CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis’s enhanced performance, guiding developers of GPU-accelerated code.

1.
F.
De Proft
,
P.
Geerlings
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
, “
Conceptual density functional theory
,” in
Comprehensive Computational Chemistry
, 1st ed. (
Elsevier
,
2024
), pp.
306
321
.
2.
P. L.
Ayers
,
R. J.
Boyd
,
P.
Bultinck
,
M.
Caffarel
,
R.
Carbó-Dorca
,
M.
Causá
,
J.
Cioslowski
,
J.
Contreras-Garcia
,
D. L.
Cooper
,
P.
Coppens
,
C.
Gatti
,
S.
Grabowsky
,
P.
Lazzeretti
,
P.
Macchi
,
Á.
Martín Pendás
,
P. L.
Popelier
,
K.
Ruedenberg
,
H.
Rzepa
,
A.
Savin
,
A.
Sax
,
W. E.
Schwarz
,
S.
Shahbazian
,
B.
Silvi
,
M.
Solà
, and
V.
Tsirelson
, “
Six questions on topology in theoretical chemistry
,”
Comput. Theor. Chem.
1053
,
2
16
(
2015
), special Issue: Understanding structure and reactivity from topology and beyond.
3.
J.
Andrés
,
P. W.
Ayers
,
R. A.
Boto
,
R.
Carbó-Dorca
,
H.
Chermette
,
J.
Cioslowski
,
J.
Contreras-García
,
D. L.
Cooper
,
G.
Frenking
,
C.
Gatti
,
F.
Heidar-Zadeh
,
L.
Joubert
,
A.
Martín Pendás
,
E.
Matito
,
I.
Mayer
,
A.
Misquitta
,
Y.
Mo
,
J.
Pilmé
,
P. L. A.
Popelier
,
M.
Rahm
,
E.
Ramos-Cordoba
,
P.
Salvador
,
W. H. E.
Schwarz
,
S.
Shahbazian
,
B.
Silvi
,
M.
Solà
,
K.
Szalewicz
,
V.
Tognetti
,
F.
Weinhold
, and
E.-L.
Zins
, “
Nine questions on energy decomposition analysis
,”
J. Comput. Chem.
40
,
2248
2283
(
2019
).
4.
P.
Geerlings
,
E.
Chamorro
,
P. K.
Chattaraj
,
F.
De Proft
,
J. L.
Gázquez
,
S.
Liu
,
C.
Morell
,
A.
Toro-Labbé
,
A.
Vela
, and
P.
Ayers
, “
Conceptual density functional theory: Status, prospects, issues
,”
Theor. Chem. Acc.
139
,
36
(
2020
).
5.
Á. M.
Pendás
and
J.
Contreras-García
,
Topological Approaches to the Chemical Bond
(
Springer Nature
,
2023
).
6.
M.
Gallegos
,
E.
Francisco
, and
A. M.
Pendás
, “
Chapter 4—New developments in the interacting quantum atoms (IQA) approach
,” in
Chemical Reactivity
, edited by
S.
Kaya
,
L.
von Szentpály
,
G.
Serdaro
, and
L.
Guo
(
Elsevier
,
2023
), pp.
83
112
.
7.
A.
Martín Pendás
,
E.
Francisco
,
D.
Suárez
,
A.
Costales
,
N.
Díaz
,
J.
Munárriz
,
T.
Rocha-Rinza
, and
J. M.
Guevara-Vela
, “
Atoms in molecules in real space: A fertile field for chemical bonding
,”
Phys. Chem. Chem. Phys.
25
,
10231
10262
(
2023
).
8.
S.
Liu
,
Conceptual Density Functional Theory: Towards a New Chemical Reactivity Theory
(
John Wiley & Sons
,
2022
).
9.
I.
Casademont-Reig
,
E.
Ramos-Cordoba
,
M.
Torrent-Sucarrat
, and
E.
Matito
, “
7—Aromaticity descriptors based on electron delocalization
,” in
Aromaticity
, edited by
I.
