Despite the power and flexibility of configuration interaction (CI) based methods in computational chemistry, their broader application is limited by an exponential increase in both computational and storage requirements, particularly due to the substantial memory needed for excitation lists that are crucial for scalable parallel computing. The objective of this work is to develop a new CI framework, namely, the small tensor product distributed active space (STP-DAS) framework, aimed at drastically reducing memory demands for extensive CI calculations on individual workstations or laptops, while simultaneously enhancing scalability for extensive parallel computing. Moreover, the STP-DAS framework can support various CI-based techniques, such as complete active space (CAS), restricted active space, generalized active space, multireference CI, and multireference perturbation theory, applicable to both relativistic (two- and four-component) and non-relativistic theories, thus extending the utility of CI methods in computational research. We conducted benchmark studies on a supercomputer to evaluate the storage needs, parallel scalability, and communication downtime using a realistic exact-two-component CASCI (X2C-CASCI) approach, covering a range of determinants from 109 to 1012. Additionally, we performed large X2C-CASCI calculations on a single laptop and examined how the STP-DAS partitioning affects performance.
REFERENCES
1.
I.
Shavitt
, in Methods of Electronic Structure Theory
, edited by
H. F. I.
Schafer
(
Plentum
,
New York
, 1977
), pp. 189
–275
.2.
I.
Shavitt
, “
The history and evolution of configuration interaction
,” Mol. Phys.
94
, 3
–17
(1998
).3.
C. D.
Sherrill
and
H. F.
Schaefer
, “
The configuration interaction method: advances in highly correlated approaches
,” Adv. Quantum Chem
34
, 143
–269
(1999
).4.
P.
Čársky
, in Encyclopedia of Computational Chemistry
, edited by
P. V. R.
Schleyer
(
John Wiley & Sons, Ltd
., 2002
).5.
J. A.
Karwowski
and
I.
Shavitt
, in Handbook of Molecular Physics and Quantum Chemistry
, edited by
S.
Wilson
(
John Wiley & Sons, Ltd
., 2003
).6.
P. G.
Szalay
,
T.
Müller
,
G.
Gidofalvi
,
H.
Lischka
, and
R.
Shepard
, “
Multiconfiguration self-consistent field and multireference configuration interaction methods and applications
,” Chem. Rev.
112
, 108
–181
(2012
).7.
B. O.
Roos
, Complete Active Space Self-Consistent Field Method its Applications in Electronic Structure Calculations
(
Wiley
, 1987
), Vol.
69
, pp. 399
–445
.8.
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
).9.
B.
Liu
, “
Ab initio potential energy surface for linear H3
,” J. Chem. Phys.
58
, 1925
–1937
(1973
).10.
H.
Lischka
,
R.
Shepard
,
F. B.
Brown
, and
I.
Shavitt
, “
New implementation of the graphical unitary group approach for multireference direct configuration interaction calculations
,” Int. J. Quantum Chem.
20
, 91
–100
(2009
).11.
H.-J.
Werner
and
P. J.
Knowles
, “
An efficient internally contracted multiconfiguration-reference configuration interaction method
,” J. Chem. Phys
89
, 5803
–5814
(1988
).12.
13.
H.
Lischka
,
T.
Müller
,
P. G.
Szalay
,
I.
Shavitt
,
R. M.
Pitzer
, and
R.
Shepard
, “
Columbus—a program system for advanced multireference theory calculations
,” WIREs Comput. Mol. Sci.
1
, 191
–199
(2011
).14.
H.
Hu
,
A. J.
Jenkins
,
H.
Liu
,
J. M.
Kasper
,
M. J.
Frisch
, and
X.
Li
, “
Relativistic two-component multireference configuration interaction method with tunable correlation space
,” J. Chem. Theory Comput.
16
, 2975
–2984
(2020
).15.
K.
Andersson
,
P. A.
Malmqvist
,
B. O.
Roos
,
A. J.
Sadlej
, and
K.
Wolinski
, “
Second-order perturbation theory with a CASSCF reference function
,” J. Phys. Chem.
94
, 5483
–5488
(1990
).16.
K.
Andersson
,
P.
