(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_integral_screen(threshold)

Return a temporary mol context which has the required integral screen threshold

with_long_range_coulomb(omega)

Return a temporary mol context for long-range part of range-separated Coulomb operator.

with_range_coulomb(omega)

Return a temporary mol context which sets the required parameter omega for range-separated Coulomb operator. If omega = None, return the context for regular Coulomb integrals. See also mol.set_range_coulomb()

Examples:

>>> with mol.with_range_coulomb(omega=1.5):
...     mol.intor('int2e')

with_rinv_as_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_at_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_orig(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_origin(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_zeta(zeta)

Return a temporary mol context which has the rquired Gaussian charge distribution placed at “rinv_origin”: rho(r) = Norm * exp(-zeta * r^2). See also mol.set_rinv_zeta()

Examples:

>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
...     mol.intor('int1e_rinv')

with_short_range_coulomb(omega)

Return a temporary mol context for short-range part of range-separated Coulomb operator.

class vayesta.lattmod.latt.Hubbard2D(nsites, nelectron=None, spin=0, hubbard_t=1.0, hubbard_u=0.0, boundary='auto', tiles=(1, 1), order=None, **kwargs)

Bases: Hubbard

get_index(i, j)

get_eri(hubbard_u=None, v_nn=None)

lattice_vectors()

Lattice vectors of 1D Hubbard model.

An arbitrary value of 1 A is assumed between sites. The lattice vectors, however, are saved in units of Bohr.

atom_coords()

Sites are ordered by default as:

6 7 8 3 4 5 0 1 2

static get_tiles_order(nsites, tiles)

property Gv

ao2mo(mo_coeffs, compact=False)

ao_labels(fmt=True)

Labels of AO basis functions

Kwargs:

fmtstr or bool

if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

property ao_loc

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_loc_2c()

Offset of every shell in the spinor basis function spectrum

Returns:

list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

ao_loc_nr(cart=None)

Offset of every shell in the spherical basis function spectrum

Returns:

list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_rotation_matrix(orientation)

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

aoslice_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_by_atom()

One basis function per site (“atom”).

aoslice_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

atom_charge(atm_id)

Nuclear effective charge of the given atom id Note “atom_charge /= charge(atom_symbol)” when ECP is enabled. Number of electrons screened by ECP can be obtained by charge(atom_symbol)-atom_charge

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17

atom_charges()

np.asarray([mol.atom_charge(i) for i in range(mol.natm)])

atom_coord(atm_id, unit='Bohr')

Coordinates (ndarray) of the given atom id

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0.          0.          2.07869874]

atom_mass_list(isotope_avg=False)

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean

Whether to use the isotope average mass as the atomic mass

atom_nelec_core(atm_id)

Number of core electrons for pseudo potential.

atom_nshells(atm_id)

Number of basis/shells of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5

atom_pure_symbol(site)

For the given atom id, return the standard symbol (striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H

atom_shell_ids(atm_id)

A list of the shell-ids of the given atom

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.atom_shell_ids(1)
[3, 4, 5, 6, 7]

atom_symbol(site)

For the given atom id, return the input symbol (without striping special characters)

Parameters:

atm_id – int 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2

bas_angular(bas_id)

The angular momentum associated with the given basis

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2

bas_atom(bas_id)

The atom (0-based id) that the given basis sits on

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1

bas_coord(bas_id)

Coordinates (ndarray) associated with the given basis id

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0.          0.          2.07869874]

bas_ctr_coeff(bas_id)

Contract coefficients (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.M(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_ctr_coeff(0)
[[ 10.03400444]
 [  4.1188704 ]
 [  1.53971186]]

bas_exp(bas_id)

exponents (ndarray) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(0)
[ 13.01     1.962    0.4446]

bas_exps()

exponents of all basis return [mol.bas_exp(i) for i in range(self.nbas)]

bas_kappa(bas_id)

Kappa (if l < j, -l-1, else l) of the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0

bas_len_cart(bas_id)

The number of Cartesian function associated with given basis

bas_len_spinor(bas_id)

The number of spinor associated with given basis If kappa is 0, return 4l+2

bas_nctr(bas_id)

The number of contracted GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3

bas_nprim(bas_id)

The number of primitive GTOs for the given shell

Parameters:

bas_id – int 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11

bas_rcut(bas_id, precision=None)

Estimate the largest distance between the function and its image to reach the precision in overlap

precision ~ int g(r-0) g(r-Rcut)

build(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

build_lattice_symmetry(check_mesh_symmetry=True)

Build cell.lattice_symmetry object.

Kwargs:

check_mesh_symmetrybool

For nonsymmorphic symmetry groups, cell.mesh may have lower symmetry than the lattice. In this case, if check_mesh_symmetry is True, the lower symmetry group will be used. Otherwise, if check_mesh_symmetry is False, the mesh grid will be modified to satisfy the higher symmetry. Default value is True.

Note

This function modifies the attributes of cell.

cart = False

cart2sph_coeff(normalized='sp')

Transformation matrix that transforms Cartesian GTOs to spherical GTOs for all basis functions

Kwargs:

normalizedstring or boolean

How the Cartesian GTOs are normalized. Except s and p functions, Cartesian GTOs do not have the universal normalization coefficients for the different components of the same shell. The value of this argument can be one of ‘sp’, ‘all’, None. ‘sp’ means the Cartesian s and p basis are normalized. ‘all’ means all Cartesian functions are normalized. None means none of the Cartesian functions are normalized. The default value ‘sp’ is the convention used by libcint library.

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> c = mol.cart2sph_coeff()
>>> s0 = mol.intor('int1e_ovlp_sph')
>>> s1 = c.T.dot(mol.intor('int1e_ovlp_cart')).dot(c)
>>> print(abs(s1-s0).sum())
>>> 4.58676826646e-15

cart_labels(fmt=True, base=0)

Labels of Cartesian GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

charge = 0

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

condense_to_shell(mat, compressor='max')

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Parameters:

compressor – string or function if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

copy(deep=True)

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

cutoff_to_mesh(ke_cutoff)

Convert KE cutoff to FFT-mesh

Parameters:

ke_cutoff – float KE energy cutoff in a.u.

Returns:

(3,) array

Return type:

mesh

decontract_basis(atoms=None, to_cart=False, aggregate=False)

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str

Atoms on which the basis to be decontracted. By default, all basis are decontracted

to_cart: bool

Decontract basis and transfer to Cartesian basis

aggregate: bool

Whether to aggregate the transformation coefficients into a giant transformation matrix

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

property drop_exponent

dump_input()

dumps()

Serialize Cell object to a JSON formatted str.

property elements

A list of elements in the molecule

energy_nuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

property enuc

nuclear repulsion energy

static etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

property ew_cut

property ew_eta

ewald(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

exp_to_discard = None

static expand_etb(l, n, alpha, beta)

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Parameters:

• l – int Angular momentum

• n – int Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

static expand_etbs(etbs)

Generate even tempered basis. See also expand_etb()

Parameters:

[ (etbs =) –

Returns:

Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

format_atom(atoms, origin=0, axes=None, unit='angstrom')

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to separate the individual terms for an atom. Blank line will be ignored.