Fernandez
(
Elsevier
,
2021
), pp.
235
259
.
10.
D. M.
Andrada
and
C.
Foroutan-Nejad
, “
Energy components in energy decomposition analysis (EDA) are path functions; why does it matter?
,”
Phys. Chem. Chem. Phys.
22
,
22459
22464
(
2020
).
11.
K.
Carter-Fenk
,
M.
Liu
,
L.
Pujal
,
M.
Loipersberger
,
M.
Tsanai
,
R. M.
Vernon
,
J. D.
Forman-Kay
,
M.
Head-Gordon
,
F.
Heidar-Zadeh
, and
T.
Head-Gordon
, “
The energetic origins of pi–pi contacts in proteins
,”
J. Am. Chem. Soc.
145
,
24836
24851
(
2023
).
12.
F.
Heidar-Zadeh
,
P. W.
Ayers
,
T.
Verstraelen
,
I.
Vinogradov
,
E.
Vöhringer-Martinez
, and
P.
Bultinck
, “
Information-theoretic approaches to atoms-in-molecules: Hirshfeld family of partitioning schemes
,”
J. Phys. Chem. A
122
,
4219
4245
(
2018
).
13.
S.
Fias
,
F.
Heidar-Zadeh
,
P.
Geerlings
, and
P. W.
Ayers
, “
Chemical transferability of functional groups follows from the nearsightedness of electronic matter
,”
Proc. Natl. Acad. Sci. U. S. A.
114
,
11633
11638
(
2017
).
14.
M.
Gimferrer
,
A.
Aldossary
,
P.
Salvador
, and
M.
Head-Gordon
, “
Oxidation state localized orbitals: A method for assigning oxidation states using optimally fragment-localized orbitals and a fragment orbital localization index
,”
J. Chem. Theory Comput.
18
,
309
322
(
2022
).
15.
F.
Heidar-Zadeh
,
R. A.
Miranda-Quintana
,
T.
Verstraelen
,
P.
Bultinck
, and
P. W.
Ayers
, “
When is the Fukui function not normalized? The danger of inconsistent energy interpolation models in density functional theory
,”
J. Chem. Theory Comput.
12
,
5777
5787
(
2016
).
16.
R. A.
Miranda-Quintana
and
P. W.
Ayers
, “
Fractional electron number, temperature, and perturbations in chemical reactions
,”
Phys. Chem. Chem. Phys.
18
,
15070
15080
(
2016
).
17.
R. A.
Miranda-Quintana
,
F.
Heidar-Zadeh
,
S.
Fias
,
A. E. A.
Chapman
,
S.
Liu
,
C.
Morell
,
T.
Gómez
,
C.
Cárdenas
, and
P. W.
Ayers
, “
Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles
,”
Front. Chem.
10
,
929464
(
2022
).
18.
R. A.
Miranda-Quintana
,
F.
Heidar-Zadeh
,
S.
Fias
,
A. E. A.
Chapman
,
S.
Liu
,
C.
Morell
,
T.
Gómez
,
C.
Cárdenas
, and
P. W.
Ayers
, “
Molecular interactions from the density functional theory for chemical reactivity: The interaction energy between two-reagents
,”
Front. Chem.
10
,
906674
(
2022
).
19.
G.
Hoffmann
,
F.
Guégan
,
V.
Labet
,
L.
Joubert
,
H.
Chermette
,
C.
Morell
, and
V.
Tognetti
, “
Expanding horizons in conceptual density functional theory: Novel ensembles and descriptors to decipher reactivity patterns
,”
J. Comput. Chem.
45
,
1716
(
2024
).
20.
P. W.
Ayers
,
C.
Morell
,
F.
De Proft
, and
P.
Geerlings
, “
Understanding the woodward–hoffmann rules by using changes in electron density
,”
Chem.—Eur. J.
13
,
8240
8247
(
2007
).
21.
J. L.
Gázquez
,
A.
Cedillo
, and
A.
