Density fitting reduces the computational cost of both energy and gradient calculations by avoiding the computation and manipulation of four-index electron repulsion integrals. With this algorithm, one can efficiently optimize the geometries of large systems with an accurate multireference treatment. Here, we present the derivation of multiconfiguration pair-density functional theory for energies and analytic gradients with density fitting. Six systems are studied, and the results are compared to those obtained with no approximation to the electron repulsion integrals and to the results obtained by complete active space second-order perturbation theory. With the new approach, there is an increase in the speed of computation with a negligible loss in accuracy. Smaller grid sizes have also been used to reduce the computational cost of multiconfiguration pair-density functional theory with little effect on the optimized geometries and gradient values.
REFERENCES
1.
B. O.
Roos
, P. R.
Taylor
, and P. E. M.
Siegbahn
, Chem. Phys.
48
(2
), 157
–173
(1980
).2.
B. O.
Roos
, Advances in Chemical Physics
(Wiley, New York
, 1987
), Vol. 69, pp. 399
–445
.3.
G.
Li Manni
, R. K.
Carlson
, S.
Luo
, D.
Ma
, J.
Olsen
, D. G.
Truhlar
, and L.
Gagliardi
, J. Chem. Theory Comput.
10
(9
), 3669
–3680
(2014
).4.
L.
Gagliardi
, D. G.
Truhlar
, G.
Li Manni
, R. K.
Carlson
, C. E.
Hoyer
, and J. L.
Bao
, Acc. Chem. Res.
50
(1
), 66
–73
(2017
).5.
S. J.
Stoneburner
, D. G.
Truhlar
, and L.
Gagliardi
, J. Chem. Phys.
148
(6
), 064108
(2018
).6.
P.
Sharma
, V.
Bernales
, D. G.
Truhlar
, and L.
Gagliardi
, J. Phys. Chem. Lett.
10
(1
), 75
–81
(2018
).7.
M. d. C.
Marín
, L.
De Vico
, S. S.
Dong
, L.
Gagliardi
, D. G.
Truhlar
, and M.
Olivucci
, J. Chem. Theory Comput.
15
(3
), 1915
–1923
(2019
).8.
A. M.
Sand
, C. E.
Hoyer
, K.
Sharkas
, K. M.
Kidder
, R.
Lindh
, D. G.
Truhlar
, and L.
Gagliardi
, J. Chem. Theory Comput.
14
(1
), 126
–138
(2018
).9.
T. R.
Scott
, M. R.
Hermes
, A. M.
Sand
, M. S.
Oakley
, D. G.
Truhlar
, and L.
Gagliardi
, J. Chem. Phys.
153
(1
), 014106
(2020
).10.
T. R.
Scott
, R.
Nieman
, A.
Luxon
, B.
Zhang
, H.
Lischka
, L.
Gagliardi
, and C. A.
Parish
, J. Phys. Chem. A
123
(10
), 2049
–2057
(2019
).11.
A. M.
Sand
, K. M.
Kidder
, D. G.
Truhlar
, and L.
Gagliardi
, J. Phys. Chem. A
123
(45
), 9809
–9817
(2019
).12.
M.
Schütz
, H.-J.
Werner
, R.
Lindh
, and F. R.
Manby
, J. Chem. Phys.
121
(2
), 737
–750
(2004
).13.
D. M.
Schrader
and S.
Prager
, J. Chem. Phys.
37
(7
), 1456
–1460
(1962
).14.
E. J.
Baerends
, D. E.
Ellis
, and P.
Ros
, Chem. Phys.
2
(1
), 41
–51
(1973
).15.
J. L.
Whitten
, J. Chem. Phys.
58
(10
), 4496
–4501
(1973
).16.
B. I.
Dunlap
, J. W.
Connolly
, and J. R.
Sabin
, Int. J. Quantum Chem.
12
(S11
), 81
–87
(1977
).17.
B. I.
Dunlap
, J. W. D.
Connolly
, and J. R.
Sabin
, J. Chem. Phys.
71
(12
), 4993
–4999
(1979
).18.
M.
Feyereisen
, G.
Fitzgerald
, and A.
Komornicki
, Chem. Phys. Lett.
208
(5-6
), 359
–363
(1993
).19.
O.
Vahtras
, J.
Almlöf
, and M.