Parameters:

atoms – list or str the same to Mole.atom

Kwargs:

originndarray

new axis origin.

axesndarray

(new_x, new_y, new_z), new coordinates

unitstr or number

If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is

atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

static format_basis(basis_tab, sort_basis=True)

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..)))], … }``

Parameters:

basis_tab – dict Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

static format_ecp(ecp_tab)

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1

(exp_2, c_2), …),

((exp_1, c_1), # for r^2

…))))),

…}

static format_pseudo(pseudo_tab)

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Parameters:

pseudo_tab – dict Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

from_ase(ase_atom)

Update cell based on given ase atom object

Examples:

>>> from ase.lattice import bulk
>>> cell.from_ase(bulk('C', 'diamond', a=LATTICE_CONST))

gen_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

get_Gv(mesh=None, **kwargs)

Calculate three-dimensional G-vectors for the cell; see MH (3.8).

Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.

Parameters:

cell – instance of Cell

Returns:

(ngrids, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_Gv_weights(mesh=None, **kwargs)

Calculate G-vectors and weights.

Returns:

(ngris, 3) ndarray of floats

The array of G-vectors.

Return type:

Gv

get_SI(Gv=None, mesh=None, atmlst=None)

Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).

Parameters:

• cell – instance of Cell

• Gv – (N,3) array G vectors

• atmlst – list of ints, optional Indices of atoms for which the structure factors are computed.

Returns:

(natm, ngrids) ndarray, dtype=np.complex128

The structure factor for each atom at each G-vector.

Return type:

SI

get_abs_kpts(scaled_kpts)

Get absolute k-points (in 1/Bohr), given “scaled” k-points in fractions of lattice vectors.

Parameters:

scaled_kpts – (nkpts, 3) ndarray of floats

Returns:

(nkpts, 3) ndarray of floats

Return type:

abs_kpts

get_ao_indices(bas_list, ao_loc=None)

Generate (dis-continued) AO indices for basis specified in bas_list

get_bounding_sphere(rcut)

Finds all the lattice points within a sphere of radius rcut.

Defines a parallelepiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85

Parameters:

rcut – number real space cut-off for interaction

Returns:

ndarray of 3 ints defining N_x

Return type:

cut

get_enuc(ew_eta=None, ew_cut=None)

Perform real (R) and reciprocal (G) space Ewald sum for the energy.

Formulation of Martin, App. F2.

Returns:

float

The Ewald energy consisting of overlap, self, and G-space sum.

See also

pyscf.pbc.gto.get_ewald_params

get_ewald_params(precision=None, mesh=None)

Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}

Choice is based on largest G vector and desired relative precision.

The relative error in the G-space sum is given by

precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}

which determines eta. Then, real-space cutoff is determined by (exp. factors only)

precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}

Returns:

float

The Ewald ‘eta’ and ‘cut’ parameters.

Return type:

ew_eta, ew_cut

get_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

get_lattice_Ls(nimgs=None, rcut=None, dimension=None, discard=True)

Get the (Cartesian, unitful) lattice translation vectors for nearby images. The translation vectors can be used for the lattice summation.

Kwargs:

discard:

Drop less important Ls based on AO values on grid

get_nimgs(precision=None)

Choose number of basis function images in lattice sums to include for given precision in overlap, using

precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}

where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.

get_overlap_cond(shls_slice=None)

Overlap magnitudes measured by -log(overlap) between two shells

Parameters:

mol – an instance of Mole

Returns:

2D mask array of shape (nbas,nbas)

get_scaled_atom_coords(a=None)

Get scaled atomic coordinates.

get_scaled_kpts(abs_kpts, kpts_in_ibz=True)

Get scaled k-points, given absolute k-points in 1/Bohr.

Parameters:

• abs_kpts – (nkpts, 3) ndarray of floats or KPoints object

• kpts_in_ibz – bool If True, return k-points in IBZ; otherwise, return k-points in BZ. Default value is True. This has effects only if abs_kpts is a KPoints object

Returns:

(nkpts, 3) ndarray of floats

Return type:

scaled_kpts

get_uniform_grids(mesh=None, wrap_around=True)

Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).

Parameters:

cell – instance of Cell

Returns:

(ngx*ngy*ngz, 3) ndarray

The real-space grid point coordinates.

Return type:

coords

property gs

gto_norm(l, expnt)

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Parameters:

• l (int) – angular momentum

• expnt – exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

property h

has_ecp()

Whether pseudo potential is used in the system.

has_ecp_soc()

Whether spin-orbit coupling is enabled in ECP.

incore_anyway = False

intor(intor, comp=None, hermi=0, aosym='s1', out=None, shls_slice=None, grids=None)

Integral generator.

Parameters:

intor – str Name of the 1e or 2e AO integrals. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

hermiint

Symmetry of the integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian

shls_slice4-element, 6-element or 8-element tuple

Label the start-stop shells for each index in the integral. For example, the 8-element tuple for the 2-electron integral tensor (ij|kl) = intor(‘int2e’) are specified as (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor('int1e_ipnuc_sph', comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]
>>> mol.intor('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_asymmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be anti-hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_asymmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j  0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j  0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_by_shell(intor, shells, comp=None, grids=None)

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Parameters:

• intor_name – str See also getints() for the supported intor_name

• shls – list of int The AO shell-ids of the integrals

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

intor_symmetric(intor, comp=None, grids=None)

One-electron integral generator. The integrals are assumed to be hermitian

Parameters:

intor – str Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint

Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.

gridsndarray

Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_symmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

kernel(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, use_loose_rcut=None, use_particle_mesh_ewald=None, fractional=None, *args, **kwargs)

Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of Cell, you need call this function to refresh the internal data of Cell.