Vela
, “
Electrodonating and electroaccepting powers
,”
J. Phys. Chem. A
111
,
1966
1970
(
2007
).
22.
J. L.
Gázquez
,
M.
Franco-Pérez
,
P. W.
Ayers
, and
A.
Vela
, “
Conceptual density functional theory in the grand canonical ensemble
,” in
Chemical Reactivity in Confined Systems
(
Wiley Online Library
,
2021
), pp.
191
211
.
23.
T.
Verstraelen
,
S.
Vandenbrande
,
F.
Heidar-Zadeh
,
L.
Vanduyfhuys
,
V.
Van Speybroeck
,
M.
Waroquier
, and
P. W.
Ayers
, “
Minimal basis iterative stockholder: Atoms in molecules for force-field development
,”
J. Chem. Theory Comput.
12
,
3894
3912
(
2016
).
24.
M.
Franco-Pérez
,
F.
Heidar-Zadeh
,
P. W.
Ayers
,
J. L.
Gázquez
, and
A.
Vela
, “
Going beyond the three-state ensemble model: The electronic chemical potential and Fukui function for the general case
,”
Phys. Chem. Chem. Phys.
19
,
11588
11602
(
2017
).
25.
F.
Heidar-Zadeh
and
P. W.
Ayers
, “
How pervasive is the Hirshfeld partitioning?
,”
J. Chem. Phys.
142
,
044107
(
2015
).
26.
F.
Heidar Zadeh
,
P.
Fuentealba
,
C.
Cárdenas
, and
P. W.
Ayers
, “
An information-theoretic resolution of the ambiguity in the local hardness
,”
Phys. Chem. Chem. Phys.
16
,
6019
6026
(
2014
).
27.
F.
Heidarzadeh
and
S.
Shahbazian
, “
The quantum divided basins: A new class of quantum subsystems
,”
Int. J. Quantum Chem.
111
,
2788
2801
(
2011
).
28.
R. A.
Miranda-Quintana
,
M.
Franco-Pérez
,
J. L.
Gázquez
,
P. W.
Ayers
, and
A.
Vela
, “
Chemical hardness: Temperature dependent definitions and reactivity principles
,”
J. Chem. Phys.
149
,
124110
(
2018
).
29.
A.
Vela
,
J. L.
Gázquez
, and
U.
Orozco-Valencia
, “
Charge transfer models in conceptual DFT
,” in
Conceptual Density Functional Theory: Towards a New Chemical Reactivity Theory
(
Wiley-VCH GmbH
,
2022
), pp.
209
228
.
30.
S.
Shahbazian
, “
Why bond critical points are not “bond” critical points
,”
Chem.—Eur. J.
24
,
5401
5405
(
2018
).
31.
E.
Matito
,
M.
Duran
, and
M.
Solà
, “
The aromatic fluctuation index (FLU): A new aromaticity index based on electron delocalization
,”
J. Chem. Phys.
122
,
014109
(
2004
).
32.
X.
He
,
M.
Li
,
C.
Rong
,
D.
Zhao
,
W.
Liu
,
P. W.
Ayers
, and
S.
Liu
, “
Some recent advances in density-based reactivity theory
,”
J. Phys. Chem. A
128
,
1183
1196
(
2024
).
33.
X.
He
,
T.
Lu
,
C.
Rong
,
S.
Liu
,
P. W.
Ayers
, and
W.
Liu
, “
Topological analysis of information-theoretic quantities in density functional theory
,”
J. Chem. Phys.
159
,
054112
(
2023
).
34.
C.
Rong
,
B.
Wang
,
D.
Zhao
, and
S.
Liu
, “
Information-theoretic approach in density functional theory and its recent applications to chemical problems
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
10
,
e1461
(
2020
).
35.
X.
An
,
W.
Zhang
,
X.
He
,
M.
Li
,
C.
Rong
, and
S.
Liu
, “
Density-based reactivity theory applied to excited states
,”
AAPPS Bull.
34
,
8
(
2024
).
36.
J.
