PyCI is a free and open-source Python library for setting up and running arbitrary determinant-driven configuration interaction (CI) computations, as well as their generalizations to cases where the coefficients of the determinant are nonlinear functions of optimizable parameters. PyCI also includes functionality for computing the residual correlation energy, along with the ability to compute spin-polarized one- and two-electron (transition) reduced density matrices. PyCI was originally intended to replace the ab initio quantum chemistry functionality in the HORTON library but emerged as a standalone research tool, primarily intended to aid in method development, while maintaining high performance so that it is suitable for practical calculations. To this end, PyCI is written in Python, adopting principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. Computationally intensive steps, notably operations related to generating Slater determinants and computing their expectation values, are delegated to low-level C++ code. This article marks the official release of the PyCI library, showcasing its functionality and scope.
REFERENCES
1.
T. D.
Kim
, R. A.
Miranda-Quintana
, M.
Richer
, and P. W.
Ayers
, “Flexible ansatz for N-body configuration interaction
,” Comput. Theor. Chem.
1202
, 113187
(2021
).2.
A. A.
Holmes
, N. M.
Tubman
, and C.
Umrigar
, “Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling
,” J. Chem. Theory Comput.
12
, 3674
–3680
(2016
).3.
S.
Sharma
, A. A.
Holmes
, G.
Jeanmairet
, A.
Alavi
, and C. J.
Umrigar
, “Semistochastic heat-bath configuration interaction method: Selected configuration interaction with semistochastic perturbation theory
,” J. Chem. Theory Comput.
13
, 1595
–1604
(2017
).4.
J.
Li
, M.
Otten
, A. A.
Holmes
, S.
Sharma
, and C. J.
Umrigar
, “Fast semistochastic heat-bath configuration interaction
,” J. Chem. Phys.
149
, 214110
(2018
).5.
Q.
Sun
, T. C.
Berkelbach
, N. S.
Blunt
, G. H.
Booth
, S.
Guo
, Z.
Li
, J.
Liu
, J. D.
McClain
, E. R.
Sayfutyarova
, S.
Sharma
et al, “PySCF: The Python-based simulations of chemistry framework
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1340
(2018
).6.
F. A.
Evangelista
, C.
Li
, P.
Verma
, K. P.
Hannon
, J. B.
Schriber
, T.
Zhang
, C.
Cai
, S.
Wang
, N.
He
, N. H.
Stair
et al, “Forte: A suite of advanced multireference quantum chemistry methods
,” arXiv:2405.10197 (2024
).7.
A.
Tehrani
, J. S. M.
Anderson
, D.
Chakraborty
, J. I.
Rodriguez-Hernandez
, D. C.
Thompson
, T.
Verstraelen
, P. W.
Ayers
, and F.
Heidar-Zadeh
, “An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions
,” J. Comput. Chem.
44
, 1998
–2015
(2023
).8.
F.
Meng
, M.
Richer
, A.
Tehrani
, J.
La
, T. D.
Kim
, P. W.
Ayers
, and F.
Heidar-Zadeh
, “Procrustes: A python library to find transformations that maximize the similarity between matrices
,” Comput. Phys. Commun.
276
, 108334
(2022
).9.
V.
Chuiko
, A. D. S.
Richards
, G.
Sánchez Díaz
, M.
Martínez-González
, W.
Sanchez
, M.
Richer
, Y.
Zhao
, W.
Adams
, P.
Johnson
, F.
Heidar-Zadeh
, and P. W.
Ayers
, “Model Hamiltonian: A Python-scriptable library for generating 0-, 1-, and 2-electron integrals
” (unpublished).10.
G.
Sánchez Díaz
, M.
Richer
, M.
Martínez-González
, M.
van Zyl
, L.
Pujal
, A.
Tehrani
, J.
Bianchi
, P. W.
Ayers
, and F.
Heidar-Zadeh
, “AtomDB: A Python library for atomic and promolecular properties
” (unpublished).11.
T.
Verstraelen
, P.
Tecmer
, F.
Heidar-Zadeh
, C. E.
González-Espinoza
, M.
Chan
, T. D.
Kim
, K.
Boguslawski
, S.
Fias
, S.
Vandenbrande
, D.
Berrocal
, and P. W.
Ayers
, HORTON 2.1.1
, http://theochem.github.io/horton/2.1.1/, 2017
.12.