Kwargs:

a(3,3) ndarray

The real-space cell lattice vectors. Each row represents a lattice vector.

fractionalbool

Whether the atom postions are specified in fractional coordinates. The default value is False, which means the coordinates are interpreted as Cartesian coordinate.

mesh(3,) ndarray of ints

The number of positive G-vectors along each direction.

ke_cutofffloat

If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on precision

precisionfloat

To control Ewald sums and lattice sums accuracy

nimgs(3,) ndarray of ints

Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

rcutfloat

Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.

h(3,3) ndarray

a.T. Deprecated

dimensionint

Default is 3

low_dim_ft_typestr

For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.

space_group_symmetrybool

Whether to consider space group symmetry. Default is False.

symmorphicbool

Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.

classmethod loads(molstr)

Deserialize a str containing a JSON document to a Cell object.

loads_(molstr)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

make_atm_env(atom, ptr=0, nucmod=1, nucprop=None)

Convert the internal format Mole._atom to the format required by libcint integrals

make_bas_env(basis_add, atom_id=0, ptr=0)

Convert Mole.basis to the argument bas for libcint integrals

make_ecp_env(_atm, _ecp, pre_env=[])

Generate the input arguments _ecpbas for ECP integrals

make_env(atoms, basis, pre_env=[], nucmod={}, nucprop=None)

Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

make_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)

Given number of kpoints along x,y,z , generate kpoints

Parameters:

nks – (3,) ndarray

Kwargs:

wrap_aroundbool

To ensure all kpts are in first Brillouin zone.

with_gamma_pointbool

Whether to shift Monkhorst-pack grid to include gamma-point.

scaled_center(3,) array

Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]

space_group_symmetrybool

Whether to consider space group symmetry

time_reversal_symmetrybool

Whether to consider time reversal symmetry

Returns:

kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of KPoints if k-point symmetry is considered

Examples:

>>> cell.make_kpts((4,4,4))

max_memory = 4000

property mesh

property ms

Spin quantum number. multiplicity = ms*2+1

property multiplicity

property nao

nao_2c()

Total number of contracted spinor GTOs for the given Mole object

nao_2c_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id, 0-based

• bas_id1 – int stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

nao_cart()

Total number of contracted cartesian GTOs for the given Mole object

nao_nr()

Total number of contracted GTOs for the given Mole object

nao_nr_range(bas_id0, bas_id1)

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Parameters:

• mol – Mole object

• bas_id0 – int start shell id

• bas_id1 – int stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

property natm

property nbas

property nelec

property nelectron

property nimgs

npgto_nr(cart=None)

Total number of primitive spherical GTOs for the given Mole object

offset_2c_by_atom()

2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_ao_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_nr_by_atom(ao_loc=None)

AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

property omega

output = None

pack()

Pack the input args of Cell to a dict, which can be serialized with pickle

pbc_eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)

Evaluate PBC-AO function value on the given grids,

Parameters:

• eval_name –

  str:

  ==========================  =======================
  Function                    Expression
  ==========================  =======================
  "GTOval_sph"                \sum_T exp(ik*T) |AO>
  "GTOval_ip_sph"             nabla \sum_T exp(ik*T) |AO>
  "GTOval_cart"               \sum_T exp(ik*T) |AO>
  "GTOval_ip_cart"            nabla \sum_T exp(ik*T) |AO>
  ==========================  =======================
  

• atm – int32 ndarray libcint integral function argument

• bas – int32 ndarray libcint integral function argument

• env – float64 ndarray libcint integral function argument

• coords – 2D array, shape (N,3) The coordinates of the grids.

Kwargs:

shls_slice2-element list

(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in cell will be evaluated.

non0tab2D bool array

mask array to indicate whether the AO values are zero. The mask array can be obtained by calling dft.gen_grid.make_mask()

cutofffloat

AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)

outndarray

If provided, results are written into this array.

Returns:

A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).

Examples:

>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
>>> coords = cell.get_uniform_grids([10,10,10])
>>> kpts = cell.make_kpts([3,3,3])
>>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts)
>>> len(ao_value)
27
>>> ao_value[0].shape
(1000, 2)
>>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3)
>>> print(ao_value.shape)
>>> len(ao_value)
27
>>> ao_value[0].shape
(3, 1000, 2)

pbc_intor(intor, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)

One-electron integrals with PBC.

\[\sum_T \int \mu(r) * [intor] * \nu (r-T) dr\]

See also Mole.intor

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

precision = 1e-08

property rcut

rcut_by_shells(precision=None, rcut=0, return_pgf_radius=False)

Compute shell and primitive gaussian function radii.

reciprocal_vectors(norm_to=6.283185307179586)

\[\begin{split}\begin{align} \mathbf{b_1} &= 2\pi \frac{\mathbf{a_2} \times \mathbf{a_3}}{\mathbf{a_1} \cdot (\mathbf{a_2} \times \mathbf{a_3})} \\ \mathbf{b_2} &= 2\pi \frac{\mathbf{a_3} \times \mathbf{a_1}}{\mathbf{a_2} \cdot (\mathbf{a_3} \times \mathbf{a_1})} \\ \mathbf{b_3} &= 2\pi \frac{\mathbf{a_1} \times \mathbf{a_2}}{\mathbf{a_3} \cdot (\mathbf{a_1} \times \mathbf{a_2})} \end{align}\end{split}\]

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

search_ao_label()

Find the index of the AO basis function based on the given ao_label

Parameters:

ao_label – string or a list of strings The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

search_ao_nr(atm_id, l, m, atmshell)

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Parameters:

• atm_id – int atom id, 0-based

• l – int angular momentum

• m – int magnetic angular momentum

• atmshell – int principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

search_ao_r(atm_id, l, j, m, atmshell)

search_shell_id(atm_id, l)

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

set_common_orig(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_orig_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin_(coord)

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_f12_zeta(zeta)

Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals

set_geom_(atoms_or_coords, unit=None, symmetry=None, inplace=True)

Update geometry

set_nuc_mod(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_nuc_mod_(atm_id, zeta)

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_range_coulomb(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_range_coulomb_(omega)

Switch on range-separated Coulomb operator for all 2e integrals

Parameters:

omega –

double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_rinv_orig(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_orig_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin_(coord)

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_zeta(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

set_rinv_zeta_(zeta)

Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

sph2spinor_coeff()

Transformation matrix that transforms real-spherical GTOs to spinor GTOs for all basis functions

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> ca, cb = mol.sph2spinor_coeff()
>>> s0 = mol.intor('int1e_ovlp_spinor')
>>> s1 = ca.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(ca)
>>> s1+= cb.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(cb)
>>> print(abs(s1-s0).max())
>>> 6.66133814775e-16

sph_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spheric_labels(fmt=True, base=0)

Labels for spherical GTO functions

Kwargs:

fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spin = 0

spinor_labels(fmt=True, base=0)

Labels of spinor GTO functions

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

symmetrize_mesh(mesh=None)

symmetry = False

symmetry_subgroup = None

time_reversal_map()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

tmap()

The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

to_mol()

Return a Mole object using the same atoms and basis functions as the Cell object.

to_uncontracted_cartesian_basis()

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

tot_electrons(nkpts=1)

Total number of electrons

unit = 'angstrom'

classmethod unpack(moldic)

Convert the packed dict to a Cell object, to generate the input arguments for Cell object.

unpack_(moldic)

classmethod(function) -> method

Convert a function to be a class method.

A class method receives the class as implicit first argument, just like an instance method receives the instance. To declare a class method, use this idiom:

class C:

@classmethod def f(cls, arg1, arg2, …):

…

It can be called either on the class (e.g. C.f()) or on an instance (e.g. C().f()). The instance is ignored except for its class. If a class method is called for a derived class, the derived class object is passed as the implied first argument.

