3.2.1. horton.correlatedwfn.geminal – Correlated wavefunction implementations

This is a general geminals class.

class horton.correlatedwfn.geminal.Geminal(lf, occ_model, npairs=None, nvirt=None)

Bases: object

Arguments:

lf

A LinalgFactory instance.

occ_model

Occupation model

Optional arguments:

npairs

Number of electron pairs, if not specified, npairs = number of occupied orbitals

nvirt

Number of virtual orbitals, if not specified, nvirt = (nbasis-npairs)

__call__(one, two, core, orb, olp, scf, **kwargs)

Optimize geminal coefficients and—if required—find optimal set of orbitals.

Arguments:

one, two

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

core

The core energy (not included in ‘one’ and ‘two’).

orb

An expansion instance. It contains the MO coefficients (orbitals).

olp

The AO overlap matrix. A TwoIndex instance.

scf

A boolean. If True: Initializes orbital optimization.

Keywords:

See RAp1rog.solve() and RAp1rog.solve_scf()

__init__(lf, occ_model, npairs=None, nvirt=None)

Arguments:

lf

A LinalgFactory instance.

occ_model

Occupation model

Optional arguments:

npairs

Number of electron pairs, if not specified, npairs = number of occupied orbitals

nvirt

Number of virtual orbitals, if not specified, nvirt = (nbasis-npairs)

check_convergence(e0, e1, gradient, thresh)

Check convergence.

Arguements:

e0, e1

Used to calculate energy difference e0-e1

gradient

The gradient, a OneIndex instance

thresh

Dictionary containing threshold parameters (‘energy’, ‘gradientmax’, ‘gradientnorm’)

Returns:

True if energy difference, norm of orbital gradient, largest element of orbital gradient are smaller than some threshold values.

check_stepsearch(linesearch)

Check trustradius. Abort calculation if trustradius is smaller than 1e-8

clear()

Clear all wavefunction information

clear_dm()

Clear RDM information

clear_geminal()

Clear geminal information

clear_lagrange()

Clear lagrange information

compute_rotation_matrix(coeff)

Compute orbital rotation matrix

generate_guess(guess, dim=None)

Generate a guess of type ‘guess’.

Arguments:

guess

A dictionary, containing the type of guess.

Optional arguments:

dim

Length of guess.

get_auxmatrix(select)

Get auxiliary matrices

get_four_dm(select)

Get a density matrix (4-RDM). If not available, it will be created (if possible)

Arguments:

select

get_one_dm(select)

Get a density matrix (1-RDM). If not available, it will be created (if possible)

Arguments:

select

‘ps2’, or ‘response’.

get_three_dm(select)

Get a density matrix (3-RDM). If not available, it will be created (if possible)

Arguments:

select

get_two_dm(select)

Get a density matrix (2-RDM). If not available, it will be created (if possible)

Arguments:

select

‘(r(esponse))ppqq’, or ‘(r(esponse))pqpq’.

init_four_dm(select)

Initialize 4-RDM

Arguments

select

init_one_dm(select)

Initialize 1-RDM as OneIndex object

The 1-RDM expressed in the natural orbital basis is diagonal and only the diagonal elements are stored.

Arguments

select

‘ps2’ or ‘response’.

init_three_dm(select)

Initialize 3-RDM

Arguments

select

init_two_dm(select)

Initialize 2-RDM as TwoIndex object

Only the symmetry-unique elements of the (response) 2-RDM are stored. These are matrix elements of type

\[Gamma_{p\bar{q}p\bar{q}}\]

(spin-up and spin-down (bar-sign)) or

\[Gamma_{p\bar{p}q\bar{q}}\]

and are stored as elements \({pq}\) of two_dm_pqpq, and two_dm_ppqq.

Arguments

select

‘(r(esponse))ppqq’, or ‘(r(esponse))pqpq’.

perm(a)

Calculate the permament of a matrix

Arguements

a

A np array

prod(lst)

solve(one, two, core, orb, olp, **kwargs)

solve_scf(one, two, core, orb, olp, **kwargs)

update_auxmatrix(select, two_mo, one_mo=None)

Update auxiliary matrices

update_ecore(new)

Update core energy

update_four_dm(four_dm=None)

Update 2-RDM

Optional arguments:

four_dm

When provided, this 4-RDM is stored.

update_geminal(geminal=None)

Update geminal matrix

Optional arguments:

geminal

When provided, this geminal matrix is stored.

update_lagrange(lagrange=None, dim1=None, dim2=None)

Update Lagragne multipliers

Optional arguments:

lagrange

When provided, this set of Lagrange multipliers is stored.

update_one_dm(one_dm=None)

Update 1-RDM

Optional arguments:

one_dm

When provided, this 1-RDM is stored.

update_three_dm(three_dm=None)

Update 3-RDM

Optional arguments:

three_dm

When provided, this 3-RDM is stored.

update_two_dm(two_dm=None)

Update 2-RDM

Optional arguments:

two_dm

When provided, this 2-RDM is stored.

dimension

The number of unknowns (i.e. the number of geminal coefficients)

ecore

The core energy

geminal

The geminal coefficients

lagrange

The Lagrange multipliers

lf

The LinalgFactory instance

nbasis

The number of basis functions

nocc

The number of occupied orbitals

npairs

The number of electron pairs

nvirt

The number of virtual orbitals

one_dm_ps2

Alpha 1-RDM

one_dm_response

Alpha 1-RDM

two_dm_ppqq

Alpha-beta PS2 (ppqq) 2-RDM

two_dm_pqpq

Alpha-beta PS2 (pqpq) 2-RDM

two_dm_rppqq

Alpha-beta (ppqq) 2-RDM

two_dm_rpqpq

Alpha-beta (pqpq) 2-RDM