M.
Chan
, T.
Verstraelen
, A.
Tehrani
, M.
Richer
, X. D.
Yang
, T. D.
Kim
, E.
Vöhringer-Martinez
, F.
Heidar-Zadeh
, and P. W.
Ayers
, “The tale of HORTON: Lessons learned in a decade of scientific software development
,” J. Chem. Phys.
160
, 162501
(2024
).13.
F.
Heidar-Zadeh
, M.
Richer
, S.
Fias
, R. A.
Miranda-Quintana
, M.
Chan
, M.
Franco-Perez
, C. E.
Gonzalez-Espinoza
, T. D.
Kim
, C.
Lanssens
, A. H. G.
Patel
, X. D.
Yang
, E.
Vohringer-Martinez
, C.
Cardenas
, T.
Verstraelen
, and P. W.
Ayers
, “An explicit approach to conceptual density functional theory descriptors of arbitrary order
,” Chem. Phys. Lett.
660
, 307
–312
(2016
).14.
L.
Pujal
, A.
Tehrani
, and F.
Heidar-Zadeh
, “ChemTools: Gain chemical insight form quantum chemistry calculations
,” in Conceptual Density Functional Theory: Towards a New Chemical Reactivity Theory
, 1st ed., edited by S.
Liu
(Wiley
, 2022
).15.
T.
Verstraelen
, W.
Adams
, L.
Pujal
, A.
Tehrani
, B. D.
Kelly
, L.
Macaya
, F.
Meng
, M.
Richer
, R.
Hernández-Esparza
, X. D.
Yang
et al, “IOData: A python library for reading, writing, and converting computational chemistry file formats and generating input files
,” J. Comput. Chem.
42
, 458
–464
(2021
).16.
T. D.
Kim
, L.
Pujal
, M.
Richer
, M.
van Zyl
, M.
Martínez-González
, A.
Tehrani
, V.
Chuiko
, G.
Sánchez-Díaz
, W.
Sanchez
, W.
Adams
et al, “GBasis: A Python library for evaluating functions, functionals, and integrals expressed with Gaussian basis functions
,” J. Chem. Phys.
161
, 042503
(2024
).17.
A.
Tehrani
, M.
Richer
, and F.
Heidar-Zadeh
, “CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems
,” J. Chem. Phys.
161
, 072501
(2024
).18.
A.
Tehrani
, X. D.
Yang
, M.
Martínez-González
, L.
Pujal
, R.
Hernández-Esparza
, M.
Chan
, E.
Vöhringer-Martinez
, T.
Verstraelen
, P. W.
Ayers
, and F.
Heidar-Zadeh
, “Grid: A Python library for molecular integration, interpolation, differentiation, and more
,” J. Chem. Phys.
160
, 172503
(2024
).19.
W.
Jakob
, J.
Rhinelander
, and D.
Moldovan
, pybind11—Seamless Operability between C++11 and Python
, http://github.com/pybind/pybind11/, 2017
.20.
C. R.
Harris
, K. J.
Millman
, S. J.
Van Der Walt
, R.
Gommers
, P.
Virtanen
, D.
Cournapeau
, E.
Wieser
, J.
Taylor
, S.
Berg
, N. J.
Smith
et al, “Array programming with NumPy
,” Nature
585
, 357
–362
(2020
).21.
P. J.
Knowles
and N. C.
Handy
, “A determinant based full configuration interaction program
,” Comput. Phys. Commun.
54
, 75
–83
(1989
).22.
H.-J.
Werner
, P. J.
Knowles
, F. R.
Manby
, J. A.
Black
, K.
Doll
, A.
Heßelmann
, D.
Kats
, A.
Köhn
, T.
Korona
, D. A.
Kreplin
et al, “The Molpro quantum chemistry package
,” J. Chem. Phys.
152
, 144107
(2020
).23.
P. S.
Epstein
, “The Stark effect from the point of view of Schroedinger’s quantum theory
,” Phys. Rev.
28
, 695
–710
(1926
).24.
R. K.
Nesbet
, “Configuration interaction in orbital theories
,” Proc. R. Soc. A
230
, 312
–321
(1997
).25.
T. H.
Cormen
, C. E.
Leiserson
, R. L.
Rivest
, and C.