Class methods are different than C++ or Java static methods. If you want those, see the staticmethod builtin.

update(chkfile)

update_from_chk(chkfile)

verbose = 3

view(cls)

New view of object with the same attributes.

property vol

with_common_orig(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_common_origin(coord)

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_integral_screen(threshold)

Return a temporary mol context which has the required integral screen threshold

with_long_range_coulomb(omega)

Return a temporary mol context for long-range part of range-separated Coulomb operator.

with_range_coulomb(omega)

Return a temporary mol context which sets the required parameter omega for range-separated Coulomb operator. If omega = None, return the context for regular Coulomb integrals. See also mol.set_range_coulomb()

Examples:

>>> with mol.with_range_coulomb(omega=1.5):
...     mol.intor('int2e')

with_rinv_as_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_at_nucleus(atm_id)

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_orig(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_origin(coord)

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_zeta(zeta)

Return a temporary mol context which has the rquired Gaussian charge distribution placed at “rinv_origin”: rho(r) = Norm * exp(-zeta * r^2). See also mol.set_rinv_zeta()

Examples:

>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
...     mol.intor('int1e_rinv')

with_short_range_coulomb(omega)

Return a temporary mol context for short-range part of range-separated Coulomb operator.

class vayesta.lattmod.latt.HubbardDF(mol)

Bases: object

ao2mo(*args, **kwargs)

get_naoaux()

loop(blksize=None)

Note that blksize is ignored.

class vayesta.lattmod.latt.LatticeSCF(mol, *args, **kwargs)

Bases: object

property cell

get_hcore(*args, **kwargs)

get_ovlp(mol=None)

density_fit()

class vayesta.lattmod.latt.LatticeRHF(mol, *args, **kwargs)

Bases: LatticeSCF, RHF

get_init_guess(mol=None, key=None, s1e=None)

get_jk(mol=None, dm=None, *args, **kwargs)

Compute J, K matrices for all input density matrices

Parameters:

• mol – an instance of Mole

• dm – ndarray or list of ndarrays A density matrix or a list of density matrices

Kwargs:

hermiint

Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian

vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

with_jboolean

Whether to compute J matrices

with_kboolean

Whether to compute K matrices

omegafloat

Parameter of range-separated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-separated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

check_lattice_symmetry(dm=None)

CCSD(frozen=None, mo_coeff=None, mo_occ=None)

restricted CCSD

verbose

int Print level. Default value equals to Mole.verbose

max_memory

float or int Allowed memory in MB. Default value equals to Mole.max_memory

conv_tol

float converge threshold. Default is 1e-7.

conv_tol_normt

float converge threshold for norm(t1,t2). Default is 1e-5.

max_cycle

int max number of iterations. Default is 50.

diis_space

int DIIS space size. Default is 6.

diis_start_cycle

int The step to start DIIS. Default is 0.

iterative_damping

float The self consistent damping parameter.

direct

bool AO-direct CCSD. Default is False.

async_io

bool Allow for asynchronous function execution. Default is True.

incore_complete

bool Avoid all I/O (also for DIIS). Default is False.

level_shift

float A shift on virtual orbital energies to stabilize the CCSD iteration

frozen

int or list If integer is given, the inner-most orbitals are frozen from CC amplitudes. Given the orbital indices (0-based) in a list, both occupied and virtual orbitals can be frozen in CC calculation.

>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> # freeze 2 core orbitals
>>> mycc = cc.CCSD(mf).set(frozen = 2).run()
>>> # auto-generate the number of core orbitals to be frozen (1 in this case)
>>> mycc = cc.CCSD(mf).set_frozen().run()
>>> # freeze 2 core orbitals and 3 high lying unoccupied orbitals
>>> mycc.set(frozen = [0,1,16,17,18]).run()

callback

function(envs_dict) => None callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current environment.

Saved results:

convergedbool

Whether the CCSD iteration converged

e_corrfloat

CCSD correlation correction

e_totfloat

Total CCSD energy (HF + correlation)

t1, t2 :

T amplitudes t1[i,a], t2[i,j,a,b] (i,j in occ, a,b in virt)

l1, l2 :

Lambda amplitudes l1[i,a], l2[i,j,a,b] (i,j in occ, a,b in virt)

cyclesint

The number of iteration cycles performed

CISD(*args, **kwargs)

DFMP2(*args, **kwargs)

DIIS

alias of CDIIS

MP2(*args, **kwargs)

restricted MP2 with canonical HF and non-canonical HF reference

verbose

int Print level. Default value equals to Mole.verbose

max_memory

float or int Allowed memory in MB. Default value equals to Mole.max_memory

conv_tol

float For non-canonical MP2, converge threshold for MP2 correlation energy. Default value is 1e-7.

conv_tol_normt

float For non-canonical MP2, converge threshold for norm(t2). Default value is 1e-5.

max_cycle

int For non-canonical MP2, max number of MP2 iterations. Default value is 50.

diis_space

int For non-canonical MP2, DIIS space size in MP2 iterations. Default is 6.

level_shift

float A shift on virtual orbital energies to stabilize the MP2 iterations.

frozen

int or list If integer is given, the inner-most orbitals are excluded from MP2 amplitudes. Given the orbital indices (0-based) in a list, both occupied and virtual orbitals can be frozen in MP2 calculation.

>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> # freeze 2 core orbitals
>>> pt = mp.MP2(mf).set(frozen = 2).run()
>>> # auto-generate the number of core orbitals to be frozen (1 in this case)
>>> pt = mp.MP2(mf).set_frozen().run()
>>> # freeze 2 core orbitals and 3 high lying unoccupied orbitals
>>> pt.set(frozen = [0,1,16,17,18]).run()

Saved results

e_corrfloat

MP2 correlation correction

e_corr_ss/osfloat

Same-spin and opposite-spin component of the MP2 correlation energy

e_totfloat

Total MP2 energy (HF + correlation)

t2 :

T amplitudes t2[i,j,a,b] (i,j in occ, a,b in virt)

QCISD(frozen=None, mo_coeff=None, mo_occ=None)

restricted QCISD

analyze(verbose=None, with_meta_lowdin=True, **kwargs)

Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

as_scanner()

Generating a scanner/solver for HF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total HF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters assigned in the SCF object (DIIS, conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf
>>> hf_scanner = scf.RHF(gto.Mole().set(verbose=0)).as_scanner()
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.1'))
-98.552190448277955
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.5'))
-98.414750424294368

build(mol=None)

callback = None

canonicalize(mo_coeff, mo_occ, fock=None)

Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy).

property cell

check_convergence = None

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

conv_check = True

conv_tol = 1e-09

conv_tol_cpscf = 1e-08

conv_tol_grad = None

convert_from_(mf)

Convert the input mean-field object to RHF/ROHF

copy()

Returns a shallow copy

damp = 0

density_fit()

diis = True

diis_damp = 0

diis_file = None

diis_space = 8

diis_space_rollback = 0

diis_start_cycle = 1

dip_moment(mol=None, dm=None, unit='Debye', origin=None, verbose=3, **kwargs)

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Parameters:

• mol – an instance of Mole

• dm – a 2D ndarrays density matrices

• origin – optional; length 3 list, tuple, or 1D array Location of the origin. By default, the point (0, 0, 0) is used.