Malmqvist
, and
B. O.
Roos
, “
Second-order perturbation theory with a complete active space self–consistent field reference function
,” J. Chem. Phys.
96
, 1218
–1226
(1992
).17.
B. O.
Roos
,
K.
Andersson
,
M. P.
Fülscher
,
P-â.
Malmqvist
,
L.
Serrano-Andrés
,
K.
Pierloot
, and
M.
Merchán
, “
Multiconfigurational perturbation theory: Applications in electronic spectroscopy
,” in Advances in Chemical Physics
(
Wiley
, 1996
), Vol.
93
, pp. 219
–331
.18.
P.
Celani
and
H.-J.
Werner
, “
Multireference perturbation theory for large restricted and selected active space reference wave functions
,” J. Chem. Phys
112
, 5546
–5557
(2000
).19.
T.
Shiozaki
and
W.
Mizukami
, “
Relativistic internally contracted multireference electron correlation methods
,” J. Chem. Theory Comput.
11
, 4733
–4739
(2015
).20.
D.
Ma
,
G.
Li Manni
,
J.
Olsen
, and
L.
Gagliardi
, “
Second-order perturbation theory for generalized active space self-consistent-field wave functions
,” J. Chem. Theory Comput.
12
, 3208
–3213
(2016
).21.
B.
Vlaisavljevich
and
T.
Shiozaki
, “
Nuclear energy gradients for internally contracted complex active space second-order perturbation theory: Multistate extensions
,” J. Chem. Theory Comput.
12
, 3781
–3787
(2016
).22.
L.
Lu
,
H.
Hu
,
A. J.
Jenkins
, and
X.
Li
, “
Exact-two-component relativistic multireference second-order perturbation theory
,” J. Chem. Theory Comput.
18
, 2983
–2992
(2022
).23.
P. Å.
Malmqvist
,
B. O.
Roos
, and
B.
Schimmelpfennig
, “
The Restricted Active Space (RAS) state interaction approach with spin-orbit coupling
,” Chem. Phys. Lett
357
, 230
–240
(2002
).24.
M.
Klene
,
M. A.
Robb
,
L.
Blancafort
, and
M. J.
Frisch
, “
A new efficient approach to the direct restricted active space self-consistent field method
,” J. Chem. Phys.
119
, 713
–728
(2003
).25.
J.
Ivanic
, “
Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. I. Method
,” J. Chem. Phys.
119
, 9364
–9376
(2003
).26.
J.
Ivanic
, “
Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. II. Application to oxoMn(salen) and N2O4
,” J. Chem. Phys.
119
, 9377
–9385
(2003
).27.
T.
Fleig
,
J.
Olsen
, and
C. M.
Marian
, “
The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction
,” J. Chem. Phys.
114
, 4775
–4790
(2001
).28.
T.
Fleig
,
J.
Olsen
, and
L.
Visscher
, “
The generalized active space concept for the relativistic treatment of electron correlation. II. Large-scale configuration interaction implementation based on relativistic 2- and 4-spinors and its application
,” J. Chem. Phys.
119
, 2963
–2971
(2003
).29.
T.
Fleig
,
H. J. A.
Jensen
,
J.
Olsen
, and
L.
Visscher
, “
The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2
,” J. Chem. Phys.
124
, 104106
(2006
).30.
S.
Knecht
,
H. J. A.
Jensen
, and
T.
Fleig
, “
Large-scale parallel configuration interaction. I. nonrelativistic and scalar-relativistic general active space implementation with application to Rb–Ba
,” J. Chem. Phys.
128
, 014108
(2008
).31.
S.
Knecht
,
H. J. A.
Jensen
, and
T.
Fleig
, “
Large-scale parallel configuration interaction. II. Two- and four-component double-group general active space implementation with application to BiH
,” J. Chem. Phys.
132
, 014108
(2010
).32.
D.
Ma
,
G.
Li Manni
, and
L.
Gagliardi
, “
The generalized active space concept in multiconfigurational self-consistent field methods
,” J. Chem. Phys.
135
, 044128
(2011
).33.
K. D.
Vogiatzis
,
G.