Stein
, Introduction to Algorithms
(MIT Press
, 2022
).26.
J.
Olsen
, B. O.
Roos
, P.
Jørgensen
, and H. J. A.
Jensen
, “Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces
,” J. Chem. Phys.
89
, 2185
–2192
(1988
).27.
A. G.
Konheim
, Hashing in Computer Science: Fifty Years of Slicing and Dicing
(John Wiley & Sons
, 2010
).28.
29.
B.
Jenkins
, SpookyHash: a 128-bit noncryptographic hash
, http://burtleburtle.net/bob/hash/spooky.html, 2012
.30.
K.
Suzuki
, D.
Tonien
, K.
Kurosawa
, and K.
Toyota
, “Birthday paradox for multi-collisions
,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
E91-A
, 39
–45
(2008
).31.
F.
Kossoski
, Y.
Damour
, and P.-F.
Loos
, “Hierarchy configuration interaction: Combining seniority number and excitation degree
,” J. Phys. Chem. Lett.
13
, 4342
–4349
(2022
).32.
F.
Kossoski
and P.-F.
Loos
, “Seniority and hierarchy configuration interaction for radicals and excited states
,” J. Chem. Theory Comput.
19
, 8654
–8670
(2023
).33.
D. R.
Alcoba
, A.
Torre
, L.
Lain
, O. B.
Oña
, P.
Capuzzi
, M.
Van Raemdonck
, P.
Bultinck
, and D.
Van Neck
, “A hybrid configuration interaction treatment based on seniority number and excitation schemes
,” J. Chem. Phys.
141
, 244118
(2014
).34.
M.
Van Raemdonck
, D. R.
Alcoba
, W.
Poelmans
, S.
De Baerdemacker
, A.
Torre
, L.
Lain
, G. E.
Massaccesi
, D.
Van Neck
, and P.
Bultinck
, “Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions
,” J. Chem. Phys.
143
, 104106
(2015
).35.
D.
Calvetti
, L.
Reichel
, and D. C.
Sorensen
, “An implicitly restarted lanczos method for large symmetric eigenvalue problems
,” Electron. Trans. Numer. Anal.
2
, 21
(1994
), http://etna.math.kent.edu/volumes/1993-2000/vol2/abstract.php?vol=2&pages=1-21.36.
Y.
Qiu
, Spectra 1.0.1: A header-only C++ library for large scale eigenvalue problems
, https://github.com/yixuan/spectra, 2022
.37.
P. J.
Knowles
and N. C.
Handy
, “A new determinant-based full configuration interaction method
,” Chem. Phys. Lett.
111
, 315
–321
(1984
).38.
H.-J.
Werner
and P. J.
Knowles
, “An efficient internally contracted multiconfiguration–reference configuration interaction method
,” J. Chem. Phys.
89
, 5803
–5814
(1988
).39.
J. S.
Anderson
, F.
Heidar-Zadeh
, and P. W.
Ayers
, “Breaking the curse of dimension for the electronic Schrödinger equation with functional analysis
,” Comput. Theor. Chem.
1142
, 66
–77
(2018
).40.
P. A.
Johnson
, P. W.
Ayers
, P. A.
Limacher
, S. D.
Baerdemacker
, D. V.
Neck
, and P.
Bultinck
, “A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals
,” Comput. Theor. Chem.
1003
, 101
–113
(2013
).41.
P. A.
Limacher
, P. W.
Ayers
, P. A.
Johnson
, S.
De Baerdemacker
, D.
Van Neck
, and P.
Bultinck
, “A new mean-field method suitable for strongly correlated electrons: Computationally facile antisymmetric products of nonorthogonal geminals
,” J. Chem. Theory Comput.
9
, 1394
–1401
(2013
).42.
P. A.
Johnson
, P. A.
Limacher
, T. D.
Kim
, M.
Richer
, R. A.
Miranda-Quintana
, F.
Heidar-Zadeh
, P. W.
Ayers
, P.
Bultinck
, S.
De Baerdemacker
, and D.
Van Neck
, “Strategies for extending geminal-based wavefunctions: Open shells and beyond
,” Comput. Theor. Chem.
1116
, 207
–219
(2017
).43.
A.
Hurley
, J.
Lennard-Jones
, and J. A.
Pople
, “The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic molecules
,” Proc. R. Soc. A
220
, 446
–455
(1953
).44.
