Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-index integral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8–14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.
REFERENCES
1.
G. E.
Scuseria
and H. F.
Schaefer
, Chem. Phys. Lett.
142
, 354
(1987
).2.
C. D.
Sherrill
, A. I.
Krylov
, E. F. C.
Byrd
, and M.
Head-Gordon
, J. Chem. Phys.
109
, 4171
(1998
).3.
A. I.
Krylov
, C. D.
Sherrill
, E. F. C.
Byrd
, and M.
Head-Gordon
, J. Chem. Phys.
109
, 10669
(1998
).4.
T. B.
Pedersen
, H.
Koch
, and C.
Hättig
, J. Chem. Phys.
110
, 8318
(1999
).5.
A. I.
Krylov
, C. D.
Sherrill
, and M.
Head-Gordon
, J. Chem. Phys.
113
, 6509
(2000
).6.
S. R.
Gwaltney
, C. D.
Sherrill
, M.
Head-Gordon
, and A. I.
Krylov
, J. Chem. Phys.
113
, 3548
(2000
).7.
T. B.
Pedersen
, B.
Fernández
, and H.
Koch
, J. Chem. Phys.
114
, 6983
(2001
).8.
A.
Köhn
and J.
Olsen
, J. Chem. Phys.
122
, 084116
(2005
).9.
R. C.
Lochan
and M.
Head-Gordon
, J. Chem. Phys.
126
, 164101
(2007
).10.
F.
Neese
, T.
Schwabe
, S.
Kossmann
, B.
Schirmer
, and S.
Grimme
, J. Chem. Theory Comput.
5
, 3060
(2009
).11.
W.
Kurlancheek
and M.
Head-Gordon
, Mol. Phys.
107
, 1223
(2009
).12.
S.
Kossmann
and F.
Neese
, J. Phys. Chem. A
114
, 11768
(2010
).13.
U.
Bozkaya
, J. M.
Turney
, Y.
Yamaguchi
, H. F.
Schaefer
, and C. D.
Sherrill
, J. Chem. Phys.
135
, 104103
(2011
).14.
U.
Bozkaya
, J. Chem. Phys.
135
, 224103
(2011
).15.
U.
Bozkaya
and H. F.
Schaefer
, J. Chem. Phys.
136
, 204114
(2012
).16.
W.
Kurlancheek
, R.
Lochan
, K.
Lawler
, and M.
Head-Gordon
, J. Chem. Phys.
136
, 054113
(2012
).17.
U.
Bozkaya
and C. D.
Sherrill
, J. Chem. Phys.
138
, 184103
(2013
).18.
U.
Bozkaya
and C. D.
Sherrill
, J. Chem. Phys.
139
, 054104
(2013
).19.
U.
Bozkaya
, J. Chem. Phys.
139
, 104116
(2013
).20.
A. Y.
Sokolov
and H. F.
Schaefer
, J. Chem. Phys.
139
, 204110
(2013
).21.
U.
Bozkaya
, J. Chem. Theory Comput.
10
, 2371
(2014
).22.
U.
Bozkaya
, J. Chem. Theory Comput.
10
, 4389
(2014
).23.
U.
Bozkaya
and C. D.
Sherrill
, J. Chem. Phys.
141
, 204105
(2014
).24.
J.
Lee
and M.
Head-Gordon
, J. Chem. Theory Comput.
14
, 5203
(2018
).25.
J.
Lee
and M.
Head-Gordon
, J. Chem. Phys.
150
, 244106
(2019
).26.
L. W.
Bertels
, J.
Lee
, and M.
Head-Gordon
, J. Phys. Chem. Lett.
10
, 4170
(2019
).27.
U.
Bozkaya
, A.
Ünal
, and Y.
Alagöz
, J. Chem. Phys.
153
, 244115
(2020
).28.
C.
Kollmar
and A.
Heßelmann
, Theor. Chem. Acc.
127
, 311
(2010
).29.
C.
Kollmar
and F.