Li Manni
,
S. J.
Stoneburner
,
D.
Ma
, and
L.
Gagliardi
, “
Systematic expansion of active spaces beyond the CASSCF limit: A GASSCF/SplitGAS benchmark study
,” J. Chem. Theory Comput.
11
, 3010
–3021
(2015
).34.
H. J. A.
Jensen
,
K. G.
Dyall
,
T.
Saue
, and
K.
Faegri
, “
Relativistic four-component multiconfigurational self-consistent-field theory for molecules: Formalism
,” J. Chem. Phys.
104
, 4083
–4097
(1996
).35.
J.
Thyssen
,
T.
Fleig
, and
H. J. A.
Jensen
, “
A direct relativistic four-component multiconfiguration self-consistent-field method for molecules
,” J. Chem. Phys.
129
, 034109
(2008
).36.
S.
Knecht
,
O.
Legeza
, and
M.
Reiher
, “
Communication: Four-component density matrix renormalization group
,” J. Chem. Phys.
140
, 041101
(2014
).37.
J. E.
Bates
and
T.
Shiozaki
, “
Fully relativistic complete active space self-consistent field for large molecules: Quasi-second-order minimax optimization
,” J. Chem. Phys.
142
, 044112
(2015
).38.
A.
Almoukhalalati
,
S.
Knecht
,
H. J. A.
Jensen
,
K. G.
Dyall
, and
T.
Saue
, “
Electron correlation within the relativistic no-pair approximation
,” J. Chem. Phys.
145
, 074104
(2016
).39.
R. D.
Reynolds
,
T.
Yanai
, and
T.
Shiozaki
, “
Large-scale relativistic complete active space self-consistent field with robust convergence
,” J. Chem. Phys.
149
, 014106
(2018
).40.
S.
Battaglia
,
S.
Keller
, and
S.
Knecht
, “
Efficient relativistic density-matrix renormalization group implementation in a matrix-product formulation
,” J. Chem. Theory Comput.
14
, 2353
–2369
(2018
).41.
S.
Knecht
,
H. J. A.
Jensen
, and
T.
Saue
, “
Relativistic quantum chemical calculations show that the uranium molecule U2 has a quadruple bond
,” Nat. Chem.
11
, 40
–44
(2019
).42.
A. J.
Jenkins
,
H.
Hu
,
L.
Lu
,
M. J.
Frisch
, and
X.
Li
, “
Two-component multireference restricted active space configuration interaction for the computation of l-edge x-ray absorption spectra
,” J. Chem. Theory Comput.
18
, 141
–150
(2022
).43.
P.
Sharma
,
A. J.
Jenkins
,
G.
Scalmani
,
M. J.
Frisch
,
D. G.
Truhlar
,
L.
Gagliardi
, and
X.
Li
, “
Exact-two-component multiconfiguration pair-density functional theory
,” J. Chem. Theory Comput.
18
, 2947
–2954
(2022
).44.
C. E.
Hoyer
,
L.
Lu
,
H.
Hu
,
K. D.
Shumilov
,
S.
Sun
,
S.
Knecht
, and
X.
Li
, “
Correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field methods
,” J. Chem. Phys.
158
, 044101
(2023
).45.
K. G.
Dyall
and
K.
Faegri
, Jr., Introduction to Relativistic Quantum Chemistry
(
Oxford University Press
, 2007
).46.
47.
P.
Knowles
and
N.
Handy
, “
A new determinant-based full configuration interaction method
,” Chem. Phys. Lett.
111
, 315
–321
(1984
).48.
B. R.
Brooks
and
H. F.
Schaefer III
, “
The graphical unitary group approach to the electron correlation problem. Methods and preliminary applications
,” J. Chem. Phys.
70
, 5092
–5106
(1979
).49.
P. E.
Siegbahn
, “
A new direct CI method for large CI expansions in a small orbital space
,” Chem. Phys. Lett.
109
, 417
–423
(1984
).50.
S.
Zarrabian
,
C.
Sarma
, and
J.
Paldus
, “
Vectorizable approach to molecular CI problems using determinantal basis
,” Chem. Phys. Lett.
