3.2.2. `horton.correlatedwfn.perturbation` – Perturbation theory module¶

Variables used in this module:

nocc:	number of occupied orbitals in the principle configuration
nvirt:	number of virtual orbitals in the principle configuration
nbasis:	total number of basis functions
energy:	the energy correction, list that can contain different contributions
amplitudes:	the optimized amplitudes, list that can contain different contributions

Indexing convention:

i,j,k,..:	occupied orbitals of principle configuration
a,b,c,..:	virtual orbitals of principle configuration
p,q,r,..:	general indices (occupied, virtual)

class horton.correlatedwfn.perturbation.Perturbation(lf, occ_model)¶

Bases: object

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

__call__(*args, **kwargs)¶

Performs a perturbation theory calculation.

Arguments:

one, two

One- (TwoIndex) and two-body (FourIndex) integrals (some Hamiltonian matrix elements)

args

If Psi_0 = RHF, first argument is the MO coefficient matrix (Expansion instance), if Psi_0 = AP1roG, first argument is again the MO coefficient matrix the second argument is the geminal coefficient matrix (TwoIndex).

Keywords:

Contains reference energy and solver specific input parameters:

eref: (float) reference energy (default float(‘nan’))
ecore: (float) core energy (default float(‘nan’))
threshold: (float) tolerance for amplitudes (default 1e-6)
maxiter: (int) maximum number of iterations (default 200)
guess: (np.array) initial guess (default None)
indextrans: (str) 4-index transformation. One of einsum,

tensordot (default tensordot)

Returns

List of energy contributions (total energy, seniority-0, seniority-2, and seniority-4) and PT amplitudes (doubles)

__init__(lf, occ_model)¶

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

calculate_energy(amplitudes, args)¶

clear()¶: Clear all wavefunction information

clear_aux_matrix()¶: Clear the auxiliary matrices

get_aux_matrix(select)¶

Get an auxiliary matrix.

Arguments:

select: Suffix of auxiliary matrix. See RMP2.init_aux_matrix(), PTa.init_aux_matrix(), and PTb.init_aux_matrix() for possible choices

get_guess()¶

update_amplitudes(new)¶

update_energy(args)¶: Update PT energy

vfunction(coeffs, matrix)¶

amplitudes¶: The PT amplitudes

energy¶: The PT energy

lf¶: The linalg factory

nbasis¶: The number of basis functions

nocc¶: The number of occupied orbitals

nvirt¶: The number of virtual orbitals

class horton.correlatedwfn.perturbation.RMP2(lf, occ_model)¶

Bases: horton.correlatedwfn.perturbation.Perturbation

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

__call__(*args, **kwargs)¶

Performs a perturbation theory calculation.

Arguments:

one, two

One- (TwoIndex) and two-body (FourIndex) integrals (some Hamiltonian matrix elements)

args

If Psi_0 = RHF, first argument is the MO coefficient matrix (Expansion instance), if Psi_0 = AP1roG, first argument is again the MO coefficient matrix the second argument is the geminal coefficient matrix (TwoIndex).

Keywords:

Contains reference energy and solver specific input parameters:

eref: (float) reference energy (default float(‘nan’))
ecore: (float) core energy (default float(‘nan’))
threshold: (float) tolerance for amplitudes (default 1e-6)
maxiter: (int) maximum number of iterations (default 200)
guess: (np.array) initial guess (default None)
indextrans: (str) 4-index transformation. One of einsum,

tensordot (default tensordot)

Returns

List of energy contributions (total energy, seniority-0, seniority-2, and seniority-4) and PT amplitudes (doubles)

__init__(lf, occ_model)¶

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

calculate_amplitudes(*args, **kwargs)¶

Calculates MP2 amplitudes

Arguments:

matrix: Sliced 2-el MO integrals

calculate_aux_matrix(*args)¶

Compute auxiliary matrices

Arguments:

args: One- and two-electron integrals (some Hamiltonian matrix elements) in the MO basis.

calculate_energy(amplitudes, args)¶

calculate_ex_matrix(*args, **kwargs)¶

Calculates excitation matrix with elements (jbkc)

Arguments:

mo2: 2-el MO integrals

check_input(**kwargs)¶: Check input parameters

check_result(**kwargs)¶: Check if amplitudes are symmetric (within a given threshold).

clear()¶: Clear all wavefunction information

clear_aux_matrix()¶: Clear the auxiliary matrices

get_aux_matrix(select)¶

Get an auxiliary matrix.