Contreras-García
,
E. R.
Johnson
,
S.
Keinan
,
R.
Chaudret
,
J.-P.
Piquemal
,
D. N.
Beratan
, and
W.
Yang
, “
Nciplot: A program for plotting noncovalent interaction regions
,”
J. Chem. Theory Comput.
7
,
625
632
(
2011
).
37.
P. W.
Ayers
,
S.
Fias
, and
F.
Heidar-Zadeh
, “
The axiomatic approach to chemical concepts
,”
Comput. Theor. Chem.
1142
,
83
87
(
2018
).
38.
A.
Robles
,
M.
Franco-Pérez
,
J. L.
Gázquez
,
C.
Cárdenas
, and
P.
Fuentealba
, “
Local electrophilicity
,”
J. Mol. Modell.
24
,
245
(
2018
).
39.
R.
Pino-Rios
,
O.
Yañez
,
D.
Inostroza
,
L.
Ruiz
,
C.
Cardenas
,
P.
Fuentealba
, and
W.
Tiznado
, “
Proposal of a simple and effective local reactivity descriptor through a topological analysis of an orbital-weighted Fukui function
,”
J. Comput. Chem.
38
,
481
488
(
2017
).
40.
C.
Cárdenas
,
P. W.
Ayers
, and
A.
Cedillo
, “
Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory
,”
J. Chem. Phys.
134
,
174103
(
2011
).
41.
C.
Cárdenas
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
, “
Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series
,”
Phys. Chem. Chem. Phys.
18
,
25721
25734
(
2016
).
42.
F.
Heidar-Zadeh
,
S.
Fias
,
E.
Vöhringer-Martinez
,
T.
Verstraelen
, and
P. W.
Ayers
, “
The local response of global descriptors
,”
Theor. Chem. Acc.
136
,
19
(
2017
).
43.
F.
Heidar-Zadeh
,
I.
Vinogradov
, and
P. W.
Ayers
, “
Hirshfeld partitioning from non-extensive entropies
,”
Theor. Chem. Acc.
136
,
54
(
2017
).
44.
S.
Fias
,
F.
Heidar-Zadeh
,
J. S. M.
Anderson
,
P. W.
Ayers
, and
R. G.
Parr
, “
A reference-free stockholder partitioning method based on the force on electrons
,”
J. Comput. Chem.
39
,
1044
1050
(
2018
).
45.
B.
Wang
,
P.
Geerlings
,
C.
Van Alsenoy
,
F.
Heider-Zadeh
,
P. W.
Ayers
, and
F.
De Proft
, “
Investigating the linear response function under approximations following the coupled-perturbed approach for atoms and molecules
,”
J. Chem. Theory Comput.
19
,
3223
3236
(
2023
).
46.
M.
Richer
,
F.
Heidar-Zadeh
,
M.
Ríos-Gutiérrez
,
X. D.
Yang
, and
P. W.
Ayers
, Spin-polarized conceptual density functional theory from the convex hull (
2024
).
47.
G.
Hermann
,
V.
Pohl
,
J. C.
Tremblay
,
B.
Paulus
,
H.-C.
Hege
, and
A.
Schild
, Orbkit: A modular python toolbox for cross-platform postprocessing of quantum chemical wavefunction data (
2016
).
48.
T.
Lu
and
F.
Chen
, “
Multiwfn: A multifunctional wavefunction analyzer
,”
J. Comput. Chem.
33
,
580
592
(
2012
).
49.
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
).
50.
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
).
51.
L. F.
Pacios
and
A.
Fernandez
, “
Checkden, a program to compute quantum molecular properties on spatial grids
,”
J. Mol. Graphics Modell.
28
,
102
112
(
2009
).
52.
L. F.
Pacios
, “
Checkden: A computer program to generate 1D, 2D and 3D grids of functions dependent on the molecular ab initio electron density
,”
Comput. Biol. Chem.
27
,
197
209
(
2003
).
53.
R.
Laplaza
,
F.
Peccati
,
R. A.
Boto
,
C.