D. M.
Silver
, “Natural orbital expansion of interacting geminals
,” J. Chem. Phys.
50
, 5108
–5116
(1969
).45.
P. R.
Surjan
, “An introduction to the theory of geminals
,” in Correlation and Localization
, Topics in Current Chemistry
, edited by P. R.
Surjan
(1999
), Vol. 203
, pp. 63
–88
.46.
P. R.
Surjan
, A.
Szabados
, P.
Jeszenszki
, and T.
Zoboki
, “Strongly orthogonal geminals: Size-extensive and variational reference states
,” J. Math. Chem.
50
, 534
–551
(2012
).47.
T.
Zoboki
, P.
Jeszenszki
, and P. R.
Surjan
, “Composite particles in quantum chemistry: From two-electron bonds to cold atoms
,” Int. J. Quantum Chem.
113
, 185
–189
(2013
).48.
P.
Tecmer
, K.
Boguslawski
, P. A.
Johnson
, P. A.
Limacher
, M.
Chan
, T.
Verstraelen
, and P. W.
Ayers
, “Assessing the accuracy of new geminal-based approaches
,” J. Phys. Chem. A
118
, 9058
–9068
(2014
).49.
P.
Tecmer
and K.
Boguslawski
, “Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry
,” Phys. Chem. Chem. Phys.
24
, 23026
(2022
).50.
L.
Carrier
, C. E.
Fecteau
, and P. A.
Johnson
, “Bethe ansatz of electrons as a mean-field wavefunction for chemical systems
,” Int. J. Quantum Chem.
120
, e26255
(2020
).51.
P. A.
Johnson
, C.-É.
Fecteau
, F.
Berthiaume
, S.
Cloutier
, L.
Carrier
, M.
Gratton
, P.
Bultinck
, S.
De Baerdemacker
, D.
Van Neck
, P.
Limacher
, and P. W.
Ayers
, “Richardson–Gaudin mean-field for strong correlation in quantum chemistry
,” J. Chem. Phys.
153
, 104110
(2020
).52.
P. A.
Johnson
and A. E. I.
DePrince
, “Single reference treatment of strongly correlated H4 and H10 isomers with Richardson–Gaudin states
,” J. Chem. Theory Comput.
19
, 8129
–8146
(2023
).53.
S. R.
White
, “Density matrix formulation for quantum renormalization groups
,” Phys. Rev. Lett.
69
, 2863
–2866
(1992
).54.
G. K. L.
Chan
, “An algorithm for large scale density matrix renormalization group calculations
,” J. Chem. Phys.
120
, 3172
–3178
(2004
).55.
G. K. L.
Chan
and M.
Head-Gordon
, “Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
,” J. Chem. Phys.
116
, 4462
–4476
(2002
).56.
K. H.
Marti
and M.
Reiher
, “The density matrix renormalization group algorithm in quantum chemistry
,” Z. Phys. Chem.
224
, 583
–599
(2010
).57.
S.
Wouters
, W.
Poelmans
, P. W.
Ayers
, and D.
Van Neck
, “CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
,” Comput. Phys. Commun.
185
, 1501
–1514
(2014
).58.
S.
Wouters
, P. A.
Limacher
, D.
Van Neck
, and P. W.
Ayers
, “Longitudinal static optical properties of hydrogen chains: Finite field extrapolations of matrix product state calculations
,” J. Chem. Phys.
136
, 134110
(2012
).59.
G. K.-L.
Chan
, A.
Keselman
, N.
Nakatani
, Z.
Li
, and S. R.
White
, “Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
,” J. Chem. Phys.
145
, 014102
(2016
).60.
R.
Olivares-Amaya
, W.
Hu
, N.
Nakatani
, S.
Sharma
, J.
Yang
, and G. K.-L.
Chan
, “The ab-initio density matrix renormalization group in practice
,” J. Chem. Phys.
142
, 034102
(2015
).61.
G. K. L.
Chan
and S.
Sharma
, “The density matrix renormalization group in quantum chemistry
,” Annu. Rev. Phys. Chem.
62
, 465
–481
(2011
).62.
G. K. L.
Chan
, J. J.
Dorando
, D.
Ghosh
, J.
Hachmann
, E.
Neuscamman
, H.
Wang
, and T.
