API Documentation

Contents

API Documentation#

Constants#

__version__ = '0.6.1'#

PyCI version string.

Numerical Types#

c_long = dtype('int64')#

Signed integer C++ dtype.

c_ulong = dtype('uint64')#

Unsigned integer C++ dtype.

c_double = dtype('float64')#

Floating point C++ dtype.

Classes#

Second-quantized operator class#

class secondquant_op#

Second-quantized operator class.

For arbitrary-seniority systems:

\[O = \sum_{pq}{t_{pq} a^\dagger_p a_q} + \sum_{pqrs}{g_{pqrs} a^\dagger_p a^\dagger_q a_s a_r}\]

For seniority-zero systems:

\[\]

O = sum_{p}{h_p N_p} + sum_{p neq q}{v_{pq} P^dagger_p P_q} + sum_{pq}{w_{pq} N_p N_q}

where

\[h_{p} = \left<p|T|p\right> = t_{pp}\]
\[v_{pq} = \left<pp|V|qq\right> = g_{ppqq}\]
\[w_{pq} = 2 \left<pq|V|pq\right> - \left<pq|V|qp\right> = 2 * g_{pqpq} - g_{pqqp}\]
property ecore#

Constant (or "zero-particle") integral.

Returns:

ecore – Constant (or "zero-particle") integral.

Return type:

float

property h#

Seniority-zero one-particle molecular integral array.

Returns:

h – Seniority-zero one-particle molecular integral array.

Return type:

numpy.ndarray

property nbasis#

Number of spatial orbital basis functions.

Returns:

nbasis – Number of spatial orbital basis functions.

Return type:

int

property one_mo#

One-particle molecular integral array.

Returns:

one_mo – One-particle molecular integral array.

Return type:

numpy.ndarray

to_file()#

Write this operator to an FCIDUMP file.

Parameters:

  • filename (TextIO) – Name of FCIDUMP file to write.

  • nelec (int, default=0) – Number of electrons to write.

  • ms2 (int, default=0) – Spin number to write.

  • tol (float, default=0.0) – Only write integrals with magnitude larger than this value.

property two_mo#

Two-particle molecular integral array.

Returns:

two_mo – Two-particle molecular integral array.

Return type:

numpy.ndarray

property v#

Seniority-zero two-particle molecular integral array.

Returns:

v – Seniority-zero two-particle molecular integral array.

Return type:

numpy.ndarray

property w#

Seniority-two two-particle molecular integral array.

Returns:

w – Seniority-two two-particle molecular integral array.

Return type:

numpy.ndarray

hamiltonian#

alias of secondquant_op

Base wave function classes#

class wavefunction#

Wave function base class.

property nbasis#

Number of spatial orbital functions.

Returns:

nbasis – Number of spatial orbital functions.

Return type:

int

property nocc#

Number of occupied spin-orbitals.

Returns:

nocc – Number of occupied spin-orbitals.

Return type:

int

property nocc_dn#

Number of occupied spin-down orbitals.

Returns:

nocc_dn – Number of occupied spin-down orbitals.

Return type:

int

property nocc_up#

Number of occupied spin-up orbitals.

Returns:

nocc_up – Number of occupied spin-up orbitals.

Return type:

int

property nvir#

Number of virtual spin-orbitals.

Returns:

nvir – Number of virtual spin-orbitals.

Return type:

int

property nvir_dn#

Number of virtual spin-down orbitals.

Returns:

nvir_dn – Number of virtual spin-down orbitals.

Return type:

int

property nvir_up#

Number of virtual spin-up orbitals.

Returns:

nvir_up – Number of virtual spin-up orbitals.

Return type:

int

squeeze()#

Free any unused memory allocated to this object.

class one_spin_wfn#

One-spin wave function base class.

add_all_dets()#

Add all determinants to the wave function.

Parameters:

nthread (int) – Number of threads to use.

add_det()#

Add determinant det to the wave function.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

index – Index of added determinant in wave function, or -1 if the determinant was not added.

Return type:

int

add_dets_from_wfn()#

Add the determinants from another wave function.

Parameters:

wfn (pyci.one_spin_wfn) – Wave function.

add_excited_dets()#

Add excited determinants to the wave function.

Parameters:

  • exc (int) – Excitation order.

  • ref (numpy.ndarray, default=None) – Reference determinant. Default is the Hartree-Fock determinant.

add_hartreefock_det()#

Add the Hartree-Fock determinant to the wave function.

add_occs()#

Add occupation vector occs to the wave function.

