The third-order incremental dual-basis set zero-buffer approach was combined with CCSD(T)-F12x (x = a, b) theory to develop a new approach, i.e., the inc3-db-B0-CCSD(T)-F12 method, which can be applied as a black-box procedure to efficiently obtain the near complete basis set (CBS) limit of the CCSD(T) energies also for large systems. We tested this method for several cases of different chemical nature: four complexes taken from the standard benchmark sets S66 and X40, the energy difference between isomers of water hexamer and the rotation barrier of biphenyl. The results show that our method has an error relative to the best estimation of CBS energy of only 0.2 kcal/mol or less. By parallelization, our method can accomplish the CCSD(T)-F12 calculations of about 60 correlated electrons and 800 basis functions in only several days, which by standard implementation are impossible for ordinary hardware. We conclude that the inc3-db-B0-CCSD(T)-F12a/AVTZ method, which is of CCSD(T)/AV5Z quality, is close to the limit of accuracy that one can achieve for large systems currently.

1.
K.
Raghavachari
,
G. W.
Trucks
,
J. A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
2.
N.
Flocke
and
R. J.
Bartlett
,
J. Chem. Phys.
121
,
10935
(
2004
).
3.
T. F.
Hughes
,
N.
Flocke
, and
R. J.
Bartlett
,
J. Phys. Chem. A
112
,
5994
(
2008
).
4.
S.
Li
,
J.
Ma
, and
Y.
Jiang
,
J. Comput. Chem.
23
,
237
(
2002
).
5.
S.
Li
,
J.
Shen
,
W.
Li
, and
Y.
Jiang
,
J. Chem. Phys.
125
,
074109
(
2006
).
6.
W.
Li
,
P.
Piecuch
,
J. R.
Gour
, and
S.
Li
,
J. Chem. Phys.
131
,
114109
(
2009
).
7.
W.
Li
,
Y.
Guo
, and
S.
Li
,
Phys. Chem. Chem. Phys.
14
,
7854
(
2012
).
8.
M.
Ziolkowski
,
B.
Jansik
,
P.
Jørgensen
, and
J.
Olsen
,
J. Chem. Phys.
131
,
124112
(
2009
).
9.
M.
Ziolkowski
,
B.
Jansik
,
T.
Kjæbørgard
, and
P.
Jørgensen
,
J. Chem. Phys.
133
,
014107
(
2010
).
10.
K.
Kristensen
,
M.
Ziolkowski
,
B.
Jansik
,
T.
Kjæbørgard
, and
P.
Jørgensen
,
J. Chem. Theor. Comput.
7
,
1677
(
2011
).
11.
J. E.
Subotnik
and
M.
Head-Gordon
,
J. Chem. Phys.
123
,
064108
(
2005
).
12.
J. E.
Subotnik
,
A.
Sodt
, and
M.
Head-Gordon
,
J. Chem. Phys.
125
,
074116
(
2006
).
13.
A.
Sodt
,
J. E.
Subotnik
, and
M.
Head-Gordon
,
J. Chem. Phys.
125
,
194109
(
2006
).
14.
J. E.
Subotnik
,
A.
Sodt
, and
M.
Head-Gordon
,
J. Chem. Phys.
128
,
034103
(
2008
).
15.
J. E.
Subotnik
and
M.
Head-Gordon
,
J. Phys.: Condens. Matter
20
,
294211
(
2008
).
16.
Y.
Mochizuki
,
K.
Yamashita
,
T.
Nakano
,
Y.
Okiyama
,
K.
Fukuzawa
,
N.
Taguchi
, and
S.
Tanaka
,
Theor. Chem. Acc.
130
,
515
(
2011
).
17.
P.
Pulay
,
Chem. Phys. Lett.
100
,
151
(
1983
).
18.
S.
Sæbø
and
P.
Pulay
,
Chem. Phys. Lett.
113
,
13
(
1985
).
19.
P.
Pulay
and
S.
Sæbø
,
Theor. Chim. Acta
69
,
357
(
1986
).
20.
S.
Sæbø
and
P.
Pulay
,
J. Chem. Phys.
86
,
914
(
1987
).
21.
S.
Sæbø
and
P.
Pulay
,
J. Chem. Phys.
88
,
1884
(
1988
).