Yanai
, “An introduction to the density matrix renormalization group ansatz in quantum chemistry
,” in Frontiers in Quantum Systems in Chemistry and Physics
, Progress in Theoretical Chemistry and Physics
, edited by S.
Wilson
, P. J.
Grout
, J.
Maruani
, G.
DelgadoBarrio
, and P.
Piecuch
(2008
), Vol. 18
, pp. 49
–65
.63.
N.
Nakatani
and G. K. L.
Chan
, “Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
,” J. Chem. Phys.
138
, 134113
(2013
).64.
H. J.
Changlani
, J. M.
Kinder
, C. J.
Umrigar
, and G. K. L.
Chan
, “Approximating strongly correlated wave functions with correlator product states
,” Phys. Rev. B
80
, 245116
(2009
).65.
R. J.
Bartlett
, “The coupled-cluster revolution
,” Mol. Phys.
108
, 2905
–2920
(2010
).66.
R. J.
Bartlett
, “Coupled-cluster theory and its equation-of-motion extensions
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 126
–138
(2012
).67.
R. J.
Bartlett
and M.
Musial
, “Coupled-cluster theory in quantum chemistry
,” Rev. Mod. Phys.
79
, 291
–352
(2007-01/2007-03
).68.
I.
Shavitt
and R. J.
Bartlett
, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory
(Cambridge University Press
, Cambridge
, 2009
).69.
T. M.
Henderson
, I. W.
Bulik
, T.
Stein
, and G. E.
Scuseria
, “Seniority-based coupled cluster theory
,” J. Chem. Phys.
141
, 244104
(2014
).70.
T.
Stein
, T. M.
Henderson
, and G. E.
Scuseria
, “Seniority zero pair coupled cluster doubles theory
,” J. Chem. Phys.
140
, 214113
(2014
).71.
K.
Boguslawski
and P. W.
Ayers
, “Linearized coupled cluster correction on the antisymmetric product of 1-reference orbital geminals
,” J. Chem. Theory Comput.
11
, 5252
–5261
(2015
).72.
I. W.
Bulik
, T. M.
Henderson
, and G. E.
Scuseria
, “Can single-reference coupled cluster theory describe static correlation?
,” J. Chem. Theory Comput.
11
, 3171
–3179
(2015
).73.
T. M.
Henderson
, G. E.
Scuseria
, J.
Dukelsky
, A.
Signoracci
, and T.
Duguet
, “Quasiparticle coupled cluster theory for pairing interactions
,” Phys. Rev. C
89
, 054305
(2014
).74.
A.
Nowak
and K.
Boguslawski
, “A configuration interaction correction on top of pair coupled cluster doubles
,” Phys. Chem. Chem. Phys.
25
, 7289
–7301
(2023
).75.
P. B.
Gaikwad
, T. D.
Kim
, M.
Richer
, R. A.
Lokhande
, G.
Sánchez-Díaz
, P. A.
Limacher
, P. W.
Ayers
, and R. A.
Miranda-Quintana
, “Coupled cluster-inspired geminal wavefunctions
,” J. Chem. Phys.
160
, 144108
(2024
).76.
T. D.
Kim
, M.
Richer
, G.
Sánchez-Díaz
, R. A.
Miranda-Quintana
, T.
Verstraelen
, F.
Heidar-Zadeh
, and P. W.
Ayers
, “Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry
,” J. Comput. Chem.
44
, 697
–709
(2023
).77.
P. A.
Johnson
, P. W.
Ayers
, S.
De Baerdemacker
, P. A.
Limacher
, and D.
Van Neck
, “Bivariational principle for an antisymmetrized product of nonorthogonal geminals appropriate for strong electron correlation
,” Comput. Theor. Chem.
1212
, 113718
(2022
).78.
P. A.
Limacher
, T. D.
Kim
, P. W.
Ayers
, P. A.
Johnson
, S.
De Baerdemacker
, D.
Van Neck
, and P.
Bultinck
, “The influence of orbital rotation on the energy of closed-shell wavefunctions
,” Mol. Phys.
112
, 853
–862
(2014
).79.
K.
Boguslawski
, P.
Tecmer
, P. A.
Limacher
, P. A.
Johnson
, P. W.
Ayers
, P.
Bultinck
, S.
De Baerdemacker
, and D.