Feyereisen
, Chem. Phys. Lett.
213
(5-6
), 514
–518
(1993
).20.
F.
Weigend
and M.
Häser
, Theor. Chem. Acc.
97
(1-4
), 331
–340
(1997
).21.
F.
Weigend
, M.
Häser
, H.
Patzelt
, and R.
Ahlrichs
, Chem. Phys. Lett.
294
(1-3
), 143
–152
(1998
).22.
B. I.
Dunlap
, Phys. Chem. Chem. Phys.
2
(10
), 2113
–2116
(2000
).23.
F.
Weigend
, Phys. Chem. Chem. Phys.
4
(18
), 4285
–4291
(2002
).24.
F.
Weigend
, A.
Köhn
, and C.
Hättig
, J. Chem. Phys.
116
(8
), 3175
–3183
(2002
).25.
F.
Weigend
and R.
Ahlrichs
, Phys. Chem. Chem. Phys.
7
(18
), 3297
–3305
(2005
).26.
F.
Weigend
, Phys. Chem. Chem. Phys.
8
(9
), 1057
–1065
(2006
).27.
M. G.
Delcey
, T. B.
Pedersen
, F.
Aquilante
, and R.
Lindh
, J. Chem. Phys.
143
(4
), 044110
(2015
).28.
A. D.
McLean
, Proc. Conf. Potential Energy Surfaces in Chemistry, IBM Rep. RA
18
, (1971
).29.
N. H. F.
Beebe
and J.
Linderberg
, Int. J. Quantum Chem.
12
(4
), 683
–705
(1977
).30.
F.
Aquilante
, L.
Gagliardi
, T. B.
Pedersen
, and R.
Lindh
, J. Chem. Phys.
130
(15
), 154107
(2009
).31.
I.
Fdez
, M.
Galván Vacher
, A.
Alavi
, C.
Angeli
, F.
Aquilante
, J.
Autschbach
, J. J.
Bao
, S. I.
Bokarev
, N. A.
Bogdanov
, and R. K.
Carlson
, J. Chem. Theory Comput.
15
(11
), 5925
–5964
(2019
).32.
Q.
Sun
, T. C.
Berkelbach
, N. S.
Blunt
, G. H.
Booth
, S.
Guo
, Z.
Li
, J.
Liu
, J. D.
McClain
, E. R.
Sayfutyarova
, and S.
Sharma
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
(1
), e1340
(2018
).33.
K.
Andersson
, P. A.
Malmqvist
, B. O.
Roos
, A. J.
Sadlej
, and K.
Wolinski
, J. Phys. Chem.
94
(14
), 5483
–5488
(1990
).34.
K.
Andersson
, P. Å.
Malmqvist
, and B. O.
Roos
, J. Chem. Phys.
96
(2
), 1218
–1226
(1992
).35.
J.
Baker
, J. Comput. Chem.
14
(9
), 1085
–1100
(1993
).36.
F.
Aquilante
, M. G.
Delcey
, T. B.
Pedersen
, I. F.
Galván
, and R.
Lindh
, Mol. Phys.
115
(17-18
), 2052
–2064
(2017
).37.
M. G.
Delcey
, L.
Freitag
, T. B.
Pedersen
, F.
Aquilante
, R.
Lindh
, and L.
González
, J. Chem. Phys.
140
(17
), 174103
(2014
).38.
D. L.
Barker
and R. E.
Marsh
, Acta Crystallogr.
17
(12
), 1581
–1587
(1964
).39.
A.
Nakayama
, S.
Yamazaki
, and T.
Taketsugu
, J. Phys. Chem. A
118
(40
), 9429
–9437
(2014
).40.
J. W.
Park
and T.
Shiozaki
, J. Chem. Theory Comput.
13
(6
), 2561
–2570
(2017
).41.
J. W.
Park
and T.
Shiozaki
, Mol. Phys.
116
(19-20
), 2583
–2590
(2018
).42.
J. J.
Bao
, C.
Zhou
, and D. G.
Truhlar
, J. Chem. Theory Comput.
16
, 7444
(2020
).43.
J. J.
Bao
, C.
Zhou
, Z.
Varga
, S.
Kanchanakungwankul
, L.
Gagliardi
, and D. G.
Truhlar
, Faraday Discuss.
224
, 348
(2020
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