Parameters:

occs (numpy.ndarray) – Occupation vector.

Returns:

index – Index of added determinant in wave function, or -1 if the determinant was not added.

Return type:

int

index_det()#

Return the index of determinant det in the wave function.

If the determinant is not in the wave function, this function returns -1.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

index – Index of determinant or -1.

Return type:

int

index_det_from_rank()#

Return the index of determinant with rank rank in the wave function.

If the determinant is not in the wave function, this function returns -1.

Parameters:

rank (int) – Rank of determinant.

Returns:

index – Index of determinant or -1.

Return type:

int

rank_det()#

Return the rank of determinant det.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

rank – Rank of determinant.

Return type:

int

reserve()#

Reserve space in memory for n determinants in the wave function object.

Parameters:

n (int) – Number of determinants for which to reserve space.

to_det_array()#

Return a section of the wave function as a numpy.ndarray of determinants.

Arguments low and high behave like the first two arguments to range. By default, if neither are specified, the whole determinant is returned.

Parameters:

  • low (int, default=-1) – Beginning of section.

  • end (int, default=-1) – End of section.

Returns:

array – Array of determinants.

Return type:

numpy.ndarray

to_file()#

Write the wave function to a binary file.

Parameters:

filename (TextIO) – Name of the file to write.

to_occ_array()#

Return a section of the wave function as a numpy.ndarray of occupation vectors.

Arguments low and high behave like the first two arguments to range(). By default, if neither are specified, the whole determinant is returned.

Parameters:

  • low (int, default=-1) – Beginning of section.

  • end (int, default=-1) – End of section.

Returns:

array – Array of occupation vectors.

Return type:

numpy.ndarray

class two_spin_wfn#

Two-spin wave function base class.

add_all_dets()#

Add all determinants to the wave function.

Parameters:

nthread (int) – Number of threads to use.

add_det()#

Add determinant det to the wave function.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

index – Index of added determinant in wave function, or -1 if the determinant was not added.

Return type:

int

add_dets_from_wfn()#

Add the determinants from another wave function.

Parameters:

wfn (pyci.two_spin_wfn) – Wave function.

add_excited_dets()#

Add excited determinants to the wave function.

Parameters:

  • exc (int) – Excitation order.

  • ref (numpy.ndarray, default=None) – Reference determinant. Default is the Hartree-Fock determinant.

add_hartreefock_det()#

Add the Hartree-Fock determinant to the wave function.

add_occs()#

Add occupation vector occs to the wave function.

Parameters:

occs (numpy.ndarray) – Occupation vector.

Returns:

index – Index of added determinant in wave function, or -1 if the determinant was not added.

Return type:

int

index_det()#

Return the index of determinant det in the wave function.

If the determinant is not in the wave function, this function returns -1.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

index – Index of determinant or -1.

Return type:

int

index_det_from_rank()#

Return the index of determinant with rank rank in the wave function.

If the determinant is not in the wave function, this function returns -1.

Parameters:

rank (int) – Rank of determinant.

Returns:

index – Index of determinant or -1.

Return type:

int

rank_det()#

Return the rank of determinant det.

Parameters:

det (numpy.ndarray) – Determinant.

Returns:

rank – Rank of determinant.

Return type:

int

reserve()#

Reserve space in memory for n determinants in the wave function object.

Parameters:

n (int) – Number of determinants for which to reserve space.

to_det_array()#

Return a section of the wave function as a numpy.ndarray of determinants.

Arguments low and high behave like the first two arguments to range. By default, if neither are specified, the whole determinant is returned.

Parameters:

  • low (int, default=-1) – Beginning of section.

  • end (int, default=-1) – End of section.

Returns:

array – Array of determinants.

Return type:

numpy.ndarray

to_file()#

Write the wave function to a binary file.

Parameters:

filename (TextIO) – Name of the file to write.

to_occ_array()#

Return a section of the wave function as a numpy.ndarray of occupation vectors.

Arguments low and high behave like the first two arguments to range(). By default, if neither are specified, the whole determinant is returned.

Parameters:

  • low (int, default=-1) – Beginning of section.

  • end (int, default=-1) – End of section.

Returns:

array – Array of occupation vectors.

Return type:

numpy.ndarray

DOCI wave function#

class doci_wfn#

DOCI wave function base class.