Van Neck
, “Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal
,” J. Chem. Phys.
140
, 214114
(2014
).80.
K.
Boguslawski
, P.
Tecmer
, P. W.
Ayers
, P.
Bultinck
, S.
De Baerdemacker
, and D.
Van Neck
, “Efficient description of strongly correlated electrons with mean-field cost
,” Phys. Rev. B
89
, 201106
(2014
).81.
K.
Boguslawski
, P.
Tecmer
, P.
Bultinck
, S.
De Baerdemacker
, D.
Van Neck
, and P. W.
Ayers
, “Nonvariational orbital optimization techniques for the AP1roG wave function
,” J. Chem. Theory Comput.
10
, 4873
–4882
(2014
).82.
H.
Koch
, H. J. A.
Jensen
, P.
Jørgensen
, T.
Helgaker
, G. E.
Scuseria
, and H. F.
Schaefer
, “Coupled cluster energy derivatives. Analytic Hessian for the closed-shell coupled cluster singles and doubles wave-function: Theory and applications
,” J. Chem. Phys.
92
, 4924
–4940
(1990
).83.
C.
Lanssens
, P. W.
Ayers
, D.
Van Neck
, S.
De Baerdemacker
, K.
Gunst
, and P.
Bultinck
, “Method for making 2-electron response reduced density matrices approximately N-representable
,” J. Chem. Phys.
148
, 084104
(2018
).84.
L.
Lemmens
, X.
De Vriendt
, D.
Van Hende
, T.
Huysentruyt
, P.
Bultinck
, and G.
Acke
, “GQCP: The Ghent quantum chemistry package
,” J. Chem. Phys.
155
, 084802
(2021
).85.
D. G. A.
Smith
, L. A.
Burns
, A. C.
Simmonett
, R. M.
Parrish
, M. C.
Schieber
, R.
Galvelis
, P.
Kraus
, H.
Kruse
, R.
Di Remigio
, A.
Alenaizan
, A. M.
James
, S.
Lehtola
, J. P.
Misiewicz
, M.
Scheurer
, R. A.
Shaw
, J. B.
Schriber
, Y.
Xie
, Z. L.
Glick
, D. A.
Sirianni
, J. S.
O’Brien
, J. M.
Waldrop
, A.
Kumar
, E. G.
Hohenstein
, B. P.
Pritchard
, B. R.
Brooks
, H. F.
Schaefer
III, A. Y.
Sokolov
, K.
Patkowski
, A. E.
DePrince
III, U.
Bozkaya
, R. A.
King
, F. A.
Evangelista
, J. M.
Turney
, T. D.
Crawford
, and C. D.
Sherrill
, “PSI4 1.4: Open-source software for high-throughput quantum chemistry
,” J. Chem. Phys.
152
, 184108
(2020
).86.
R. A.
Miranda-Quintana
, T. D.
Kim
, R. A.
Lokhande
, M.
Richer
, G.
Sánchez-Díaz
, P. B.
Gaikwad
, and P. W.
Ayers
, “Flexible ansatz for N-body perturbation theory
,” J. Phys. Chem. A
128
, 3458
(2024
).87.
I.
Shavitt
, “Graph theoretical concepts for the unitary group approach to the many-electron correlation problem
,” Int. J. Quantum Chem.
12
, 131
–148
(1977
).88.
P.
Virtanen
, R.
Gommers
, T. E.
Oliphant
, M.
Haberland
, T.
Reddy
, D.
Cournapeau
, E.
Burovski
, P.
Peterson
, W.
Weckesser
, J.
Bright
, S. J.
van der Walt
, M.
Brett
, J.
Wilson
, K. J.
Millman
, N.
Mayorov
, A. R. J.
Nelson
, E.
Jones
, R.
Kern
, E.
Larson
, C. J.
Carey
, İ.
Polat
, Y.
Feng
, E. W.
Moore
, J.
VanderPlas
, D.
Laxalde
, J.
Perktold
, R.
Cimrman
, I.
Henriksen
, E. A.
Quintero
, C. R.
Harris
, A. M.
Archibald
, A. H.
Ribeiro
, F.
Pedregosa
, P.
van Mulbregt
, A.
Vijaykumar
et al, “SciPy 1.0: Fundamental algorithms for scientific computing in Python
,” Nat. Methods
17
, 261
–272
(2020
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
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