Quan
,
A.
Carbone
,
J.-P.
Piquemal
,
Y.
Maday
, and
J.
Contreras-García
, “
Nciplot and the analysis of noncovalent interactions using the reduced density gradient
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
11
,
e1497
(
2021
).
54.
A. O.
de-la Roza
,
M.
Blanco
,
A. M.
Pendás
, and
V. L.
na
, “
Critic: A new program for the topological analysis of solid-state electron densities
,”
Comput. Phys. Commun.
180
,
157
166
(
2009
).
55.
A. O.
de-la Roza
,
E. R.
Johnson
, and
V. L.
na
, “
Critic2: A program for real-space analysis of quantum chemical interactions in solids
,”
Comput. Phys. Commun.
185
,
1007
1018
(
2014
).
56.
E. D.
Glendening
,
C. R.
Landis
, and
F.
Weinhold
, “
Nbo 7.0: New vistas in localized and delocalized chemical bonding theory
,”
J. Comput. Chem.
40
,
2234
2241
(
2019
).
57.
T. A.
Keith
,
Aimall (version 19.10.12)
,
TK Gristmill Software
,
Overland Park, KS
,
2019
, p.
23
.
58.
R.
Hernández-Esparza
,
S.-M.
Mejía-Chica
,
A. D.
Zapata-Escobar
,
A.
Guevara-García
,
A.
Martínez-Melchor
,
J.-M.
Hernández-Pérez
,
R.
Vargas
, and
J.
Garza
, “
Grid-based algorithm to search critical points, in the electron density, accelerated by graphics processing units
,”
J. Comput. Chem.
35
,
2272
2278
(
2014
).
59.
R.
Hernández-Esparza
,
Á.
Vázquez-Mayagoitia
,
L.-A.
Soriano-Agueda
,
R.
Vargas
, and
J.
Garza
, “
Gpus as boosters to analyze scalar and vector fields in quantum chemistry
,”
Int. J. Quantum Chem.
119
,
e25671
(
2019
).
60.
J. C.
Cruz
,
R.
Hernández-Esparza
,
Á.
Vázquez-Mayagoitia
,
R.
Vargas
, and
J.
Garza
, “
Implementation of the molecular electrostatic potential over graphics processing units
,”
J. Chem. Inf. Model.
59
,
3120
3127
(
2019
).
61.
M.
Haghighatlari
,
J.
Li
,
F.
Heidar-Zadeh
,
Y.
Liu
,
X.
Guan
, and
T.
Head-Gordon
, “
Learning to make chemical predictions: The interplay of feature representation, data, and machine learning methods
,”
Chem
6
,
1527
1542
(
2020
).
62.
NVIDIA,
P.
Vingelmann
and
F. H.
Fitzek
, Cuda, release: 10.2.89 (
2020
).
63.
M.
Valiev
,
E. J.
Bylaska
,
N.
Govind
,
K.
Kowalski
,
T. P.
Straatsma
,
H. J. J.
Van Dam
,
D.
Wang
,
J.
Nieplocha
,
E.
Aprà
,
T. L.
Windus
, and
W.
de Jong
, “
Nwchem: A comprehensive and scalable open-source solution for large scale molecular simulations
,”
Comput. Phys. Commun.
181
,
1477
1489
(
2010
).
64.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
G. A.
Petersson
,
H.
Nakatsuji
,
X.
Li
,
M.
Caricato
,
A. V.
Marenich
,
J.
Bloino
,
B. G.
Janesko
,
R.
Gomperts
,
B.
Mennucci
,
H. P.
Hratchian
,
J. V.
Ortiz
,
A. F.
Izmaylov
,
J. L.
Sonnenberg
,
D.
Williams-Young
,
F.
Ding
,
F.
Lipparini
,
F.
Egidi
,
J.
Goings
,
B.
Peng
,
A.
Petrone
,
T.
Henderson
,
D.
Ranasinghe
,
V. G.
Zakrzewski
,
J.
Gao
,
N.