Returns:

the dipole moment on x, y and z component

Return type:

A list

direct_scf = True

direct_scf_tol = 1e-13

disp = None

do_disp(disp=None)

Check whether to apply dispersion correction based on the xc attribute. If dispersion is allowed, return the DFTD3 disp version, such as d3bj, d3zero, d4.

dump_chk(envs_or_file)

Serialize the SCF object and save it to the specified chkfile.

Parameters:

envs_or_file – If this argument is a file path, the serialized SCF object is saved to the file specified by this argument. If this attribute is a dict (created by locals()), the necessary variables are saved to the file specified by the attribute mf.chkfile.

dump_flags(verbose=None)

dump_scf_summary(verbose=5)

eig(h, s)

Solver for generalized eigenvalue problem

\[HC = SCE\]

energy_elec(dm=None, h1e=None, vhf=None)

Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential

… math:

E = \sum_{ij}h_{ij} \gamma_{ji}
  + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle

Note this function has side effects which cause mf.scf_summary updated.

Parameters:

mf – an instance of SCF class

Kwargs:

dm2D ndarray

one-particle density matrix

h1e2D ndarray

Core hamiltonian

vhf2D ndarray

HF potential

Returns:

Hartree-Fock electronic energy and the Coulomb energy

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> dm = mf.make_rdm1()
>>> scf.hf.energy_elec(mf, dm)
(-1.5176090667746334, 0.60917167853723675)
>>> mf.energy_elec(dm)
(-1.5176090667746334, 0.60917167853723675)

energy_nuc()

energy_tot(dm=None, h1e=None, vhf=None)

Total Hartree-Fock energy, electronic part plus nuclear repulsion See scf.hf.energy_elec() for the electron part

Note this function has side effects which cause mf.scf_summary updated.

from_chk(chkfile=None, project=None)

Read the HF results from checkpoint file, then project it to the basis defined by mol

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to switch off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

Returns:

Density matrix, 2D ndarray

gen_response(mo_coeff=None, mo_occ=None, singlet=None, hermi=0, max_memory=None)

Generate a function to compute the product of RHF response function and RHF density matrices.

Kwargs:

singlet (None or boolean)If singlet is None, response function for

orbital hessian or CPHF will be generated. If singlet is boolean, it is used in TDDFT response kernel.

get_dispersion(disp=None, with_3body=None, verbose=None)

get_fock(h1e=None, s1e=None, vhf=None, dm=None, cycle=-1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None, fock_last=None)

F = h^{core} + V^{HF}

Special treatment (damping, DIIS, or level shift) will be applied to the Fock matrix if diis and cycle is specified (The two parameters are passed to get_fock function during the SCF iteration)

Kwargs:

h1e2D ndarray

Core hamiltonian

s1e2D ndarray

Overlap matrix, for DIIS

vhf2D ndarray

HF potential matrix

dm2D ndarray

Density matrix, for DIIS

cycleint

Then present SCF iteration step, for DIIS

diisan object of SCF.DIIS class

DIIS object to hold intermediate Fock and error vectors

diis_start_cycleint

The step to start DIIS. Default is 0.

level_shift_factorfloat or int

Level shift (in AU) for virtual space. Default is 0.

get_grad(mo_coeff, mo_occ, fock=None)

RHF orbital gradients

Parameters:

• mo_coeff – 2D ndarray Obital coefficients

• mo_occ – 1D ndarray Orbital occupancy

• fock_ao – 2D ndarray Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_hcore(*args, **kwargs)

get_j(mol=None, dm=None, hermi=1, omega=None)

Compute J matrices for all input density matrices

get_k(mol=None, dm=None, hermi=1, omega=None)

Compute K matrices for all input density matrices

get_occ(mo_energy=None, mo_coeff=None)

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray

Obital energies

mo_coeff2D ndarray

Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)

Hartree-Fock potential matrix for the given density matrix

Parameters:

• mol – an instance of Mole

• dm – ndarray or list of ndarrays A density matrix or a list of density matrices

Kwargs:

dm_lastndarray or a list of ndarrays or 0

The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.

vhf_lastndarray or a list of ndarrays or 0

The reference HF potential matrix.

hermiint

Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian

vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True

init_direct_scf(mol=None)

init_guess = 'minao'

init_guess_by_1e(mol=None)

Generate initial guess density matrix from core hamiltonian

Returns:

Density matrix, 2D ndarray

init_guess_by_atom(mol=None)

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:

Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)

Read the HF results from checkpoint file, then project it to the basis defined by mol

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to switch off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

Returns:

Density matrix, 2D ndarray

init_guess_by_huckel(mol=None)

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:

Density matrix, 2D ndarray

init_guess_by_minao(mol=None)

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:

Density matrix, 2D ndarray

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.init_guess_by_minao(mol)
array([[ 0.94758917,  0.09227308],
       [ 0.09227308,  0.94758917]])

init_guess_by_mod_huckel(updated_rule, mol=None)

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

In contrast to init_guess_by_huckel, this routine employs the updated GWH rule from doi:10.1021/ja00480a005 to form the guess.

Returns:

Density matrix, 2D ndarray

init_guess_by_sap(mol=None, **kwargs)

Generate initial guess density matrix from a superposition of atomic potentials (SAP), doi:10.1021/acs.jctc.8b01089. This is the Gaussian fit implementation, see doi:10.1063/5.0004046.

Parameters:

• mol – MoleBase object the molecule object for which the initial guess is evaluated

• sap_basis – dict SAP basis in internal format (python dictionary)

Returns:

ndarray

SAP initial guess density matrix

Return type:

dm0

istype(type_code)

Checks if the object is an instance of the class specified by the type_code. type_code can be a class or a str. If the type_code is a class, it is equivalent to the Python built-in function isinstance. If the type_code is a str, it checks the type_code against the names of the object and all its parent classes.

kernel(dm0=None, **kwargs)

SCF main driver

Kwargs:

dm0ndarray

If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

level_shift = 0

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)

One-particle density matrix in AO representation

Parameters:

• mo_coeff – 2D ndarray Orbital coefficients. Each column is one orbital.

• mo_occ – 1D ndarray Occupancy

Returns:

One-particle density matrix, 2D ndarray

make_rdm2(mo_coeff=None, mo_occ=None, **kwargs)

Two-particle density matrix in AO representation

Parameters:

• mo_coeff – 2D ndarray Orbital coefficients. Each column is one orbital.

• mo_occ – 1D ndarray Occupancy

Returns:

Two-particle density matrix, 4D ndarray

max_cycle = 50

mulliken_meta(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

mulliken_pop(mol=None, dm=None, s=None, verbose=5)

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

mulliken_pop_meta_lowdin_ao(*args, **kwargs)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

newton()

Create an SOSCF object based on the mean-field object

nuc_grad_method()

Hook to create object for analytical nuclear gradients.

property opt

pop(*args, **kwargs)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

quad_moment(mol=None, dm=None, unit='DebyeAngstrom', origin=None, verbose=3, **kwargs)

Calculates traceless quadrupole moment tensor.