Neese
, J. Chem. Phys.
135
, 084102
(2011
).30.
U.
Bozkaya
, Phys. Chem. Chem. Phys.
18
, 11362
(2016
).31.
U.
Bozkaya
, J. Chem. Theory Comput.
12
, 1179
(2016
).32.
U.
Bozkaya
, J. Comput. Chem.
39
, 351
(2018
).33.
J. B.
Robinson
and P. J.
Knowles
, J. Chem. Phys.
135
, 044113
(2011
).34.
J. B.
Robinson
and P. J.
Knowles
, J. Chem. Phys.
136
, 054114
(2012
).35.
J. B.
Robinson
and P. J.
Knowles
, J. Chem. Phys.
138
, 074104
(2013
).36.
E.
Soydaş
and U.
Bozkaya
, J. Chem. Theory Comput.
9
, 1452
(2013
).37.
E.
Soydaş
and U.
Bozkaya
, J. Comput. Chem.
35
, 1073
(2014
).38.
E.
Soydaş
and U.
Bozkaya
, J. Chem. Theory Comput.
11
, 1564
(2015
).39.
J. B.
Robinson
and P. J.
Knowles
, J. Chem. Theory Comput.
8
, 2653
(2012
).40.
E.
Soydaş
and U.
Bozkaya
, J. Chem. Theory Comput.
9
, 4679
(2013
).41.
U.
Bozkaya
, J. Chem. Phys.
139
, 154105
(2013
).42.
U.
Bozkaya
, J. Chem. Theory Comput.
10
, 2041
(2014
).43.
D.
Yildiz
and U.
Bozkaya
, J. Comput. Chem.
37
, 345
(2016
).44.
J.
Čížek
, J. Chem. Phys.
45
, 4256
(1966
).45.
R. J.
Bartlett
, Annu. Rev. Phys. Chem.
32
, 359
(1981
).46.
R. J.
Bartlett
, J. Phys. Chem.
93
, 1697
(1989
).47.
G. D.
Purvis
and R. J.
Bartlett
, J. Chem. Phys.
76
, 1910
(1982
).48.
R. J.
Bartlett
, H.
Sekino
, and G. D.
Purvis
III, Chem. Phys. Lett.
98
, 66
(1983
).49.
Y. S.
Lee
, S. A.
Kucharski
, and R. J.
Bartlett
, J. Chem. Phys.
81
, 5906
(1984
).50.
J. A.
Pople
, M.
Head‐Gordon
, and K.
Raghavachari
, J. Chem. Phys.
87
, 5968
(1987
).51.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, Chem. Phys. Lett.
157
, 479
(1989
).52.
R. J.
Bartlett
, J. D.
Watts
, S. A.
Kucharski
, and J.
Noga
, Chem. Phys. Lett.
165
, 513
(1990
).53.
G. E.
Scuseria
and T. J.
Lee
, J. Chem. Phys.
93
, 5851
(1990
).54.
G. E.
Scuseria
, T. P.
Hamilton
, and H. F.
Schaefer
, J. Chem. Phys.
92
, 568
(1990
).55.
M.
Urban
, J.
Noga
, S. J.
Cole
, and R. J.
Bartlett
, J. Chem. Phys.
83
, 4041
(1985
).56.
T. J.
Lee
and G. E.
Scuseria
, in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy
, edited by S. R.
Langhoff
(Kluwer Academic
, Dordrecht
, 1995
), pp. 47
–108
.57.
J. D.
Watts
, J. F.
Stanton
, and R. J.
Bartlett
, Chem. Phys. Lett.
178
, 471
(1991
).58.
G. E.
Scuseria
, Chem. Phys. Lett.
176
, 423
(1991
).59.
J.
Gauss
, W. J.
Lauderdale
, J. F.
Stanton
, J. D.
Watts
, and R. J.
Bartlett
, Chem. Phys. Lett.
182
, 207
(1991
).60.
J. D.
Watts
and R. J.
Bartlett
, J. Chem. Phys.