22.
C.
Hampel
and
H.-J.
Werner
,
J. Chem. Phys.
104
,
6286
(
1996
).
23.
G.
Hetzer
,
P.
Pulay
, and
H.-J.
Werner
,
Chem. Phys. Lett.
290
,
143
(
1998
).
24.
M.
Schütz
,
G.
Hetzer
, and
H.-J.
Werner
,
J. Chem. Phys.
111
,
5691
(
1999
).
25.
G.
Hetzer
,
M.
Schütz
,
H.
Stoll
, and
H.-J.
Werner
,
J. Chem. Phys.
113
,
9443
(
2000
).
26.
M.
Schütz
,
J. Chem. Phys.
113
,
9986
(
2000
).
27.
M.
Schütz
and
H.-J.
Werner
,
J. Chem. Phys.
114
,
661
(
2001
).
28.
M.
Schütz
,
Phys. Chem. Chem. Phys.
4
,
3941
(
2002
).
29.
F.
Neese
,
F.
Wennmohs
, and
A.
Hansen
,
J. Chem. Phys.
130
,
114108
(
2009
).
30.
F.
Neese
,
A.
Hansen
, and
D. G.
Liakos
,
J. Chem. Phys.
131
,
064103
(
2009
).
31.
A.
Hansen
,
D. G.
Liakos
, and
F.
Neese
,
J. Chem. Phys.
135
,
214102
(
2011
).
32.
D. G.
Liakos
,
A.
Hansen
, and
F.
Neese
,
J. Chem. Theory Comput.
7
,
76
(
2011
).
33.
L. M. J.
Huntington
,
A.
Hansen
,
F.
Neese
, and
M.
Nooijen
,
J. Chem. Phys.
136
,
064101
(
2012
).
34.
D. G.
Liakos
and
F.
Neese
,
J. Phys. Chem. A
116
,
4801
(
2012
).
35.
C.
Riplinger
and
F.
Neese
,
J. Chem. Phys.
138
,
034106
(
2013
).
36.
J.
Yang
,
Y.
Kurashige
,
F. R.
Manby
, and
G. K. L.
Chan
,
J. Chem. Phys.
134
,
044123
(
2011
).
37.
J.
Yang
,
G. K.-L.
Chan
,
F. R.
Manby
,
M.
Schütz
, and
H.-J.
Werner
,
J. Chem. Phys.
136
,
144105
(
2012
).
38.
H.
Stoll
,
Chem. Phys. Lett.
191
,
548
(
1992
).
39.
H.
Stoll
,
J. Chem. Phys.
97
,
8449
(
1992
).
40.
H.
Stoll
,
Phys. Rev. B
46
,
6700
(
1992
).
41.
B.
Paulus
,
P.
Fulde
, and
H.
Stoll
,
Phys. Rev. B
51
,
10572
(
1995
).
42.
K.
Doll
,
M.
Dolg
,
P.
Fulde
, and
H.
Stoll
,
Phys. Rev. B
52
,
4842
(
1995
).
43.
B.
Paulus
,
P.
Fulde
, and
H.
Stoll
,
Phys. Rev. B
54
,
2556
(
1996
).
44.
J.
Friedrich
,
M.
Hanrath
, and
M.
Dolg
,
J. Chem. Phys.
126
,
154110
(
2007
).
45.
J.
Friedrich
,
M.
Hanrath
, and
M.
Dolg
,
J. Phys. Chem. A
111
,
9830
(
2007
).
46.
J.
Friedrich
and
M.
Dolg
,
J. Chem. Phys.
129
,
244105
(
2008
).
47.
J.
Friedrich
,
M.
Hanrath
, and
M.
Dolg
,
Chem. Phys.
346
,
266
(
2008
).
48.
J.
Friedrich
and
M.
Dolg
,
J. Chem. Theory Comput.
5
,
287
(
2009
).
49.
J.
Friedrich
,
K.
Walczak
, and
M.
Dolg
,
Chem. Phys.
356
,
47
(
2009
).
50.
J.
Friedrich
,
D. P.
Tew
,
W.
Klopper
, and
M.
Dolg
,
J. Chem. Phys.
132
,
164114
(
2010
).
51.
J.
Zhang
and
M.
