dyson.expressions.adc

Algebraic diagrammatic construction theory (ADC) expressions [1] [2].

[1]

Banerjee, S., & Sokolov, A. Y. (2019). Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. The Journal of Chemical Physics, 151(22). https://doi.org/10.1063/1.5131771

[2]

Schirmer, J., Cederbaum, L. S., & Walter, O. (1983). New approach to the one-particle Green’s function for finite Fermi systems. Physical Review. A, General Physics, 28(3), 1237–1259. https://doi.org/10.1103/physreva.28.1237

Classes

ADC2	Collection of ADC(2) expressions for different parts of the Green's function.
ADC2_1h(mol, adc_obj, imds, eris)	ADC(2) expressions for the one-hole Green's function.
ADC2_1p(mol, adc_obj, imds, eris)	ADC(2) expressions for the one-particle Green's function.
ADC2x	Collection of ADC(2)-x expressions for different parts of the Green's function.
ADC2x_1h(mol, adc_obj, imds, eris)	ADC(2)-x expressions for the one-hole Green's function.
ADC2x_1p(mol, adc_obj, imds, eris)	ADC(2)-x expressions for the one-particle Green's function.
BaseADC(mol, adc_obj, imds, eris)	Base class for ADC expressions.
BaseADC_1h(mol, adc_obj, imds, eris)	Base class for ADC expressions with one-hole Green's function.
BaseADC_1p(mol, adc_obj, imds, eris)	Base class for ADC expressions with one-particle Green's function.

class dyson.expressions.adc.BaseADC(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseExpression

Base class for ADC expressions.

hermitian_downfolded: bool = True

hermitian_upfolded: bool = False

PYSCF_ADC: ModuleType

SIGN: int

METHOD: str = 'adc(2)'

METHOD_TYPE: str = 'ip'

classmethod from_adc(adc_obj: RADC) → BaseADC

Construct an MP2 expression from an ADC object.

Parameters:

adc_obj – ADC object.

Returns:

Expression object.

classmethod from_mf(mf: RHF) → BaseADC

Create an expression from a mean-field object.

Parameters:

mf – Mean-field object.

Returns:

Expression object.

apply_hamiltonian(vector: Array) → Array

Apply the Hamiltonian to a vector.

Parameters:

vector – Vector to apply Hamiltonian to.

Returns:

Output vector.

apply_hamiltonian_left(vector: Array) → Array

Apply the Hamiltonian to a vector on the left.

Parameters:

vector – Vector to apply Hamiltonian to.

Returns:

Output vector.

diagonal() → Array

Get the diagonal of the Hamiltonian.

Returns:

Diagonal of the Hamiltonian.

property mol: Mole

Molecule object.

property non_dyson: bool

Whether the expression produces a non-Dyson Green’s function.

class dyson.expressions.adc.BaseADC_1h(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC

Base class for ADC expressions with one-hole Green’s function.

PYSCF_ADC: ModuleType = <module 'pyscf.adc.radc_ip' from '/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/pyscf/adc/radc_ip.py'>

SIGN: int = -1

METHOD_TYPE: str = 'ip'

get_excitation_vector(orbital: int) → Array

Obtain the vector corresponding to a fermionic operator acting on the ground state.

This vector is a generalisation of

\[f_i^{\pm} \left| \Psi_0 \right>\]

where \(f_i^{\pm}\) is the fermionic creation or annihilation operator, or a product thereof, depending on the particular expression and what Green’s function it corresponds to.

The vector defines the excitaiton manifold probed by the Green’s function corresponding to the expression.

Parameters:

orbital – Orbital index.

Returns:

Excitation vector.

property nsingle: int

Number of configurations in the singles sector.

class dyson.expressions.adc.BaseADC_1p(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC

Base class for ADC expressions with one-particle Green’s function.

PYSCF_ADC: ModuleType = <module 'pyscf.adc.radc_ea' from '/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/pyscf/adc/radc_ea.py'>

SIGN: int = 1

METHOD_TYPE: str = 'ea'

get_excitation_vector(orbital: int) → Array

Obtain the vector corresponding to a fermionic operator acting on the ground state.

This vector is a generalisation of

\[f_i^{\pm} \left| \Psi_0 \right>\]

where \(f_i^{\pm}\) is the fermionic creation or annihilation operator, or a product thereof, depending on the particular expression and what Green’s function it corresponds to.

The vector defines the excitaiton manifold probed by the Green’s function corresponding to the expression.

Parameters:

orbital – Orbital index.

Returns:

Excitation vector.

property nsingle: int

Number of configurations in the singles sector.

class dyson.expressions.adc.ADC2_1h(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC_1h

ADC(2) expressions for the one-hole Green’s function.

METHOD: str = 'adc(2)'

build_se_moments(nmom: int, reduction: Reduction = Reduction.NONE) → Array

Build the self-energy moments.

Parameters:

• nmom – Number of moments to compute.

• reduction – Reduction type for the moments.

Returns:

Moments of the self-energy.

property nconfig: int

Number of configurations.

class dyson.expressions.adc.ADC2_1p(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC_1p

ADC(2) expressions for the one-particle Green’s function.

METHOD: str = 'adc(2)'

build_se_moments(nmom: int, reduction: Reduction = Reduction.NONE) → Array

Build the self-energy moments.

Parameters:

• nmom – Number of moments to compute.

• reduction – Reduction type for the moments.

Returns:

Moments of the self-energy.

property nconfig: int

Number of configurations.

class dyson.expressions.adc.ADC2x_1h(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC_1h

ADC(2)-x expressions for the one-hole Green’s function.

METHOD: str = 'adc(2)-x'

build_se_moments(nmom: int, reduction: Reduction = Reduction.NONE) → Array

Build the self-energy moments.

Parameters:

• nmom – Number of moments to compute.

• reduction – Reduction type for the moments.

Returns:

Moments of the self-energy.

property nconfig: int

Number of configurations.

class dyson.expressions.adc.ADC2x_1p(mol: Mole, adc_obj: adc.radc.RADC, imds: Any, eris: Any)

Bases: BaseADC_1p

ADC(2)-x expressions for the one-particle Green’s function.

METHOD: str = 'adc(2)-x'

build_se_moments(nmom: int, reduction: Reduction = Reduction.NONE) → Array

Build the self-energy moments.

Parameters:

• nmom – Number of moments to compute.

• reduction – Reduction type for the moments.

Returns:

Moments of the self-energy.

property nconfig: int

Number of configurations.

class dyson.expressions.adc.ADC2

Bases: ExpressionCollection

Collection of ADC(2) expressions for different parts of the Green’s function.

class dyson.expressions.adc.ADC2x

Bases: ExpressionCollection

Collection of ADC(2)-x expressions for different parts of the Green’s function.