155
, 183
–188
(1989
).51.
B. S.
Fales
and
B. G.
Levine
, “
Nanoscale multireference quantum chemistry: Full configuration interaction on graphical processing units
,” J. Chem. Theory Comput.
11
, 4708
–4716
(2015
).52.
B. S.
Fales
and
T. J.
Martínez
, “
Efficient treatment of large active spaces through multi-GPU parallel implementation of direct configuration interaction
,” J. Chem. Theory Comput.
16
, 1586
–1596
(2020
).53.
A. J.
Dobbyn
,
P. J.
Knowles
, and
R. J.
Harrison
, “
Parallel internally contracted multireference configuration interaction
,” J. Comput. Chem.
19
, 1215
–1228
(1998
).54.
K. D.
Vogiatzis
,
D.
Ma
,
J.
Olsen
,
L.
Gagliardi
, and
W. A.
de Jong
, “
Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
,” J. Chem. Phys.
147
, 184111
(2017
).55.
H.
Gao
,
S.
Imamura
,
A.
Kasagi
, and
E.
Yoshida
, “
Distributed implementation of full configuration interaction for one trillion determinants
,” J. Chem. Theory Comput.
20
, 1185
–1192
(2024
).56.
E. R.
Davidson
, “
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
,” J. Comput. Phys
17
, 87
–94
(1975
).57.
P. M.
Kozlowski
and
P.
Pulay
, “
The unrestricted natural orbital-restricted active space method: Methodology and implementation
,” Theor. Chem. Acc.
100
, 12
–20
(1998
).58.
D. B.
Williams-Young
,
A.
Petrone
,
S.
Sun
,
T. F.
Stetina
,
P.
Lestrange
,
C. E.
Hoyer
,
D. R.
Nascimento
,
L.
Koulias
,
A.
Wildman
,
J.
Kasper
,
J. J.
Goings
,
F.
Ding
,
A. E.
DePrince
III,
E. F.
Valeev
, and
X.
Li
, “
The Chronus quantum (ChronusQ) software package
,” WIREs Comput. Mol. Sci.
10
, e1436
(2020
).59.
L.
Visscher
and
K.
Dyall
, “
Dirac-fock atomic electronic structure calculations using different nuclear charge distributions
,” At. Data Nucl. Data Tables
67
, 207
–224
(1997
).60.
K. G.
Dyall
, “
Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified dirac equation
,” J. Chem. Phys.
106
, 9618
–9626
(1997
).61.
K. G.
Dyall
, “
Interfacing relativistic and nonrelativistic methods. II. Investigation of a low-order approximation
,” J. Chem. Phys.
109
, 4201
–4208
(1998
).62.
K. G.
Dyall
and
T.
Enevoldsen
, “
Interfacing relativistic and nonrelativistic methods. III. Atomic 4-spinor expansions and integral approximations
,” J. Chem. Phys.
111
, 10000
–10007
(1999
).63.
K. G.
Dyall
, “
Interfacing relativistic and nonrelativistic methods. II. One- and two-electron scalar approximations
,” J. Chem. Phys.
115
, 9136
–9143
(2001
).64.
W.
Kutzlenigg
and
W.
Liu
, “
Quasirelativistic theory equivalent to fully relativistic theory
,” J. Chem. Phys.
123
, 241102
(2005
).65.
W.
Liu
and
D.
Peng
, “
Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory
,” J. Chem. Phys.
125
, 044102
(2006
).66.
D.
Peng
,
W.
Liu
,
Y.
Xiao
, and
L.
Cheng
, “
Making four- and two-component relativistic density functional methods fully equivalent based on the idea of from atoms to molecule
,” J. Chem. Phys.
127
, 104106
(2007
).67.
M.
Ilias
and
T.
Saue
, “
An infinite-order relativistic hamiltonian by a simple one-step transformation
,” J. Chem. Phys.
126
, 064102
(2007
).68.
W.
Liu
and
D.
Peng
, “
Exact two-component Hamiltonians revisited
,” J. Chem. Phys.
131
, 031104
(2009
).69.
W.