96
, 6073
(1992
).61.
J. R.
Thomas
, B. J.
DeLeeuw
, G.
Vacek
, T. D.
Crawford
, Y.
Yamaguchi
, and H. F.
Schaefer
, J. Chem. Phys.
99
, 403
(1993
).62.
J. D.
Watts
, J.
Gauss
, and R. J.
Bartlett
, J. Chem. Phys.
98
, 8718
(1993
).63.
T. D.
Crawford
and H. F.
Schaefer
, J. Chem. Phys.
104
, 6259
(1996
).64.
T. D.
Crawford
, T. J.
Lee
, and H. F.
Schaefer
, J. Chem. Phys.
107
, 7943
(1997
).65.
A. G.
Taube
and R. J.
Bartlett
, J. Chem. Phys.
128
, 044110
(2008
).66.
U.
Bozkaya
, J. Chem. Phys.
144
, 144108
(2016
).67.
S. A.
Kucharski
and R. J.
Bartlett
, J. Chem. Phys.
108
, 5243
(1998
).68.
T. D.
Crawford
and J. F.
Stanton
, Int. J. Quantum Chem.
70
, 601
(1998
).69.
A. G.
Taube
and R. J.
Bartlett
, J. Chem. Phys.
128
, 044111
(2008
).70.
M.
Musiał
and R. J.
Bartlett
, J. Chem. Phys.
133
, 104102
(2010
).71.
S. R.
Gwaltney
and M.
Head-Gordon
, Chem. Phys. Lett.
323
, 21
(2000
).72.
S. R.
Gwaltney
and M.
Head-Gordon
, J. Chem. Phys.
115
, 2014
(2001
).73.
S.
Hirata
, P.-D.
Fan
, A. A.
Auer
, M.
Nooijen
, and P.
Piecuch
, J. Chem. Phys.
121
, 12197
(2004
).74.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
113
, 18
(2000
).75.
P.
Piecuch
and M.
Włoch
, J. Chem. Phys.
123
, 224105
(2005
).76.
P.
Piecuch
, M.
Włoch
, J. R.
Gour
, and A.
Kinal
, Chem. Phys. Lett.
418
, 467
(2006
).77.
M.
Włoch
, M. D.
Lodriguito
, P.
Piecuch
, and J. R.
Gour
, Mol. Phys.
104
, 2149
(2006
).78.
M.
Włoch
, J. R.
Gour
, and P.
Piecuch
, J. Phys. Chem. A
111
, 11359
(2007
).79.
J. J.
Eriksen
, K.
Kristensen
, T.
Kjœrgaard
, P.
Jørgensen
, and J.
Gauss
, J. Chem. Phys.
140
, 064108
(2014
).80.
J. L.
Whitten
, J. Chem. Phys.
58
, 4496
(1973
).81.
B. I.
Dunlap
, J. W. D.
Connolly
, and J. R.
Sabin
, J. Chem. Phys.
71
, 3396
(1979
).82.
M.
Feyereisen
, G.
Fitzgerald
, and A.
Komornicki
, Chem. Phys. Lett.
208
, 359
(1993
).83.
O.
Vahtras
, J.
Almlöf
, and M. W.
Feyereisen
, Chem. Phys. Lett.
213
, 514
(1993
).84.
A. P.
Rendell
and T. J.
Lee
, J. Chem. Phys.
101
, 400
(1994
).85.
F.
Weigend
, Phys. Chem. Chem. Phys.
4
, 4285
(2002
).86.
A.
Sodt
, J. E.
Subotnik
, and M.
Head-Gordon
, J. Chem. Phys.
125
, 194109
(2006
).87.
H.-J.
Werner
and M.
Schütz
, J. Chem. Phys.
135
, 144116
(2011
).88.
A. E.
DePrince
and C. D.
Sherrill
, J. Chem. Theory Comput.
9
, 2687
(2013
).89.
U.
Bozkaya
, J. Chem. Phys.
141
, 124108
(2014
).90.