The traceless quadrupole tensor is given by

\[\begin{split}Q_{ij} &= - \frac{1}{2} \sum_{\mu \nu} P_{\mu \nu} \left[ 3 (\nu | r_i r_j | \mu) - \delta_{ij} (\nu | r^2 | \mu) \right] \\ &+ \frac{1}{2} \sum_A Q_A \left( R_{iA} R_{jA} - \delta_{ij} \|\mathbf{R}_A\|^2 \right).\end{split}\]

If the molecule has a dipole, the quadrupole moment depends on the location of the origin. By default, the origin is taken to be (0, 0, 0), but it can be set manually via the keyword argument origin.

Parameters:

• mol – an instance of Mole

• dm – a 2D ndarrays density matrices

• origin – optional; length 3 list, tuple, or 1D array Location of the origin. By default, it is (0, 0, 0).

Returns:

Traceless quadrupole tensor, 2D ndarray.

remove_soscf()

Remove the SOSCF decorator

reset(mol=None)

Reset mol and relevant attributes associated to the old mol object

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

sap_basis = 'sapgrasplarge'

scf(dm0=None, **kwargs)

SCF main driver

Kwargs:

dm0ndarray

If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

sfx2c1e()

spin_square(mo_coeff=None, s=None)

Spin square and multiplicity of RHF determinant

stability(internal=True, external=False, verbose=None, return_status=False, **kwargs)

RHF/RKS stability analysis.

See also pyscf.scf.stability.rhf_stability function.

Kwargs:

internalbool

Internal stability, within the RHF optimization space.

externalbool

External stability. Including the RHF -> UHF and real -> complex stability analysis.

return_status: bool

Whether to return stable_i and stable_e

Returns:

If return_status is False (default), the return value includes two set of orbitals, which are more close to the stable condition. The first corresponds to the internal stability and the second corresponds to the external stability.

Else, another two boolean variables (indicating current status: stable or unstable) are returned. The first corresponds to the internal stability and the second corresponds to the external stability.

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

to_ghf()

Convert the input mean-field object to a GHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_gks(xc='HF')

Convert the input mean-field object to a GKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_gpu(out=None)

Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.

to_ks(xc='HF')

Convert to RKS object.

to_rhf()

Convert the input mean-field object to a RHF/ROHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_rks(xc='HF')

Convert the input mean-field object to a RKS/ROKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uhf()

Convert the input mean-field object to a UHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uks(xc='HF')

Convert the input mean-field object to a UKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

update(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk_(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

verbose = 0

view(cls)

New view of object with the same attributes.

x2c()

x2c1e()

class vayesta.lattmod.latt.LatticeUHF(mol, *args, **kwargs)

Bases: LatticeSCF, UHF

get_init_guess(mol=None, key=None, s1e=None)

get_jk(mol=None, dm=None, *args, **kwargs)

Coulomb (J) and exchange (K)

Parameters:

dm – a list of 2D arrays or a list of 3D arrays (alpha_dm, beta_dm) or (alpha_dms, beta_dms)

CCSD(frozen=None, mo_coeff=None, mo_occ=None)

restricted CCSD

verbose

int Print level. Default value equals to Mole.verbose

max_memory

float or int Allowed memory in MB. Default value equals to Mole.max_memory

conv_tol

float converge threshold. Default is 1e-7.

conv_tol_normt

float converge threshold for norm(t1,t2). Default is 1e-5.

max_cycle

int max number of iterations. Default is 50.

diis_space

int DIIS space size. Default is 6.

diis_start_cycle

int The step to start DIIS. Default is 0.

iterative_damping

float The self consistent damping parameter.

direct

bool AO-direct CCSD. Default is False.

async_io

bool Allow for asynchronous function execution. Default is True.

incore_complete

bool Avoid all I/O (also for DIIS). Default is False.

level_shift

float A shift on virtual orbital energies to stabilize the CCSD iteration

frozen

int or list If integer is given, the inner-most orbitals are frozen from CC amplitudes. Given the orbital indices (0-based) in a list, both occupied and virtual orbitals can be frozen in CC calculation.

>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> # freeze 2 core orbitals
>>> mycc = cc.CCSD(mf).set(frozen = 2).run()
>>> # auto-generate the number of core orbitals to be frozen (1 in this case)
>>> mycc = cc.CCSD(mf).set_frozen().run()
>>> # freeze 2 core orbitals and 3 high lying unoccupied orbitals
>>> mycc.set(frozen = [0,1,16,17,18]).run()

callback

function(envs_dict) => None callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current environment.

Saved results:

convergedbool

Whether the CCSD iteration converged

e_corrfloat

CCSD correlation correction

e_totfloat

Total CCSD energy (HF + correlation)

t1, t2 :

T amplitudes t1[i,a], t2[i,j,a,b] (i,j in occ, a,b in virt)

l1, l2 :

Lambda amplitudes l1[i,a], l2[i,j,a,b] (i,j in occ, a,b in virt)

cyclesint

The number of iteration cycles performed

CISD(*args, **kwargs)

DFMP2 = None

DIIS

alias of CDIIS

MP2(*args, **kwargs)

QCISD(frozen=None, mo_coeff=None, mo_occ=None)

restricted QCISD

analyze(verbose=None, with_meta_lowdin=True, **kwargs)

Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

apply(fn, *args, **kwargs)

Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

as_scanner()

Generating a scanner/solver for HF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total HF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters assigned in the SCF object (DIIS, conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf
>>> hf_scanner = scf.RHF(gto.Mole().set(verbose=0)).as_scanner()
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.1'))
-98.552190448277955
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.5'))
-98.414750424294368

build(mol=None)

callback = None

canonicalize(mo_coeff, mo_occ, fock=None)

Canonicalization diagonalizes the UHF Fock matrix within occupied, virtual subspaces separatedly (without change occupancy).

property cell

check_convergence = None

check_sanity()

Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

conv_check = True

conv_tol = 1e-09

conv_tol_cpscf = 1e-08

conv_tol_grad = None

convert_from_(mf)

Create UHF object based on the RHF/ROHF object

copy()

Returns a shallow copy

damp = 0

density_fit()

det_ovlp(mo1, mo2, occ1, occ2, ovlp=None)

Calculate the overlap between two different determinants. It is the product of single values of molecular orbital overlap matrix.

\[S_{12} = \langle \Psi_A | \Psi_B \rangle = (\mathrm{det}\mathbf{U}) (\mathrm{det}\mathbf{V^\dagger}) \prod\limits_{i=1}\limits^{2N} \lambda_{ii}\]

where \(\mathbf{U}, \mathbf{V}, \lambda\) are unitary matrices and single values generated by single value decomposition(SVD) of the overlap matrix \(\mathbf{O}\) which is the overlap matrix of two sets of molecular orbitals:

\[\mathbf{U}^\dagger \mathbf{O} \mathbf{V} = \mathbf{\Lambda}\]

Parameters:

• mo1 – 2D ndarrays Molecualr orbital coefficients

• mo2 – 2D ndarrays Molecualr orbital coefficients

• occ1 – 2D ndarrays occupation numbers

• occ2 – 2D ndarrays occupation numbers

Returns:

the product of single values: float (x_a, x_b): 1D ndarrays \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\) They are used to calculate asymmetric density matrix

Return type:

A list

diis = True

diis_damp = 0

diis_file = None

diis_space = 8

diis_space_rollback = 0

diis_start_cycle = 1

dip_moment(mol=None, dm=None, unit='Debye', origin=None, verbose=3, **kwargs)

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Parameters:

• mol – an instance of Mole

• dm – a 2D ndarrays density matrices

• origin – optional; length 3 list, tuple, or 1D array Location of the origin. By default, the point (0, 0, 0) is used.