Rega
,
G.
Zheng
,
W.
Liang
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
K.
Throssell
,
J. A.
Montgomery
, Jr.
,
J. E.
Peralta
,
F.
Ogliaro
,
M. J.
Bearpark
,
J. J.
Heyd
,
E. N.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
T. A.
Keith
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A. P.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
J. M.
Millam
,
M.
Klene
,
C.
Adamo
,
R.
Cammi
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
O.
Farkas
,
J. B.
Foresman
, and
D. J.
Fox
,
GAUSSIAN 16, Revision C.01
,
Gaussian, Inc.
,
Wallingford, CT
,
2016
.
65.
I. S.
Ufimtsev
and
T. J.
Martinez
, “
Quantum chemistry on graphical processing units. 1. strategies for two-electron integral evaluation
,”
J. Chem. Theory Comput.
4
,
222
231
(
2008
).
66.
A.
Asadchev
and
M. S.
Gordon
, “
New multithreaded hybrid CPU/GPU approach to Hartree–Fock
,”
J. Chem. Theory Comput.
8
,
4166
4176
(
2012
).
67.
M.
Rodriguez-Bautista
,
C.
Díaz-García
,
A. M.
Navarrete-López
,
R.
Vargas
, and
J.
Garza
, “
Roothaan’s approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior
,”
J. Chem. Phys.
143
,
034103
(
2015
).
68.
M.-A.
Martínez-Sánchez
,
M.
Rodriguez-Bautista
,
R.
Vargas
, and
J.
Garza
, “
Solution of the Kohn–Sham equations for many-electron atoms confined by penetrable walls
,”
Theor. Chem. Acc.
135
,
207
(
2016
).
69.
L.
Vogt
,
R.
Olivares-Amaya
,
S.
Kermes
,
Y.
Shao
,
C.
Amador-Bedolla
, and
A.
Aspuru-Guzik
, “
Accelerating resolution-of-the-identity second-order Møller−Plesset quantum chemistry calculations with graphical processing units
,”
J. Phys. Chem. A
112
,
2049
2057
(
2008
).
70.
W.
Ma
,
S.
Krishnamoorthy
,
O.
Villa
, and
K.
Kowalski
, “
GPU-based implementations of the noniterative regularized-CCSD(T) corrections: Applications to strongly correlated systems
,”
J. Chem. Theory Comput.
7
,
1316
1327
(
2011
).
71.
A. E.
DePrince
III
and
J. R.
Hammond
, “
Coupled cluster theory on graphics processing units i. the coupled cluster doubles method
,”
J. Chem. Theory Comput.
7
,
1287
1295
(
2011
).
72.
A.
Asadchev
and
M. S.
Gordon
, “
Fast and flexible coupled cluster implementation
,”
J. Chem. Theory Comput.
9
,
3385
3392
(
2013
).
73.
A. E.
DePrince
III
,
M. R.
Kennedy
,
B. G.
Sumpter
, and
C. D.
Sherrill
, “
Density-fitted singles and doubles coupled cluster on graphics processing units
,”
Mol. Phys.
112
,
844
852
(
2014
).
74.
J. J.
Eriksen
, “
Efficient and portable acceleration of quantum chemical many-body methods in mixed floating point precision using openacc compiler directives
,”
Mol. Phys.
115
,
2086
2101
(
2017
).
75.
I. A.
Kaliman
and
A. I.
Krylov
, New algorithm for tensor contractions on multi-core CPUs, GPUs, and accelerators enables ccsd and eom-ccsd calculations with over 1000 basis functions on a single compute node (
2017
).
76.
R.
Quintero-Monsebaiz
,
A.
Meneses-Viveros
,
F.
Carranza
,
C. G.
Cortés
,
A.
González-Zamudio
, and
A.
Vela
, “
Multidimensional adaptative and deterministic integration in CUDA and OpenMP
,”
J. Supercomput.
77
,
12075
12097
(
2021
).
77.
X.
Wu
,
Q.
Sun
,
Z.