Arguments:

select: Suffix of auxiliary matrix. See RMP2.init_aux_matrix(), PTa.init_aux_matrix(), and PTb.init_aux_matrix() for possible choices

get_guess()¶

init_aux_matrix(select)¶

Initialize auxiliary matrices

Arguments:

select: One of ‘fock’

print_energy(**kwargs)¶

print_info(**kwargs)¶

solve(*args, **kwargs)¶

Solve for energy and amplitudes

Arguments:

args

Contains one- and two-electron integrals in the MO basis:

[0]: wfn expansion coefficients
[1]: 1-el MO integrals
[2]: 2-el MO integrals

Keywords

eref:	reference energy
threshold:	threshold for symmetry check of MP2 amplitudes

update_amplitudes(new)¶

Update MP2 amplitudes

Arguments:

new: PT amplitudes. A FourIndex instance

update_aux_matrix(*args, **kwargs)¶

Derive all auxiliary matrices. fock_pp: one_pp + sum_m(2<pm|pm> - <pm|mp>),

Arguments:

mo1, mo2: one- and two-electron integrals.

update_energy(args)¶: Update PT energy

vfunction(coeffs, matrix)¶

amplitudes¶: The PT amplitudes

energy¶: The PT energy

lf¶: The linalg factory

nbasis¶: The number of basis functions

nocc¶: The number of occupied orbitals

nvirt¶: The number of virtual orbitals

class horton.correlatedwfn.perturbation.PTa(lf, occ_model)¶

Bases: horton.correlatedwfn.perturbation.Perturbation

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

__call__(*args, **kwargs)¶

Performs a perturbation theory calculation.

Arguments:

one, two

One- (TwoIndex) and two-body (FourIndex) integrals (some Hamiltonian matrix elements)

args

If Psi_0 = RHF, first argument is the MO coefficient matrix (Expansion instance), if Psi_0 = AP1roG, first argument is again the MO coefficient matrix the second argument is the geminal coefficient matrix (TwoIndex).

Keywords:

Contains reference energy and solver specific input parameters:

eref: (float) reference energy (default float(‘nan’))
ecore: (float) core energy (default float(‘nan’))
threshold: (float) tolerance for amplitudes (default 1e-6)
maxiter: (int) maximum number of iterations (default 200)
guess: (np.array) initial guess (default None)
indextrans: (str) 4-index transformation. One of einsum,

tensordot (default tensordot)

Returns

List of energy contributions (total energy, seniority-0, seniority-2, and seniority-4) and PT amplitudes (doubles)

__init__(lf, occ_model)¶

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

calculate_amplitudes(*args, **kwargs)¶

Calculate amplitudes

Arguments:

matrix: A FourIndex instance.

calculate_aux_matrix(*args)¶

Compute auxiliary matrices

Arguments:

args: List of arguements. Only geminal coefficients [1], one- [2] and two-body [3] integrals are used.

calculate_energy(amplitudes, *args)¶

Calculate PT energy and energy contribution of seniority sectors

Arguments:

amplitudes: PT amplitudes. A FourIndex instance
args: List containing the geminal coefficients, 1- and 2-el integrals, and auxiliary matrices

check_input(**kwargs)¶: Check input parameters.

check_result(**kwargs)¶: Check if amplitudes are reasonable.

clear()¶: Clear all wavefunction information

clear_aux_matrix()¶: Clear the auxiliary matrices

get_aux_matrix(select)¶

Get an auxiliary matrix.

Arguments:

select: Suffix of auxiliary matrix. See RMP2.init_aux_matrix(), PTa.init_aux_matrix(), and PTb.init_aux_matrix() for possible choices

get_guess()¶

init_aux_matrix(select, dim=None, dim2=None)¶

Initialize auxiliary matrices

Arguments:

select: One of fock, ocjbc, vcjkb, ocjkb, vcjbc, dcjb

Optional arguments:

dim, dim2: The dimension of the auxiliary matrices for specific axes.

print_energy(**kwargs)¶

print_info(**kwargs)¶

solve(*args, **kwargs)¶

Solve for energy and amplitudes

Arguments:

args

Contains geminal coefficients, 1- and 2-el integrals, and auxiliary matrices

Keywords

eref:	reference energy
ecore:	core energy
threshold:	threshold when checking symmetry of amplitudes

update_amplitudes(new)¶

Update cluster amplitudes

Arguments:

new: PT amplitudes. A FourIndex instance

update_aux_matrix(*args, **kwargs)¶

Arguments:

mo1, mo2: one- and two-electron integrals to be sorted.
cia: The geminal coefficients. A TwoIndex instance

update_energy(args)¶: Update PT energy

vfunction(coeffs, matrix)¶

vfunction_0(*args)¶

Elements of <bcjk|H|0>.

Arguments:

args

All function arguments needed to calculate the vector function:

[0]: wfn expansion coefficients
[1]: geminal coefficients
[2]: 1-el MO integrals
[3]: 2-el MO integrals
[4]: inactive Fock matrix
[5]: ocjbc auxilary matrix
[6]: vcjkb auxilary matrix
[7]: vcjbc auxilary matrix
[8]: ocjkb auxilary matrix

vfunction_psi0(*args, **kwargs)¶

Elements of <bcjk|H|AP1roG>.

Arguments:

args

All function arguments needed to calculate the vector function:

[0]: wfn expansion coefficients
[1]: geminal coefficients
[2]: 1-el MO integrals
[3]: 2-el MO integrals
[4]: inactive Fock matrix
[5]: ocjbc auxilary matrix
[6]: vcjkb auxilary matrix
[7]: vcjbc auxilary matrix
[8]: ocjkb auxilary matrix
[9]: dcjb auxilary matrix

amplitudes¶: The PT amplitudes

energy¶: The PT energy

lf¶: The linalg factory

nbasis¶: The number of basis functions

nocc¶: The number of occupied orbitals

nvirt¶: The number of virtual orbitals

class horton.correlatedwfn.perturbation.PTb(lf, occ_model)¶

Bases: horton.correlatedwfn.perturbation.Perturbation

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

__call__(*args, **kwargs)¶

Performs a perturbation theory calculation.