FullCI wave function#

class fullci_wfn#

FullCI wave function base class.

Generalized CI wave function#

class genci_wfn#

Generalized CI wave function base class.

Sparse matrix operator#

class sparse_op#

Sparse matrix operator class.

data()#

Return CSR matrix data vector

property dtype#

Data type of matrix.

Returns:

dtype – Data type of matrix.

Return type:

numpy.dtype

property ecore#

Constant (or “zero-particle”) integral.

Returns:

ecore – Constant (or “zero-particle”) integral.

Return type:

float

get_element()#

Return the \(\left(i, j\right)\)-th element of the sparse matrix operator.

indices()#

Return CSR matrix indices vector

indptr()#

Return CSR matrix index pointer vector

matvec()#

Compute the matrix vector product of the sparse matrix operator with vector x.

\[A \mathbf{x} = \mathbf{y}\]
Parameters:

  • x (numpy.ndarray) – Vector to which the operator will be applied.

  • out (numpy.ndarray, default=None) – Array in which to store the result. One will be created if this is not specified.

Returns:

y – Result vector.

Return type:

numpy.ndarray

reserve()#

Reserve space in memory for n nonzero elements in the sparse matrix operator.

Parameters:

n (int) – Number of elements for which to reserve space.

property shape#

Shape of the matrix.

Returns:

  • nrow (int) – Number of rows.

  • ncol (int) – Number of columns.

property size#

Number of non-zero matrix elements.

Returns:

size – Number of non-zero matrix elements.

Return type:

int

solve()#

Solve a CI eigenproblem.

Parameters:

  • n (int, default=1) – Number of lowest eigenpairs to find.

  • c0 (np.ndarray, default=[1,0,...,0]) – Initial guess for lowest eigenvector.

  • ncv (int, default=min(nrow, max(2 * n + 1, 20))) – Number of Lanczos vectors to use.

  • maxiter (int, default=nrow * n * 10) – Maximum number of iterations to perform.

  • tol (float, default=1.0e-12) – Convergence tolerance.

Returns:

  • es (np.ndarray) – Energies.

  • cs (np.ndarray) – Coefficient vectors.

squeeze()#

Free any unused memory allocated to this object.

property symmetric#

Whether the sparse matrix operator is symmetric/Hermitian.

Returns:

symmetric – Whether the sparse matrix operator is symmetric/Hermitian.

Return type:

bool

update()#

Update a sparse matrix operator for the HCI algorithm.

Parameters:

Notes

The user is responsible for using the same ham and wfn. This method doesn’t work with rectangular operators. Those must be re-initialized from the wave function object.

Functions#

Threading#

The number of threads to use is decided as follows, in decreasing priority:

  • The value of a keyword argument nthread= to a particular PyCI function or method call

  • The value of n from the most recent invokation of pyci.set_num_threads(n)

  • The value of environment variable PYCI_NUM_THREADS when Python is started

  • The number of threads supported by the hardware (std::thread::hardware_concurrency())

get_num_threads()#

Return the default number of threads to use.

Returns:

nthread – Number of threads.

Return type:

int

set_num_threads()#

Set the default number of threads to use.

Parameters:

nthread (int) – Number of threads.

Selected CI routines#

add_hci()#

Add determinants to a wave function by running an iteration of Heat-Bath CI [HCI1].

[HCI1]

Holmes, Adam A., Norm M. Tubman, and C. J. Umrigar. “Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling.” Journal of chemical theory and computation 12.8 (2016): 3674-3680.

Parameters:

  • ham (pyci.secondquant_op) – Hamiltonian.

  • wfn (pyci.wavefunction) – Wave function.

  • coeffs (numpy.ndarray) – Coefficient vector.

  • eps (float, default=1.0e-5) – \(\epsilon\) value for Heat-Bath CI routine.

  • nthread (int) – Number of threads to use.

Returns:

ndet – Number of determinants added.

Return type:

int

add_excitations(wfn, *excitations, ref=None)#

Add excited determinants to a wave function.

Parameters:

  • wfn (pyci.wavefunction) – Wave function.

  • excitations (Sequence[int]) – List of excitation levels of determinants to add.

  • ref (numpy.ndarray, optional) – Reference determinant by which to determine excitation levels. Default is the Hartree-Fock determinant.

add_seniorities(wfn, *seniorities)#

Add determinants of the specified seniority/ies to the wave function.

Parameters:

  • wfn (pyci.fullci_wfn) – FullCI wave function.