Dolg
,
J. Chem. Theory Comput.
9
,
2992
(
2013
).
52.
J.
Friedrich
,
J. Chem. Theory Comput.
8
,
1597
(
2012
).
53.
J.
Friedrich
and
K.
Walczak
,
J. Chem. Theory Comput.
9
,
408
(
2013
).
54.
J.
Yang
and
M.
Dolg
,
J. Chem. Phys.
127
,
084108
(
2007
).
55.
J.
Friedrich
,
E.
Perlt
,
M.
Roatsch
,
C.
Spickermann
, and
B.
Kirchner
,
J. Chem. Theory Comput.
7
,
843
(
2011
).
56.
C.
Spickermann
,
E.
Perlt
,
M.
von Domaros
,
M.
Roatsch
,
J.
Friedrich
, and
B.
Kirchner
,
J. Chem. Theory Comput.
7
,
868
(
2011
).
57.
T.
Kato
,
Commun. Pure Appl. Math.
10
,
151
(
1957
).
58.
J. C.
Slater
,
Phys. Rev.
31
,
333
(
1928
).
59.
D. P.
Tew
,
J. Chem. Phys.
129
,
014104
(
2008
).
60.
C.
Hättig
,
W.
Klopper
,
A.
Köhn
, and
D. P.
Tew
,
Chem. Rev.
112
,
4
(
2012
).
61.
S.
Fournais
,
M.
Hoffmann-Ostenhof
,
T.
Hoffmann-Ostenhof
, and
T. Ø.
Sørensen
,
Commun. Math. Phys.
255
,
183
(
2005
).
62.
Z.
Li
,
S.
Shao
, and
W.
Liu
,
J. Chem. Phys.
136
,
144117
(
2012
).
63.
L.
Kong
,
F. A.
Bischoff
, and
E. F.
Valeev
,
Chem. Rev.
112
,
75
(
2012
).
64.
T. B.
Adler
,
G.
Knizia
, and
H.-J.
Werner
,
J. Chem. Phys.
127
,
221106
(
2007
).
65.
G.
Knizia
,
T. B.
Adler
, and
H.-J.
Werner
,
J. Chem. Phys.
130
,
054104
(
2009
).
66.
J. M.
Foster
and
S. F.
Boys
,
Rev. Mod. Phys.
32
,
300
(
1960
).
67.
E.
Forgy
,
Biometrics
21
,
768
(
1965
).
68.
J.
MacQueen
,
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability.
Volume I, Statistics, edited by
L. M.
LeCam
, and
J.
Neyman
(
University of California Press
,
1965
).
69.
R.
Jurgens-Lutovsky
and
J.
Almlöf
,
Chem. Phys. Lett.
178
,
451
(
1991
).
70.
P.-O.
Löwdin
,
J. Chem. Phys.
18
,
365
(
1950
).
71.
B. C.
Carlson
and
J. M.
Keller
,
Phys. Rev.
105
,
102
(
1957
).
72.
W.
Yang
,
Phys. Rev. Lett.
66
,
1438
(
1991
).
73.
W.
Yang
,
Phys. Rev. A
44
,
7823
(
1991
).
74.
S.
Ten-no
,
Chem. Phys. Lett.
398
,
56
(
2004
).
75.
S.
Ten-no
,
J. Chem. Phys.
121
,
117
(
2004
).
76.
H.-J.
Werner
,
T. B.
Adler
, and
F. R.
Manby
,
J. Chem. Phys.
126
,
164102
(
2007
).
77.
G.
Knizia
and
H.-J.
Werner
,
J. Chem. Phys.
128
,
154103
(
2008
).
78.
E. F.
Valeev
,
Chem. Phys, Lett.
395
,
190
(
2004
).
79.
See supplementary material at http://dx.doi.org/10.1063/1.4862826 for the molecules and energy difference of the benchmark set for the dual-basis set and standard F12 methods.
80.
H.-J.
Werner
,
P. J.
Knowles
,
G.
Knizia
,
F. R.
Manby
,
M.
Schütz
, et al, molpro, version 2012.1, a package of ab initio programs,
2012
, see http://www.molpro.net.
81.
S.
Kozuch
and
J. M. L.
Martin
,
J. Chem. Theory Comput.
9
,
1918
(
2013
).
82.