Arguments:

one, two

One- (TwoIndex) and two-body (FourIndex) integrals (some Hamiltonian matrix elements)

args

If Psi_0 = RHF, first argument is the MO coefficient matrix (Expansion instance), if Psi_0 = AP1roG, first argument is again the MO coefficient matrix the second argument is the geminal coefficient matrix (TwoIndex).

Keywords:

Contains reference energy and solver specific input parameters:

eref: (float) reference energy (default float(‘nan’))
ecore: (float) core energy (default float(‘nan’))
threshold: (float) tolerance for amplitudes (default 1e-6)
maxiter: (int) maximum number of iterations (default 200)
guess: (np.array) initial guess (default None)
indextrans: (str) 4-index transformation. One of einsum,

tensordot (default tensordot)

Returns

List of energy contributions (total energy, seniority-0, seniority-2, and seniority-4) and PT amplitudes (doubles)

__init__(lf, occ_model)¶

Arguments:

lf: A LinalgFactory instance.
occ_model: Aufbau model

Optional arguments:

calculate_aux_matrix(*args)¶

Compute auxiliary matrices

Arguments:

mo1, mo2: One- and two-electron integrals (some Hamiltonian matrix elements) in the MO basis.
args: List of arguements. Only geminal coefficients are used.

calculate_energy(amplitudes, *args)¶

Calculate PT energy and energy contribution of seniority sectors

Arguments:

amplitudes: PT amplitudes. A FourIndex instance
args: List containing the geminal coefficients, 1- and 2-el integrals, and auxiliary matrices

check_input(**kwargs)¶: Check input parameters.

check_result(**kwargs)¶: Check if amplitudes are reasonable.

clear()¶: Clear all wavefunction information

clear_aux_matrix()¶: Clear the auxiliary matrices

get_aux_matrix(select)¶

Get an auxiliary matrix.

Arguments:

select: Suffix of auxiliary matrix. See RMP2.init_aux_matrix(), PTa.init_aux_matrix(), and PTb.init_aux_matrix() for possible choices

get_guess()¶: Generate initial guess for amplitudes

init_aux_matrix(select, dim=None, dim2=None)¶

Initialize auxiliary matrices

Arguments:

select: One of fock, ocjbc, vcjkb, ocjkb, vcjbc, dcjb

Optional arguments:

dim, dim2: The dimension of the auxiliary matrices for specific axes.

print_energy(**kwargs)¶

print_info(**kwargs)¶

solve(*args, **kwargs)¶

Solve for energy and amplitudes

Arguments:

args

Contains geminal coefficients, 1- and 2-el integrals, and auxiliary matrices

Keywords

eref:	reference energy
ecore:	core energy
threshold:	threshold when checking symmetry of amplitudes
guess:	initial guess

For more details, see Pertubation.__call__()

update_amplitudes(new)¶

Update cluster amplitudes

Arguments:

new: PT amplitudes. A FourIndex instance

update_aux_matrix(*args, **kwargs)¶

Arguments:

mo1, mo2: one- and two-electron integrals to be sorted.
cia: The geminal coefficients. A TwoIndex instance

update_energy(args)¶: Update PT energy

vfunction(*args, **kwargs)¶

.

Arguments:

amplitudes

Cluster amplitudes. Need to be determined.

args

All function arguments needed to calculated the vector function:

[0]: wfn expansion coefficients
[1]: geminal coefficients
[2]: 1-el MO integrals
[3]: 2-el MO integrals
[4]: inactive Fock matrix
[5]: ocjbc auxilary matrix
[6]: vcjkb auxilary matrix
[7]: vcjbc auxilary matrix
[8]: ocjkb auxilary matrix
[9]: dcjb auxilary matrix
[10]: eref-ecore

vfunction_psi0(*args, **kwargs)¶

Elements of <bcjk|H|AP1roG>.

Arguments:

args

All function arguments needed to calculate the vector function:

[0]: wfn expansion coefficients
[1]: geminal coefficients
[2]: 1-el MO integrals
[3]: 2-el MO integrals
[4]: inactive Fock matrix
[5]: ocjbc auxilary matrix
[6]: vcjkb auxilary matrix
[7]: vcjbc auxilary matrix
[8]: ocjkb auxilary matrix
[9]: dcjb auxilary matrix
[10]: eref-ecore

amplitudes¶: The PT amplitudes

energy¶: The PT energy

lf¶: The linalg factory

nbasis¶: The number of basis functions

nocc¶: The number of occupied orbitals

nvirt¶: The number of virtual orbitals

3.2.2. horton.correlatedwfn.perturbation – Perturbation theory module¶

3.2.2. `horton.correlatedwfn.perturbation` – Perturbation theory module¶