  • seniorities (Sequence[int]) – List of seniorities of determinants to add.

add_gkci(wfn, t=-0.5, p=1.0, mode='cntsp', dim=3, energies=None, width=None)#

Add determinants to the wave function according to the odometer algorithm (Griebel-Knapeck CI) [GKCI1].

[GKCI1]

Anderson, James SM, Farnaz Heidar-Zadeh, and Paul W. Ayers. “Breaking the curse of dimension for the electronic Schrödinger equation with functional analysis.” Computational and Theoretical Chemistry 1142 (2018): 66-77.

Parameters:

  • wfn (pyci.wavefunction) – Wave function.

  • t (float, default=-0.5) – Smoothness factor.

  • p (float, default=1.0) – Cost factor.

  • mode (Sequence[int] or ('cntsp' | 'gamma' | 'interval'), default='cntsp') – Node pattern.

  • dim (int, default=3) – Number of nodes (for ‘gamma’ mode).

  • energies (np.ndarray, optional) – Orbital energies (required for ‘interval’ mode).

  • width (float, optional) – Width of one interval (required for ‘interval’ mode).

Post-CI routines#

compute_rdms()#

Compute the one- and two- particle reduced density matrices (RDMs) of a wave function.

Parameters:

  • wfn (pyci.wavefunction) – Wave function.

  • coeffs (numpy.ndarray) – Coefficient vector.

Returns:

  • d1 (numpy.ndarray) – One-particle RDM matrix.

  • d2 (numpy.ndarray) – Two-particle RDM matrix.

Notes

For DOCI wave functions, this method returns two nbasis-by-nbasis matrices, which include the unique seniority-zero and seniority-two terms from the full 2-RDMs:

\[D_0 = \left<pp|qq\right>\]
\[D_2 = \left<pq|pq\right>\]

The diagonal elements of \(D_0\) are equal to the 1-RDM elements \(\left<p|p\right>\).

For FullCI wave functions, the leading dimension of rdm1 has length 2 and specifies the spin-block 0) “up-up” or 1) “down-down”, and the leading dimensions of rdm2 has length 3 and specifies the spin-block 0) “up-up-up-up”, 1) “down-down-down-down’, or 2) “up-down-up-down”.

For Generalized CI wave functions, rdm1 and rdm2 are the full 1-RDM and 2-RDM, respectively.

spinize_rdms(d1, d2)#

Convert the DOCI matrices or FullCI RDM spin-blocks to full, generalized RDMs.

Parameters:

  • d1 (numpy.ndarray) – \(D_0\) matrix or FullCI 1-RDM spin-blocks.

  • d2 (numpy.ndarray) – \(D_2\) matrix or FullCI 2-RDM spin-blocks.

Returns:

  • rdm1 (numpy.ndarray) – Generalized one-particle RDM.

  • rdm2 (numpy.ndarray) – Generalized two-particle RDM.

compute_enpt2()#

Compute the second-order multi-reference Epstein-Nesbet (ENPT2) energy for a wave function.

Parameters:

  • ham (pyci.secondquant_op) – Hamiltonian.

  • wfn (pyci.wavefunction) – Wave function.

  • coeffs (numpy.ndarray) – Coefficient vector.

  • energy (float) – Variational CI energy for this wave function and Hamiltonian.

  • eps (float, default=1.0e-5) – \(\epsilon\) value for ENPT2 routine.

  • nthread (int) – Number of threads to use.

Returns:

pt_energy – ENPT2 energy.

Return type:

float

compute_overlap()#

Compute the overlap \(\left<\Psi_1|\Psi_2\right>\) of two wave functions.

Parameters:

  • wfn1 (pyci.wavefunction) – First wave function.

  • wfn2 (pyci.wavefunction) – Second wave function.

  • coeffs1 (numpy.ndarray) – First coefficient vector.

  • coeffs2 (numpy.ndarray) – Second coefficient vector.

Returns:

olp – Overlap.

Return type:

float

Integral transformations#

make_senzero_integrals(one_mo, two_mo)#

Return the non-zero chunks for seniority-zero of the full one- and two- particle integrals.

Parameters:

  • one_mo (numpy.ndarray) – Full one-particle integral array.

  • two_mo (numpy.ndarray) – Full two-particle integral array.

Returns:

  • h (numpy.ndarray) – Seniority-zero one-particle integrals.