U.
Bozkaya
and C. D.
Sherrill
, J. Chem. Phys.
144
, 174103
(2016
).91.
U.
Bozkaya
and C. D.
Sherrill
, J. Chem. Phys.
147
, 044104
(2017
).92.
U.
Bozkaya
, J. Chem. Theory Comput.
15
, 4415
(2019
).93.
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
, A. Y.
Sokolov
, K.
Patkowski
, A. E.
DePrince
, U.
Bozkaya
, R. A.
King
, F. A.
Evangelista
, J. M.
Turney
, T. D.
Crawford
, and C. D.
Sherrill
, J. Chem. Phys.
152
, 184108
(2020
).94.
I.
Shavitt
and R. J.
Bartlett
, Many-Body Methods in Chemistry and Physics
, 1st ed. (Cambridge University Press
, New York
, 2009
), pp. 443
–449
.95.
T. D.
Crawford
and H. F.
Schaefer
III, Rev. Comput. Chem.
14
, 33
(2000
).96.
T.
Helgaker
and P.
Jørgensen
, Adv. Quantum Chem.
19
, 183
(1988
).97.
P.
Jørgensen
and T.
Helgaker
, J. Chem. Phys.
89
, 1560
(1988
).98.
E. A.
Salter
, G. W.
Trucks
, and R. J.
Bartlett
, J. Chem. Phys.
90
, 1752
(1989
).99.
J.
Gauss
, J. F.
Stanton
, and R. J.
Bartlett
, J. Chem. Phys.
95
, 2623
(1991
).100.
J.
Gauss
, J. F.
Stanton
, and R. J.
Bartlett
, J. Chem. Phys.
95
, 2639
(1991
).101.
J.
Gauss
and J. F.
Stanton
, J. Chem. Phys.
103
, 3561
(1995
).102.
J.
Gauss
and J. F.
Stanton
, J. Chem. Phys.
116
, 1773
(2001
).103.
E.
Dalgaard
and P.
Jørgensen
, J. Chem. Phys.
69
, 3833
(1978
).104.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic Structure Theory
, 1st ed. (John Wiley & Sons
, New York
, 2000
), pp. 496
–504
.105.
R.
Shepard
, Adv. Chem. Phys.
69
, 63
(1987
).106.
R.
Shepard
, in Modern Electronic Structure Theory: Part I
, 1st ed., Advanced Series in Physical Chemistry Vol. 2, edited by D. R.
Yarkony
(World Scientific Publishing Company
, London
, 1995
), pp. 345
–458
.107.
N. C.
Handy
, J. A.
Pople
, M.
Head-Gordon
, K.
Raghavachari
, and G. W.
Trucks
, Chem. Phys. Lett.
164
, 185
(1989
).108.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
).109.
D. E.
Woon
and T. H.
Dunning
, J. Chem. Phys.
103
, 4572
(1995
).110.
F.
Weigend
, A.
Köhn
, and C.
Hättig
, J. Chem. Phys.
116
, 3175
(2002
).111.
P. C.
Hariharan
and J. A.
Pople
, Theor. Chem. Acc.
28
, 213
(1973
).112.
A. D.
McLean
and G. S.
Chandler
, J. Chem. Phys.
72
, 5639
(1980
).113.
R.
Krishnan
, J. S.
Binkley
, R.
Seeger
, and J. A.
Pople
, J. Chem. Phys.
72
, 650
(1980
).114.
S.
Huzinaga
, J. Chem. Phys.
42
, 1293
(1965
).115.
T. H.
Dunning
, J. Chem. Phys.
53
, 2823
(1970
).116.
T. H.
Dunning
and P. J.
Hay
, in Methods of Electronic Structure Theory
, Modern Theoretical Chemistry Vol. 2, edited by H. F.
Schaefer
(Plenum Press
, New York
, 1977
), pp. 1
–27
.117.
T. H.
Dunning
, J. Chem. Phys.
55
, 716
(1971
).118.
F.