J.
Řezáč
,
K. E.
Riley
, and
P.
Hobza
,
J. Chem. Theory Comput.
7
,
2427
(
2011
).
83.
R.
Sedlak
,
T.
Janowski
,
M.
Pitoňák
,
J.
Řezáč
,
P.
Pulay
, and
P.
Hobza
,
J. Chem. Theory Comput.
9
,
3364
(
2013
).
84.
J.
Řezáč
,
K. E.
Riley
, and
P.
Hobza
,
J. Chem. Theory Comput.
8
,
4285
(
2012
).
85.
K.
Liu
,
J. D.
Cruzan
, and
R. J.
Saykally
,
Science
271
,
929
(
1996
).
86.
U.
Buck
and
F.
Huisken
,
Chem. Rev.
100
,
3863
(
2000
).
87.
S. S.
Xantheas
,
C. J.
Burnham
, and
R. J.
Harrison
,
J. Chem. Phys.
116
,
1493
(
2002
).
88.
E. E.
Dahlke
,
R. M.
Olson
,
H. R.
Leverentz
, and
D. G.
Truhlar
,
J. Phys. Chem. A
112
,
3976
(
2008
).
89.
D. M.
Bates
and
G. S.
Tschumper
,
J. Phys. Chem. A
113
,
3555
(
2009
).
90.
C.
Pérez
,
M. T.
Muckle
,
D. P.
Zaleski
,
N. A.
Seifert
,
B.
Temelso
,
G. C.
Shields
,
Z.
Kisiel
, and
B. H.
Pate
,
Science
336
,
897
(
2012
).
91.
R. J.
Saykally
and
D. J.
Wales
,
Science
336
,
814
(
2012
).
92.
Y.
Wang
,
V.
Babin
,
J. M.
Bowman
, and
F.
Paesani
,
J. Am. Chem. Soc.
134
,
11116
(
2012
).
93.
E.
Miliordos
,
E.
Aprà
, and
S. S.
Xantheas
,
J. Chem. Phys.
139
,
114302
(
2013
).
94.
H. W.
Qi
,
H. R.
Leverentz
, and
D. G.
Truhlar
,
J. Phys. Chem. A
117
,
4486
(
2013
).
95.
Y.
Wang
and
J. M.
Bowman
,
J. Phys. Chem. Lett.
4
,
1104
(
2013
).
96.
G.
Häfelinger
and
C.
Regelmann
,
J. Comput. Chem.
8
,
1057
(
1987
).
97.
S.
Tsuzuki
and
K.
Tanabe
,
J. Phys. Chem.
95
,
139
(
1991
).
98.
M.
Rubio
,
M.
Merchán
, and
E.
Ortí
,
Theor. Chim. Acta
91
,
17
(
1995
).
99.
A.
Karpfen
,
C. H.
Choi
, and
M.
Kertesz
,
J. Phys. Chem. A
101
,
7426
(
1997
).
100.
S.
Tsuzuki
,
T.
Uchimaru
,
K.
Matsumura
,
M.
Mikami
, and
K.
Tanabe
,
J. Chem. Phys.
110
,
2858
(
1999
).
101.
S.
Arulmozhiraja
and
T.
Fujii
,
J. Chem. Phys.
115
,
10589
(
2001
).
102.
F.
Grein
,
J. Phys. Chem. A
106
,
3823
(
2002
).
103.
F.
Grein
,
J. Mol. Struct.: THEOCHEM
624
,
23
(
2003
).
104.
F.
Grein
,
Theor. Chem. Acc.
109
,
274
(
2003
).
105.
J. C.
Sancho-García
and
J.
Cornil
,
J. Chem. Theory Comput.
1
,
581
(
2005
).
106.
M. P.
Johansson
and
J.
Olsen
,
J. Chem. Theory Comput.
4
,
1460
(
2008
).
107.
A.
Almenningen
,
O.
Bastiansen
,
L.
Fernholt
,
B. N.
Cyvin
,
S. J.
Cyvin
, and
S.
Samdal
,
J. Mol. Struct.
128
,
59
(
1985
).
108.
O.
Bastiansen
and
S.
Samdal
,
J. Mol. Struct.
128
,
115
(
1985
).

Supplementary Material

You do not currently have access to this content.