  • v (numpy.ndarray) – Seniority-zero two-particle integrals.

  • w (numpy.ndarray) – Seniority-two two-particle integrals.

reduce_senzero_integrals(h, v, w, nocc)#

Reduce the non-zero chunks for seniority-zero of the one- and two- particle integrals.

Parameters:

  • h (numpy.ndarray) – Seniority-zero one-particle integrals.

  • v (numpy.ndarray) – Seniority-zero two-particle integrals.

  • w (numpy.ndarray) – Seniority-two two-particle integrals.

  • nocc (int) – Number of pair-occupied orbitals.

Returns:

  • rv (numpy.ndarray) – Reduced seniority-zero two-particle integrals.

  • rw (numpy.ndarray) – Reduced seniority-two two-particle integrals.

FanCI classes#

class AP1roG(ham: secondquant_op, nocc: int, nproj: int | None = None, wfn: doci_wfn | None = None, **kwargs: Any)#

AP1roG FanCI class.

The AP1roG wave function is the Antisymmetrized Product of 1-reference-orbital Geminals [AP1roG1], which has the form

\[\left|\Psi\right> = \prod_{p=1}^{N_\text{elec}/2}{\left( a^\dagger_{\alpha;p} a^\dagger_{\beta;p} + \sum_{k=N/2+1}^K{ c_{pk} a^\dagger_{\alpha;k} a^\dagger_{\beta;k} } \right)} \left|\psi_0\right> \,.\]
[AP1roG1]

Limacher, Peter A., et al. “A new mean-field method suitable for strongly correlated electrons: Computationally facile antisymmetric products of nonorthogonal geminals.” Journal of chemical theory and computation 9.3 (2013): 1394-1401.

compute_jacobian(x: ndarray) → ndarray#

Compute the Jacobian of the FanCI objective function.

j : x[k] -> y[n, k]

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n, E].

Returns:

jac – Jacobian matrix.

Return type:

np.ndarray

compute_objective(x: ndarray) → ndarray#

Compute the FanCI objective function.

f : x[k] -> y[n]

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n, E].

Returns:

obj – Objective vector.

Return type:

np.ndarray

compute_overlap(x: ndarray) → ndarray#

Compute the FanCI overlap vector.

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

Returns:

ovlp – Overlap array.

Return type:

np.ndarray

compute_overlap_deriv(x: ndarray) → ndarray#

Compute the FanCI overlap derivative matrix.

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

Returns:

ovlp – Overlap derivative array.

Return type:

np.ndarray

class APIG(ham: secondquant_op, nocc: int, nproj: int | None = None, wfn: doci_wfn | None = None, **kwargs: Any)#

APIG FanCI class.

The APIG wave function is the Antisymmetrized Product of Interacting Geminals [APIG1], which has the form

\[\left|\Psi\right> = \prod_{p=1}^{N_\text{elec}/2}{ \sum_{k=1}^K{ \left( c_{pk} a^\dagger_{\alpha;k} a^\dagger_{\beta;k} \right) } } \left|\psi_0\right> \,.\]
[APIG1]

Silver, David M. “Natural orbital expansion of interacting geminals.” The Journal of Chemical Physics 50.12 (1969): 5108-5116.

compute_jacobian(x: ndarray) → ndarray#

Compute the Jacobian of the FanCI objective function.

j : x[k] -> y[n, k]

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n, E].

Returns:

jac – Jacobian matrix.

Return type:

np.ndarray

compute_objective(x: ndarray) → ndarray#

Compute the FanCI objective function.

f : x[k] -> y[n]

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n, E].

Returns:

obj – Objective vector.

Return type:

np.ndarray

compute_overlap(x: ndarray) → ndarray#

Compute the FanCI overlap vector.

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

Returns:

ovlp – Overlap array.

Return type:

np.ndarray

compute_overlap_deriv(x: ndarray) → ndarray#

Compute the FanCI overlap derivative matrix.

Parameters:

x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

Returns:

ovlp – Overlap derivative array.

