We implemented a screening algorithm for one-electron-three-center overlap integrals over contracted Gaussian-type orbitals into the Q-Chem program package. The respective bounds were derived using shell-bounding Gaussians and the Obara–Saika recurrence relations. Using integral screening, we reduced the computational scaling of the Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) model in terms of calculation time and memory usage to a linear relationship with the tesserae used to discretize the surface area. Further code improvements allowed for additional performance boosts. To demonstrate the algorithm’s better performance, we calculated the compressibility of fullerenes up to C180, where we were originally limited to C40 due to the high RAM usage of GOSTSHYP.

1.
W.
Grochala
,
R.
Hoffmann
,
J.
Feng
, and
N. W.
Ashcroft
, “
The chemical imagination at work in very tight places
,”
Angew. Chem., Int. Ed.
46
,
3620
3642
(
2007
).
2.
V.
Schettino
and
R.
Bini
, “
Constraining molecules at the closest approach: Chemistry at high pressure
,”
Chem. Soc. Rev.
36
,
869
880
(
2007
).
3.
G.
Jenner
, “
Role of the medium in high pressure organic reactions. A review
,”
Mini-Rev. Org. Chem.
1
,
9
26
(
2004
).
4.
H.-K.
Mao
,
X.-J.
Chen
,
Y.
Ding
,
B.
Li
, and
L.
Wang
, “
Solids, liquids, and gases under high pressure
,”
Rev. Mod. Phys.
90
,
15007
(
2018
).
5.
P. F.
McMillan
, “
Chemistry at high pressure
,”
Chem. Soc. Rev.
35
,
855
857
(
2006
).
6.
D. A.
Rychkov
, “
A short review of current computational concepts for high-pressure phase transition studies in molecular crystals
,”
Crystals
10
,
81
(
2020
).
7.
T.
Zhang
,
W.
Shi
,
D.
Wang
,
S.
Zhuo
,
Q.
Peng
, and
Z.
Shuai
, “
Pressure-induced emission enhancement in hexaphenylsilole: A computational study
,”
J. Mater. Chem. C
7
,
1388
1398
(
2019
).
8.
M.
Walker
,
C. A.
Morrison
, and
D. R.
Allan
, “
Nitric acid monohydrates at high pressure: An experimental and computational study
,”
Phys. Rev. B
72
,
224106
(
2005
).
9.
P. S.
Ghosh
,
K.
Ali
, and
A.
Arya
, “
A computational study of high pressure polymorphic transformations in monazite-type LaPO4
,”
Phys. Chem. Chem. Phys.
20
,
7621
7634
(
2018
).
10.
M.
Colligan
,
P. M.
Forster
,
A. K.
Cheetham
,
Y.
Lee
,
T.
Vogt
, and
J. A.
Hriljac
, “
Synchrotron X-ray powder diffraction and computational investigation of purely siliceous zeolite Y under pressure
,”
J. Am. Chem. Soc.
126
,
12015
12022
(
2004
).
11.
J.
Wiebke
,
E.
Pahl
, and
P.
Schwerdtfeger
, “
Melting at high pressure: Can first-principles computational chemistry challenge diamond-anvil cell experiments?
,”
Angew. Chem., Int. Ed.
52
,
13202
13205
(
2013
).
12.
C. L.
Hobday
,
C. H.
Woodall
,
M. J.
Lennox
,
M.
Frost
,
K.
Kamenev
,
T.
Düren
,
C. A.
Morrison
, and
S. A.
Moggach
, “
Understanding the adsorption process in ZIF-8 using high pressure crystallography and computational modelling
,”
Nat. Commun.
9
,
1429
(
2018
).
13.
N.
Biedermann
,
S.
Speziale
,
B.
Winkler
,
H. J.
Reichmann
,
M.
Koch-Müller
, and
G.
Heide
, “
High-pressure phase behavior of SrCO3: An experimental and computational Raman scattering study
,”
Phys. Chem. Miner.
44
,
335
343
(
2017
).
14.
G. D.
Gatta
,
G.
Tabacchi
,
E.
Fois
, and
Y.
Lee
, “
Behaviour at high pressure of Rb7NaGa8Si12O40·3H2O (a zeolite with EDI topology): A combined experimental–computational study
,”
Phys. Chem. Miner.
43
,
209
216
(
2016
).
15.
T.
Stauch
, “
Quantum chemical modeling of molecules under pressure
,”
Int. J. Quantum Chem.
121
,
e26208
(
2021
).
16.
L. F.
Pašteka
,
T.
Helgaker
,
T.
Saue
,
D.
Sundholm
,
H. J.
Werner
,
M.
Hasanbulli
,
J.
Major
, and
P.
Schwerdtfeger
, “
Atoms and molecules in soft confinement potentials
,”
Mol. Phys.
118
,
e1730989
(
2020
).
17.
T.
Novoa
,
J.
Contreras-García
,
P.
Fuentealba
, and
C.
Cárdenas
, “
The Pauli principle and the confinement of electron pairs in a double well: Aspects of electronic bonding under pressure
,”
J. Chem. Phys.
150
,
204304
(
2019
).