Returns:

the dipole moment on x, y and z component

Return type:

A list

direct_scf = True

direct_scf_tol = 1e-13

disp = None

do_disp(disp=None)

Check whether to apply dispersion correction based on the xc attribute. If dispersion is allowed, return the DFTD3 disp version, such as d3bj, d3zero, d4.

dump_chk(envs_or_file)

Serialize the SCF object and save it to the specified chkfile.

Parameters:

envs_or_file – If this argument is a file path, the serialized SCF object is saved to the file specified by this argument. If this attribute is a dict (created by locals()), the necessary variables are saved to the file specified by the attribute mf.chkfile.

dump_flags(verbose=None)

dump_scf_summary(verbose=5)

eig(fock, s)

Solver for generalized eigenvalue problem

\[HC = SCE\]

energy_elec(dm=None, h1e=None, vhf=None)

Electronic energy of Unrestricted Hartree-Fock

Note this function has side effects which cause mf.scf_summary updated.

Returns:

Hartree-Fock electronic energy and the 2-electron part contribution

energy_nuc()

energy_tot(dm=None, h1e=None, vhf=None)

Total Hartree-Fock energy, electronic part plus nuclear repulsion See scf.hf.energy_elec() for the electron part

Note this function has side effects which cause mf.scf_summary updated.

from_chk(chkfile=None, project=None)

Read the HF results from checkpoint file, then project it to the basis defined by mol

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to switch off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

Returns:

Density matrix, 2D ndarray

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)

Generate a function to compute the product of UHF response function and UHF density matrices.

get_dispersion(disp=None, with_3body=None, verbose=None)

get_fock(h1e=None, s1e=None, vhf=None, dm=None, cycle=-1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None, fock_last=None)

F = h^{core} + V^{HF}

Special treatment (damping, DIIS, or level shift) will be applied to the Fock matrix if diis and cycle is specified (The two parameters are passed to get_fock function during the SCF iteration)

Kwargs:

h1e2D ndarray

Core hamiltonian

s1e2D ndarray

Overlap matrix, for DIIS

vhf2D ndarray

HF potential matrix

dm2D ndarray

Density matrix, for DIIS

cycleint

Then present SCF iteration step, for DIIS

diisan object of SCF.DIIS class

DIIS object to hold intermediate Fock and error vectors

diis_start_cycleint

The step to start DIIS. Default is 0.

level_shift_factorfloat or int

Level shift (in AU) for virtual space. Default is 0.

get_grad(mo_coeff, mo_occ, fock=None)

RHF orbital gradients

Parameters:

• mo_coeff – 2D ndarray Obital coefficients

• mo_occ – 1D ndarray Orbital occupancy

• fock_ao – 2D ndarray Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_hcore(*args, **kwargs)

get_j(mol=None, dm=None, hermi=1, omega=None)

Compute J matrices for all input density matrices

get_k(mol=None, dm=None, hermi=1, omega=None)

Compute K matrices for all input density matrices

get_occ(mo_energy=None, mo_coeff=None)

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray

Obital energies

mo_coeff2D ndarray

Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)

Unrestricted Hartree-Fock potential matrix of alpha and beta spins, for the given density matrix

\[\begin{split}V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\ V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\beta\end{split}\]

Parameters:

• mol – an instance of Mole

• dm – a list of ndarrays A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)

Kwargs:

dm_lastndarray or a list of ndarrays or 0

The density matrix baseline. When it is not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.

vhf_lastndarray or a list of ndarrays or 0

The reference HF potential matrix.

hermiint

Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian

vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

\(V_{hf} = (V^\alpha, V^\beta)\). \(V^\alpha\) (and \(V^\beta\)) can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)

init_direct_scf(mol=None)

init_guess = 'minao'

init_guess_breaksym = 1

init_guess_by_1e(mol=None, breaksym=None)

Generate initial guess density matrix from core hamiltonian

Returns:

Density matrix, 2D ndarray

init_guess_by_atom(mol=None, breaksym=None)

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:

Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)

Read the HF results from checkpoint file, then project it to the basis defined by mol

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to switch off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

Returns:

Density matrix, 2D ndarray

init_guess_by_huckel(mol=None, breaksym=None)

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:

Density matrix, 2D ndarray

init_guess_by_minao(mol=None, breaksym=None)

Initial guess in terms of the overlap to minimal basis.

init_guess_by_mod_huckel(mol=None, breaksym=None)

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

In contrast to init_guess_by_huckel, this routine employs the updated GWH rule from doi:10.1021/ja00480a005 to form the guess.

Returns:

Density matrix, 2D ndarray

init_guess_by_sap(mol=None, breaksym=None, **kwargs)

Generate initial guess density matrix from a superposition of atomic potentials (SAP), doi:10.1021/acs.jctc.8b01089. This is the Gaussian fit implementation, see doi:10.1063/5.0004046.

Parameters:

• mol – MoleBase object the molecule object for which the initial guess is evaluated

• sap_basis – dict SAP basis in internal format (python dictionary)

Returns:

ndarray

SAP initial guess density matrix

Return type:

dm0

istype(type_code)

Checks if the object is an instance of the class specified by the type_code. type_code can be a class or a str. If the type_code is a class, it is equivalent to the Python built-in function isinstance. If the type_code is a str, it checks the type_code against the names of the object and all its parent classes.

kernel(dm0=None, **kwargs)

SCF main driver

Kwargs:

dm0ndarray

If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

level_shift = 0

make_asym_dm(mo1, mo2, occ1, occ2, x)

One-particle asymmetric density matrix

Parameters:

• mo1 – 2D ndarrays Molecualr orbital coefficients

• mo2 – 2D ndarrays Molecualr orbital coefficients

• occ1 – 2D ndarrays Occupation numbers

• occ2 – 2D ndarrays Occupation numbers

• x – 2D ndarrays \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\). See also det_ovlp()

Returns:

A list of 2D ndarrays for alpha and beta spin

Examples:

>>> mf1 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.3', basis='ccpvdz')).run()
>>> mf2 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.4', basis='ccpvdz')).run()
>>> s = gto.intor_cross('int1e_ovlp_sph', mf1.mol, mf2.mol)
>>> det, x = det_ovlp(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, s)
>>> adm = make_asym_dm(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, x)
>>> adm.shape
(2, 19, 19)

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)

One-particle density matrix in AO representation

Parameters:

• mo_coeff – tuple of 2D ndarrays Orbital coefficients for alpha and beta spins. Each column is one orbital.