Return type:

np.ndarray

class DetRatio(ham: secondquant_op, nocc: int, numerator: int, denominator: int, nproj: int | None = None, wfn: doci_wfn | None = None, **kwargs: Any)#

Determinant ratio FanCI class. This wave function has the form

\[\left|\Psi\right> = \sum_k{c_k\prod_{i=1}^N{a^\dagger_{k_i}}\left|\theta\right>}\]

where

\[c_k = \frac{ \prod_{n=1}^{n_\text{numer.}}{\text{det}\left[\vec{x_n;}_{k_1}\mid\cdots\mid\vec{x_n;}_{k_N}\right]} }{ \prod_{d=1}^{n_\text{denom.}}{\text{det}\left[\vec{y_d;}_{k_1}\mid\cdots\mid\vec{y_d;}_{k_N}\right]} } \,,\]

with the vectors \(\left\{x_n\right\}\) and \(\left\{y_d\right\}\) being the parameters of the wave function which are concatenated into matrices according to the occupied indices of each \(\psi_k\) prior to their determinants being evaluated. For seniority-zero systems, \(n_\text{numer.} + n_\text{denom.}\) is even, and otherwise it is odd.

compute_overlap(x: ndarray, occs_array: ndarray | str) → ndarray#

Compute the FanCI overlap vector.

Parameters:

  • x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

  • occs_array ((np.ndarray | 'P' | 'S')) – Array of determinant occupations for which to compute overlap. A string “P” or “S” can be passed instead that indicates whether occs_array corresponds to the “P” space or “S” space, so that a more efficient, specialized computation can be done for these.

Returns:

ovlp – Overlap array.

Return type:

np.ndarray

compute_overlap_deriv(x: ndarray, occs_array: ndarray | str) → ndarray#

Compute the FanCI overlap derivative matrix.

Parameters:

  • x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

  • occs_array ((np.ndarray | 'P' | 'S')) – Array of determinant occupations for which to compute overlap. A string “P” or “S” can be passed instead that indicates whether occs_array corresponds to the “P” space or “S” space, so that a more efficient, specialized computation can be done for these.

Returns:

ovlp – Overlap derivative array.

Return type:

np.ndarray

class pCCDS(ham: secondquant_op, nocc_up: int, nocc_dn: int, nproj: int | None = None, wfn: fullci_wfn | None = None, **kwargs: Any)#

Pair coupled cluster doubles + singles (or “AP1roGSDspin”) FanCI class.

\[\left| \Psi_\text{pCCD+S} \right> = \prod_{i=1}^{N/2} \left( 1 + \sum_{a=N/2+1}^K t_{i\bar{i};a\bar{a}} \hat{\tau}^{a\bar{a}}_{i\bar{i}} \right) \prod_{i=1}^{N/2} \left( 1 + \sum_{a=N/2+1}^K t_{i;a\bar{a}} \hat{\tau}^{a}_{i} \hat{n}_{\bar{i}} \right) \left| \psi_0 \right> \,.\]

This is AP1roG supplemented with single excitations that preserve the spin number, i.e., no alpha to beta excitation is allowed, or vice-versa. Furthermore, the single excitations added are those that break an occupied pair of spin orbitals, increasing the seniority number. This determines the sen-o part of the name (from every occupied pair only one element of the pair is excited) [pCCDS1].

[pCCDS1]

Gaikwad, Pratiksha B., et al. “Coupled Cluster-Inspired Geminal Wavefunctions.” arXiv preprint arXiv:2310.01764 (2023).

compute_overlap(x: ndarray, occs_array: ndarray | str) → ndarray#

Compute the pCCDS overlap vector.

The occupation vector is described in terms of the occupied/virtual indexes of the excitation that generates it from the reference. The indexes are further identified as corresponding to excitations of pairs or single spin-orbitals. The overlap is computed as the product of the permanents of the matrices formed by the pair and single excitations indexes.

Parameters:

  • x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

  • occs_array ((np.ndarray | 'P' | 'S')) – Array of determinant occupations for which to compute overlap. A string “P” or “S” can be passed instead that indicates whether occs_array corresponds to the “P” space or “S” space, so that a more efficient, specialized computation can be done for these.

Returns:

ovlp – Overlap array.

Return type:

np.ndarray

compute_overlap_deriv(x: ndarray, occs_array: ndarray | str) → ndarray#

Compute the FanCI overlap derivative matrix.

Parameters:

  • x (np.ndarray) – Parameter array, [p_0, p_1, …, p_n].

  • occs_array ((np.ndarray | 'P' | 'S')) – Array of determinant occupations for which to compute overlap. A string “P” or “S” can be passed instead that indicates whether occs_array corresponds to the “P” space or “S” space, so that a more efficient, specialized computation can be done for these.

Returns:

ovlp – Overlap derivative array.

Return type:

np.ndarray

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