18.
J.
Gorecki
and
W.
Byers Brown
, “
On the ground state of the hydrogen molecule–ion H+2 enclosed in hard and soft spherical boxes
,”
J. Chem. Phys.
89
,
2138
2148
(
1988
).
19.
R.
LeSar
and
D. R.
Herschbach
, “
Electronic and vibrational properties of molecules at high pressures. Hydrogen molecule in a rigid spheroidal box
,”
J. Phys. Chem.
85
,
2798
2804
(
1981
).
20.
E.
Ley-Koo
and
S.
Rubinstein
, “
The hydrogen atom within spherical boxes with penetrable walls
,”
J. Chem. Phys.
71
,
351
357
(
1979
).
21.
E. V.
Ludeña
, “
SCF calculations for hydrogen in a spherical box
,”
J. Chem. Phys.
66
,
468
470
(
1977
).
22.
D.
Suryanarayana
and
J. A.
Weil
, “
On the hyperfine splitting of the hydrogen atom in a spherical box
,”
J. Chem. Phys.
64
,
510
513
(
1976
).
23.
M.-s.
Miao
, “
Caesium in high oxidation states and as a p-block element
,”
Nat. Chem.
5
,
846
852
(
2013
).
24.
D.
Selli
,
I. A.
Baburin
,
R.
Martoňák
, and
S.
Leoni
, “
Novel metastable metallic and semiconducting germaniums
,”
Sci. Rep.
3
,
1466
(
2013
).
25.
T. D.
Huan
,
M.
Amsler
,
M. A. L.
Marques
,
S.
Botti
,
A.
Willand
, and
S.
Goedecker
, “
Low-energy polymeric phases of alanates
,”
Phys. Rev. Lett.
110
,
135502
(
2013
).
26.
H.
Wang
,
J. S.
Tse
,
K.
Tanaka
,
T.
Iitaka
, and
Y.
Ma
, “
Superconductive sodalite-like clathrate calcium hydride at high pressures
,”
Proc. Natl. Acad. Sci. U. S. A.
109
,
6463
6466
(
2012
).
27.
M.
Amsler
,
J. A.
Flores-Livas
,
L.
Lehtovaara
,
F.
Balima
,
S. A.
Ghasemi
,
D.
MacHon
,
S.
Pailhès
,
A.
Willand
,
D.
Caliste
,
S.
Botti
,
A.
San Miguel
,
S.
Goedecker
, and
M. A.
Marques
, “
Crystal structure of cold compressed graphite
,”
Phys. Rev. Lett.
108
,
065501
(
2012
).
28.
J. A.
Flores-Livas
,
M.
Amsler
,
T. J.
Lenosky
,
L.
Lehtovaara
,
S.
Botti
,
M. A. L.
Marques
, and
S.
Goedecker
, “
High pressure structures of disilane and their superconducting properties
,”
Phys. Rev. Lett.
108
,
117004
(
2012
).
29.
Y.
Yao
,
J. S.
Tse
, and
D. D.
Klug
, “
Structures of insulating phases of dense lithium
,”
Phys. Rev. Lett.
102
,
115503
(
2009
).
30.
T.
Stauch
, “
A mechanochemical model for the simulation of molecules and molecular crystals under hydrostatic pressure
,”
J. Chem. Phys.
153
,
134503
(
2020
).
31.
G.
Subramanian
,
N.
Mathew
, and
J.
Leiding
, “
A generalized force-modified potential energy surface for mechanochemical simulations
,”
J. Chem. Phys.
143
,
134109
(
2015
).
32.
R.
Cammi
,
V.
Verdolino
,
B.
Mennucci
, and
J.
Tomasi
, “
Towards the elaboration of a QM method to describe molecular solutes under the effect of a very high pressure
,”
Chem. Phys.
344
,
135
141
(
2008
).
33.
R.
Cammi
, “
A new extension of the polarizable continuum model: Toward a quantum chemical description of chemical reactions at extreme high pressure
,”
J. Comput. Chem.
36
,
2246
2259
(
2015
).
34.
B.
Chen
,
R.
Hoffmann
, and
R.
Cammi
, “
The effect of pressure on organic reactions in fluids—A new theoretical perspective
,”
Angew. Chem., Int. Ed.
56
,
11126
11142
(
2017
).
35.
M.
Scheurer
,
A.
Dreuw
,
E.
Epifanovsky
,
M.
Head-Gordon
, and
T.
Stauch
, “
Modeling molecules under pressure with Gaussian potentials
,”
J. Chem. Theory Comput.
17
,
583
597
(
2021
).
36.
M.
Häser
and
R.
Ahlrichs
, “
Improvements on the direct SCF method
,”
J. Comput. Chem.
10
,
104
111
(
1989
).
37.
J. L.
Whitten
, “
Coulombic potential energy integrals and approximations
,”
J. Chem. Phys.
58
,
4496
4501
(
1973
).
38.
D. S.
Lambrecht
,
B.
Doser
, and
C.
Ochsenfeld
, “
Rigorous integral screening for electron correlation methods
,”
J. Chem. Phys.
123
,
184102
(
2005
).