• mo_occ – tuple of 1D ndarrays Occupancies for alpha and beta spins.

Returns:

A list of 2D ndarrays for alpha and beta spins

make_rdm2(mo_coeff=None, mo_occ=None, **kwargs)

Two-particle density matrix in AO representation

Parameters:

• mo_coeff – tuple of 2D ndarrays Orbital coefficients for alpha and beta spins. Each column is one orbital.

• mo_occ – tuple of 1D ndarrays Occupancies for alpha and beta spins.

Returns:

A tuple of three 4D ndarrays for alpha,alpha and alpha,beta and beta,beta spins

max_cycle = 50

mulliken_meta(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

mulliken_meta_spin(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)

mulliken_pop(mol=None, dm=None, s=None, verbose=5)

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

mulliken_pop_meta_lowdin_ao(*args, **kwargs)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

mulliken_spin_pop(mol=None, dm=None, s=None, verbose=5)

property nelec

property nelectron_alpha

newton()

Create an SOSCF object based on the mean-field object

nuc_grad_method()

Hook to create object for analytical nuclear gradients.

property opt

pop(*args, **kwargs)

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carried out within each subsets.

Parameters:

• mol – an instance of Mole

• dm – ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr

Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

pop, charges

popnparray

Mulliken population on each atomic orbitals

chargesnparray

Mulliken charges

Return type:

A list

post_kernel(envs)

A hook to be run after the main body of the kernel function. Internal variables are exposed to post_kernel through the “envs” dictionary. Return value of post_kernel function is not required.

pre_kernel(envs)

A hook to be run before the main body of kernel function is executed. Internal variables are exposed to pre_kernel through the “envs” dictionary. Return value of pre_kernel function is not required.

quad_moment(mol=None, dm=None, unit='DebyeAngstrom', origin=None, verbose=3, **kwargs)

Calculates traceless quadrupole moment tensor.

The traceless quadrupole tensor is given by

\[\begin{split}Q_{ij} &= - \frac{1}{2} \sum_{\mu \nu} P_{\mu \nu} \left[ 3 (\nu | r_i r_j | \mu) - \delta_{ij} (\nu | r^2 | \mu) \right] \\ &+ \frac{1}{2} \sum_A Q_A \left( R_{iA} R_{jA} - \delta_{ij} \|\mathbf{R}_A\|^2 \right).\end{split}\]

If the molecule has a dipole, the quadrupole moment depends on the location of the origin. By default, the origin is taken to be (0, 0, 0), but it can be set manually via the keyword argument origin.

Parameters:

• mol – an instance of Mole

• dm – a 2D ndarrays density matrices

• origin – optional; length 3 list, tuple, or 1D array Location of the origin. By default, it is (0, 0, 0).

Returns:

Traceless quadrupole tensor, 2D ndarray.

remove_soscf()

Remove the SOSCF decorator

reset(mol=None)

Reset mol and relevant attributes associated to the old mol object

run(*args, **kwargs)

Call the kernel function of current object. args will be passed to kernel function. kwargs will be used to update the attributes of current object. The return value of method run is the object itself. This allows a series of functions/methods to be executed in pipe.

sap_basis = 'sapgrasplarge'

scf(dm0=None, **kwargs)

SCF main driver

Kwargs:

dm0ndarray

If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

set(*args, **kwargs)

Update the attributes of the current object. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

sfx2c1e()

spin_square(mo_coeff=None, s=None)

Spin square and multiplicity of UHF determinant

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

1. There are two possibilities for \(S_+ S_-\)

   1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),

   \[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

   2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

   \[\langle S_+ S_- \rangle = \langle ij|s_+ s_-|ij\rangle - \langle ij|s_+ s_-|ji\rangle = -\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle\]

2. Similarly, for \(S_- S_+\)

   1. same electron

   \[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]

   2. different electrons

   \[\langle S_- S_+ \rangle = -\langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle\]

3. For \(S_z^2\)

   1. same electron

   \[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]

   2. different electrons

   \[\begin{split}&\frac{1}{2}\sum_{ij}(\langle ij|2s_{z1}s_{z2}|ij\rangle -\langle ij|2s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}(n_\alpha^2 - n_\alpha n_\beta - n_\beta n_\alpha + n_\beta^2) -\frac{1}{4}(n_\alpha + n_\beta) \\ &=\frac{1}{4}((n_\alpha-n_\beta)^2 - (n_\alpha+n_\beta))\end{split}\]

In total

\[\begin{split}\langle S^2\rangle &= \frac{1}{2} (n_\alpha-\sum_{ij}\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle +n_\beta -\sum_{ij}\langle i^\beta|j^\alpha\rangle\langle j^\alpha|i^\beta\rangle) + \frac{1}{4}(n_\alpha-n_\beta)^2 \\\end{split}\]

Parameters:

mo – a list of 2 ndarrays Occupied alpha and occupied beta orbitals

Kwargs:

sndarray

AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

stability(internal=True, external=False, verbose=None, return_status=False, **kwargs)

Stability analysis for UHF/UKS method.

See also pyscf.scf.stability.uhf_stability function.

Parameters:

mf – UHF or UKS object

Kwargs:

internalbool

Internal stability, within the UHF space.

externalbool

External stability. Including the UHF -> GHF and real -> complex stability analysis.

return_status: bool

Whether to return stable_i and stable_e

Returns:

If return_status is False (default), the return value includes two set of orbitals, which are more close to the stable condition. The first corresponds to the internal stability and the second corresponds to the external stability.

Else, another two boolean variables (indicating current status: stable or unstable) are returned. The first corresponds to the internal stability and the second corresponds to the external stability.

stdout = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>

to_ghf()

Convert the input mean-field object to a GHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_gks(xc='HF')

Convert the input mean-field object to a GKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_gpu(out=None)

Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.

to_ks(xc='HF')

Convert to UKS object.

to_rhf()

Convert the input mean-field object to a RHF/ROHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_rks(xc='HF')

Convert the input mean-field object to a RKS/ROKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uhf()

Convert the input mean-field object to a UHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uks(xc='HF')

Convert the input mean-field object to a UKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

update(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk_(chkfile=None)

Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

verbose = 0

view(cls)

New view of object with the same attributes.

x2c()

x2c1e()

Module contents

Lattice model module

vayesta.lattmod.LatticeMF(mol, *args, **kwargs)

Use RHF by default, unless spin is not zero.