Liu
, “
Ideas of relativistic quantum chemistry
,” Mol. Phys.
108
, 1679
–1706
(2010
).70.
Z.
Li
,
Y.
Xiao
, and
W.
Liu
, “
On the spin separation of algebraic two-component relativistic Hamiltonians
,” J. Chem. Phys
137
, 154114
(2012
).71.
D.
Peng
,
N.
Middendorf
,
F.
Weigend
, and
M.
Reiher
, “
An efficient implementation of two-component relativistic exact-decoupling methods for large molecules
,” J. Chem. Phys.
138
, 184105
(2013
).72.
F.
Egidi
,
J. J.
Goings
,
M. J.
Frisch
, and
X.
Li
, “
Direct atomic-orbital-based relativistic two-component linear response method for calculating excited-state fine structures
,” J. Chem. Theory Comput.
12
, 3711
–3718
(2016
).73.
J. J.
Goings
,
J. M.
Kasper
,
F.
Egidi
,
S.
Sun
, and
X.
Li
, “
Real time propagation of the exact two component time-dependent density functional theory
,” J. Chem. Phys.
145
, 104107
(2016
).74.
L.
Konecny
,
M.
Kadek
,
S.
Komorovsky
,
O. L.
Malkina
,
K.
Ruud
, and
M.
Repisky
, “
Acceleration of relativistic electron dynamics by means of X2C transformation: Application to the calculation of nonlinear optical properties
,” J. Chem. Theory Comput.
12
, 5823
–5833
(2016
).75.
F.
Egidi
,
S.
Sun
,
J. J.
Goings
,
G.
Scalmani
,
M. J.
Frisch
, and
X.
Li
, “
Two-component non-collinear time-dependent spin density functional theory for excited state calculations
,” J. Chem. Theory Comput.
13
, 2591
–2603
(2017
).76.
J.
Liu
and
L.
Cheng
, “
Relativistic coupled-cluster and equation-of-motion coupled-cluster methods
,” WIREs Comput. Mol. Sci.
11
, e1536
(2021
).77.
C. E.
Hoyer
,
H.
Hu
,
L.
Lu
,
S.
Knecht
, and
X.
Li
, “
Relativistic Kramers-unrestricted exact-two-component density matrix renormalization group
,” J. Phys. Chem. A
126
, 5011
–5020
(2022
).78.
J.
Ehrman
,
E.
Martinez-Baez
,
A. J.
Jenkins
, and
X.
Li
, “
Improving one-electron exact-two-component relativistic methods with the Dirac–Coulomb–Breit-parameterized effective spin–orbit coupling
,” J. Chem. Theory Comput.
19
, 5785
–5790
(2023
).79.
R.-D.
Urban
,
A. H.
Bahnmaier
,
U.
Magg
, and
H.
Jones
, “
The diode laser spectrum of thallium hydride (205TlH and 203TlH) in its ground electronic state
,” Chem. Phys. Lett.
158
, 443
–446
(1989
).80.
X.
Wang
,
P. F.
Souter
, and
L.
Andrews
, “
Infrared spectra of antimony and bismuth hydrides in solid matrixes
,” J. Phys. Chem. A
107
, 4244
–4249
(2003
).81.
P.
Schwerdtfeger
, “
Metal-metal bonds in thallium(I)–thallium(I) compounds: Fact or fiction?
,” Inorg. Chem.
30
, 1660
–1663
(1991
).82.
K.
Faegri
, Jr. and
L.
Visscher
, “
Relativistic calculations on thallium hydride
,” Theor. Chem. Acc.
105
, 265
–267
(2001
).83.
P.
Pollak
and
F.
Weigend
, “
Segmented contracted error-consistent basis sets of double- and triple-ζ valence quality for one- and two-component relativistic all-electron calculations
,” J. Chem. Theory Comput.
13
, 3696
–3705
(2017
).84.
T. H.
Dunning
, “
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).85.
R. A.
Kendall
,
T. H.
Dunning
, and
R. J.
Harrison
, “
Electron affinities of the first-row atoms revisited. systematic basis sets and wave functions
,” J. Chem. Phys.
96
, 6796
–6806
(1992
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