39.
B.
Doser
,
D. S.
Lambrecht
,
J.
Kussmann
, and
C.
Ochsenfeld
, “
Linear-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria
,”
J. Chem. Phys.
130
,
064107
(
2009
).
40.
S. A.
Maurer
,
D. S.
Lambrecht
,
D.
Flaig
, and
C.
Ochsenfeld
, “
Distance-dependent Schwarz-based integral estimates for two-electron integrals: Reliable tightness vs. Rigorous upper bounds
,”
J. Chem. Phys.
136
,
144107
(
2012
).
41.
S. A.
Maurer
,
D. S.
Lambrecht
,
J.
Kussmann
, and
C.
Ochsenfeld
, “
Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory
,”
J. Chem. Phys.
138
,
014101
(
2013
).
42.
T. H.
Thompson
and
C.
Ochsenfeld
, “
Integral partition bounds for fast and effective screening of general one-, two-, and many-electron integrals
,”
J. Chem. Phys.
150
,
044101
(
2019
).
43.
G. M. J.
Barca
and
P.-F.
Loos
, “
Three- and four-electron integrals involving Gaussian geminals: Fundamental integrals, upper bounds, and recurrence relations
,”
J. Chem. Phys.
147
,
024103
(
2017
).
44.
D. S.
Hollman
,
H. F.
Schaefer
, and
E. F.
Valeev
, “
A tight distance-dependent estimator for screening three-center Coulomb integrals over Gaussian basis functions
,”
J. Chem. Phys.
142
,
154106
(
2015
).
45.
A.
Irmler
and
F.
Pauly
, “
Multipole-based distance-dependent screening of Coulomb integrals
,”
J. Chem. Phys.
151
,
084111
(
2019
).
46.
H.-Z.
Ye
and
T. C.
Berkelbach
, “
Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions
,”
J. Chem. Phys.
155
,
124106
(
2021
).
47.
S. C.
McKenzie
,
E.
Epifanovsky
,
G. M. J.
Barca
,
A. T. B.
Gilbert
, and
P. M. W.
Gill
, “
Efficient method for calculating effective core potential integrals
,”
J. Phys. Chem. A
122
,
3066
3075
(
2018
).
48.
R. A.
Shaw
and
J. G.
Hill
, “
Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials
,”
J. Chem. Phys.
147
,
074108
(
2017
).
49.
C.
Song
,
L.-P.
Wang
,
T.
Sachse
,
J.
Preiß
,
M.
Presselt
, and
T. J.
Martínez
, “
Efficient implementation of effective core potential integrals and gradients on graphical processing units
,”
J. Chem. Phys.
143
,
014114
(
2015
).
50.
E.
Epifanovsky
et al, “
Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package
,”
J. Chem. Phys.
155
,
084801
(
2021
).
51.
G. M. J.
Barca
, “
Single-determinant theory of electronic excited states and many-electron integrals for explicitly correlated methods
,” Ph.D. thesis (
Australian National University
,
2017
).
52.
G. M. J.
Barca
and
P. M. W.
Gill
, “
Two-electron integrals over Gaussian geminals
,”
J. Chem. Theory Comput.
12
,
4915
4924
(
2016
).
53.
S.
Obara
and
A.
Saika
, “
Efficient recursive computation of molecular integrals over Cartesian Gaussian functions
,”
J. Chem. Phys.
84
,
3963
3974
(
1986
).
54.
A. W.
Lange
and
J. M.
Herbert
, “
Polarizable continuum reaction-field solvation models affording smooth potential energy surfaces
,”
J. Phys. Chem. Lett.
1
,
556
561
(
2010
).
55.
N. B.
Balabanov
and
K. A.
Peterson
, “
Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn
,”
J. Chem. Phys.
123
,
064107
(
2005
).
56.
D. E.
Woon
and
T. H.
Dunning
, “
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
,”
J. Chem. Phys.
98
,
1358
1371
(
1993
).
57.
D. E.
Woon
and
T. H.
Dunning
, “
Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon
,”
J. Chem. Phys.
103
,
4572
4585
(
1995
).
58.
A. K.
Wilson
,
D. E.
Woon
,
K. A.
Peterson
, and
T. H.
Dunning
,
J. Chem. Phys.
110
(
16
),
7667
7676
(
1999
).
59.
D. R.
Hartree
, “
The wave mechanics of an atom with a non-Coulomb Central field. Part I. Theory and methods
,”
Math. Proc. Cambridge Philos. Soc.
24
,
89
110
(
1928
).
60.
D. R.
Hartree
and
W.
Hartree
, “
Self-consistent field, with exchange, for beryllium
,”
Proc. R. Soc. London, Ser. A
150
,
9
33
(
1935
).
61.
P.
Pulay
, “
Improved SCF convergence acceleration
,”
J. Comput. Chem.
3
,
556
560
(
1982
).
62.
D. L.
Strout
and
G. E.
Scuseria
, “
A quantitative study of the scaling properties of the Hartree–Fock method
,”
J. Chem. Phys.
102
,
8448
8452
(
1995
).

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