Weigend
, J. Comput. Chem.
29
, 167
(2007
).119.
S. F.
Boys
and F.
Bernardi
, Mol. Phys.
19
, 553
(1970
).120.
Y.
Shao
, L. F.
Molnar
, Y.
Jung
, J.
Kussmann
, C.
Ochsenfeld
, S. T.
Brown
, A. T. B.
Gilbert
, L. V.
Slipchenko
, S. V.
Levchenko
, D. P.
O’Neill
, R. A.
DiStasio
, Jr., R. C.
Lochan
, T.
Wang
, G. J. O.
Beran
, N. A.
Besley
, J. M.
Herbert
, C.
Yeh Lin
, T.
Van Voorhis
, S.
Hung Chien
, A.
Sodt
, R. P.
Steele
, V. A.
Rassolov
, P. E.
Maslen
, P. P.
Korambath
, R. D.
Adamson
, B.
Austin
, J.
Baker
, E. F. C.
Byrd
, H.
Dachsel
, R. J.
Doerksen
, A.
Dreuw
, B. D.
Dunietz
, A. D.
Dutoi
, T. R.
Furlani
, S. R.
Gwaltney
, A.
Heyden
, S.
Hirata
, C.-P.
Hsu
, G.
Kedziora
, R. Z.
Khalliulin
, P.
Klunzinger
, A. M.
Lee
, M. S.
Lee
, W.
Liang
, I.
Lotan
, N.
Nair
, B.
Peters
, E. I.
Proynov
, P. A.
Pieniazek
, Y.
Min Rhee
, J.
Ritchie
, E.
Rosta
, C.
David Sherrill
, A. C.
Simmonett
, J. E.
Subotnik
, H.
Lee Woodcock
III, W.
Zhang
, A. T.
Bell
, A. K.
Chakraborty
, D. M.
Chipman
, F. J.
Keil
, A.
Warshel
, W. J.
Hehre
, H. F.
Schaefer
III, J.
Kong
, A. I.
Krylov
, P. M. W.
Gill
, and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
8
, 3172
(2006
).121.
M.
Kállay
and J.
Gauss
, J. Chem. Phys.
120
, 6841
(2004
).122.
M.
Kállay
, P. G.
Szalay
, and P. R.
Surján
, J. Chem. Phys.
117
, 980
(2002
).123.
M.
Kállay
, J.
Gauss
, and P. G.
Szalay
, J. Chem. Phys.
119
, 2991
(2003
).124.
M.
Kállay
and J.
Gauss
, J. Chem. Phys.
121
, 9257
(2004
).125.
M.
Kállay
and J.
Gauss
, J. Chem. Phys.
123
, 214105
(2005
).126.
M.
Kállay
, P. R.
Nagy
, D.
Mester
, Z.
Rolik
, G.
Samu
, J.
Csontos
, J.
Csóka
, P. B.
Szabó
, L.
Gyevi-Nagy
, B.
Hégely
, I.
Ladjánszki
, L.
Szegedy
, B.
Ladóczki
, K.
Petrov
, M.
Farkas
, P. D.
Mezei
, and Á.
Ganyecz
, J. Chem. Phys.
152
, 074107
(2020
).127.
D. A.
Matthews
, L.
Cheng
, M. E.
Harding
, F.
Lipparini
, S.
Stopkowicz
, T.-C.
Jagau
, P. G.
Szalay
, J.
Gauss
, and J. F.
Stanton
, J. Chem. Phys.
152
, 214108
(2020
).128.
A.
Dutta
and C. D.
Sherrill
, J. Chem. Phys.
118
, 1610
(2003
).129.
H.
Larsen
, J.
Olsen
, P.
Jørgensen
, and O.
Christiansen
, J. Chem. Phys.
113
, 6677
(2000
).130.
G. S. F.
Dhont
, J. H.
van Lenthe
, G. C.
Groenenboom
, and A.
van der Avoird
, J. Chem. Phys.
123
, 184302
(2005
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
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