Pu
,
T.
Zheng
,
W.
Ma
,
W.
Yan
,
X.
Yu
,
Z.
Wu
,
M.
Huo
,
X.
Li
et al, “
Python-based quantum chemistry calculations with GPU acceleration
,” arXiv:2404.09452 (
2024
).
78.
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
).
79.
G.
Guennebaud
,
B.
Jacob
et al, Eigen v3 (
2010
), http://eigen.tuxfamily.org.
80.
W.
Jakob
,
J.
Rhinelander
, and
D.
Moldovan
, pybind11 – seamless operability between c++11 and python (
2017
), https://github.com/pybind/pybind11.
81.
P.
Politzer
and
J. S.
Murray
, “
The fundamental nature and role of the electrostatic potential in atoms and molecules
,”
Theor. Chem. Acc.
108
,
134
142
(
2002
).
82.
R. F.
Bader
and
A. I.
Molecules
,
A Quantum Theory
(
Clarendon
,
Oxford, UK
,
1990
).
83.
R.
McWeeny
,
Method of Molecular Quantum Mechanics
, 2nd ed. (
Academic Press
,
1989
).
84.
C. v.
Weizsäcker
, “
Zur theorie der kernmassen
,”
Z. Phys.
96
,
431
458
(
1935
).
85.
V. K.
Prasad
,
A.
Otero-de La-Roza
, and
G. A.
DiLabio
, “
Pepconf, a diverse data set of peptide conformational energies
,”
Sci. Data
6
,
180310
(
2019
).
86.
J.-D.
Chai
and
M.
Head-Gordon
, “
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections
,”
Phys. Chem. Chem. Phys.
10
,
6615
6620
(
2008
).
87.
J.-D.
Chai
and
M.
Head-Gordon
, “
Systematic optimization of long-range corrected hybrid density functionals
,”
J. Chem. Phys.
128
,
084106
(
2008
).
88.
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
,
R.
Kern
,
M.
Picus
,
S.
Hoyer
,
M. H.
van Kerkwijk
,
M.
Brett
,
A.
Haldane
,
J. F.
del Río
,
M.
Wiebe
,
P.
Peterson
,
P.
Gérard-Marchant
,
K.
Sheppard
,
T.
Reddy
,
W.
Weckesser
,
H.
Abbasi
,
C.
Gohlke
, and
T. E.
Oliphant
, “
Array programming with NumPy
,”
Nature
585
,
357
362
(
2020
).
89.
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
).
90.
W.
Humphrey
,
A.
Dalke
, and
K.
Schulten
, “
VMD: Visual molecular dynamics
,”
J. Mol. Graphics
14
,
33
38
(
1996
).
91.
Schrödinger, LLC
,
The PyMOL molecular graphics system, version 1.8
(
2015
).
92.
T.
Lewiner
,
H.
Lopes
,
A. W.
Vieira
, and
G.
Tavares
, “
Efficient implementation of marching cubes’ cases with topological guarantees
,”
J. Graphics Tools
8
,
1
15
(
2003
).
93.
S.
van der Walt
,
J. L.
Schönberger
,
J.
Nunez-Iglesias
,
F.
Boulogne
,
J. D.
Warner
,
N.
Yager
,
E.
Gouillart
,
T.
Yu
, and
the scikit-image contributors
, “
scikit-image: image processing in Python
,”
PeerJ
2
,
e453
(
2014
).
94.
A. D.
Becke
and
K. E.
Edgecombe
, “
A simple measure of electron localization in atomic and molecular systems
,”
J. Chem. Phys.
92
,
5397
5403
(
1990
).
95.
B.
Silvi
and
A.
Savin
, “
Classification of chemical bonds based on topological analysis of electron localization functions
,”
Nature
371
,
683
686
(
1994
).
96.
A.
Savin
,
R.
Nesper
,
S.
Wengert
, and
T. F.
Fässler
, “
Elf: The electron localization function
,”
Angew Chem. Int. Ed. Engl.
36
,
1808
1832
(
1997
).
97.
E. R.
Johnson
,
S.
Keinan
,
P.
Mori-Sánchez
,
J.
Contreras-García
,
A. J.
Cohen
, and
W.
Yang
, “
Revealing noncovalent interactions
,”
J. Am. Chem. Soc.
132
,
6498
6506
(
2010
).
98.
W. H.
Press
,
Numerical Recipes: The Art of Scientific Computing
, 3rd ed. (
Cambridge University Press
,
2007
).
99.
E.
Fehlberg
, “
Classical fourth-and lower order Runge-Kutta formulas with stepsize control and their application to heat transfer problems
,”
Computing
6
,
61
71
(
1970
).
100.
A.
Meurer
,
C. P.
Smith
,
M.
Paprocki
,
O.
Čertík
,
S. B.
Kirpichev
,
M.
Rocklin
,
A.
Kumar
,
S.
Ivanov
,
J. K.
Moore
,
S.
Singh
,
T.
Rathnayake
,
S.
Vig
,
B. E.
Granger
,
R. P.
Muller
,
F.
Bonazzi
,
H.
Gupta
,
S.
Vats
,
F.
Johansson
,
F.
Pedregosa
,
M. J.
Curry
,
A. R.
Terrel
,
v.
Roučka
,
A.
Saboo
,
I.
Fernando
,
S.
Kulal
,
R.
Cimrman
, and
A.
Scopatz
, “
Sympy: Symbolic computing in python
,”
PeerJ Comput. Sci.
3
,
e103
(
2017
).
101.
T. D.
Kim
,
L.
Pujal
,
M.
Richer
,
M.
Martinez-Gonzalez
,
M.
van Zyl
,
A.
Tehrani
,
V.
Chuiko
,
G.
Sánchez-Díaz
,
W.
Sanchez
,
W.
Adams
,
X.
Huang
,
B. D.
Kelly
,
E.
Vöhringer-Martinez
,
T.
Verstraelen
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
,
Gbasis: A python Library for Evaluating Functions, Functionals, and Integrals Expressed with Gaussian Basis Functions
(
AIP Publishing
,
2024
).
102.
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
).
103.
L. E.
McMurchie
and
E. R.
Davidson
, “
One- and two-electron integrals over Cartesian Gaussian functions
,”
J. Comput. Phys.
26
,
218
231
(
1978
).
104.
X.
Guan
,
I.
Leven
,
F.
Heidar-Zadeh
, and
T.
Head-Gordon
, “
Protein C-GeM: A coarse-grained electron model for fast and accurate protein electrostatics prediction
,”
J. Chem. Inf. Model.
61
,
4357
4369
(
2021
).
105.
J.
Andzelm
and
E.
Wimmer
, “
Density functional Gaussian-type-orbital approach to molecular geometries, vibrations, and reaction energies
,”
J. Chem. Phys.
96
,
1280
1303
(
1992
).
106.
B. I.
Dunlap
,
N.
Rösch
, and
S.
Trickey
, “
Variational fitting methods for electronic structure calculations
,”
Mol. Phys.
108
,
3167
3180
(
2010
).
107.
B.
Dunlap
, “
Robust and variational fitting: Removing the four-center integrals from center stage in quantum chemistry
,”
J. Mol. Struct.: THEOCHEM
529
,
37
40
(
2000
).
108.
G. A.
Cisneros
,
D.
Elking
,
J.-P.
Piquemal
, and
T. A.
Darden
, “
Numerical fitting of molecular properties to hermite Gaussians
,”
J. Phys. Chem. A
111
,
12049
12056
(
2007
).
109.
V.
García
,
D.
Zorrilla
,
J.
Sánchez-Márquez
, and
M.
Fernández-Núñez
, “
Software to obtain accurate Gaussian expansions for a wide range of radial functions
,”
J. Mol. Modell.
23
,
165
(
2017
).
110.
A.
Tehrani
,
J. S.
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
).
111.
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
).
112.
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
).
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