We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller–Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.
REFERENCES
1.
E. A.
Hylleraas
, Z. Phys.
54
, 347
(1929
).2.
W.
Kutzelnigg
, Theor. Chim. Acta
68
, 445
(1985
).3.
W.
Kutzelnigg
and W.
Klopper
, J. Chem. Phys.
94
, 1985
(1991
).4.
W.
Klopper
and C. C. M.
Samson
, J. Chem. Phys.
116
, 6397
(2002
).5.
S.
Ten-no
, Chem. Phys. Lett.
398
, 56
(2004
).6.
S.
Ten-no
, J. Chem. Phys.
121
, 117
(2004
).7.
A. J.
May
and F. R.
Manby
, J. Chem. Phys.
121
, 4479
(2004
).8.
E. F.
Valeev
, Chem. Phys. Lett.
395
, 190
(2004
).9.
D. P.
Tew
and W.
Klopper
, J. Chem. Phys.
123
, 074101
(2005
).10.
S.
Kedžuch
, M.
Milko
, and J.
Noga
, Int. J. Quantum Chem.
105
, 929
(2005
).11.
H.
Fliegl
, W.
Klopper
, and C.
Hättig
, J. Chem. Phys.
122
, 084107
(2005
).12.
H.
Fliegl
, C.
Hättig
, and W.
Klopper
, Int. J. Quantum Chem.
106
, 2306
(2006
).13.
F. R.
Manby
, H.-J.
Werner
, T. B.
Adler
, and A. J.
May
, J. Chem. Phys.
124
, 094103
(2006
).14.
H.-J.
Werner
, T. B.
Adler
, and F. R.
Manby
, J. Chem. Phys.
126
, 164102
(2007
).15.
J.
Noga
, S.
Kedžuch
, and J.
Šimunek
, J. Chem. Phys.
127
, 034106
(2007
).16.
T. B.
Adler
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
127
, 221106
(2007
).17.
S.
Ten-no
, Chem. Phys. Lett.
447
, 175
(2007
).18.
D. P.
Tew
, W.
Klopper
, C.
Neiss
, and C.
Hättig
, Phys. Chem. Chem. Phys.
9
, 1921
(2007
).19.
G.
Knizia
and H.-J.
Werner
, J. Chem. Phys.
128
, 154103
(2008
).20.
T.
Shiozaki
, M.
Kamiya
, S.
Hirata
, and E. F.
Valeev
, J. Chem. Phys.
129
, 071101
(2008
).21.
T.
Shiozaki
, M.
Kamiya
, S.
Hirata
, and E. F.
Valeev
, Phys. Chem. Chem. Phys.
10
, 3358
(2008
).22.
J.
Noga
, S.
Kedžuch
, J.
Šimunek
, and S.
Ten-no
, J. Chem. Phys.
128
, 174103
(2008
).23.
D. P.
Tew
, W.
Klopper
, and C.
Hättig
, Chem. Phys. Lett.
452
, 326
(2008
).24.
E. F.
Valeev
, Phys. Chem. Chem. Phys.
10
, 106
(2008
).25.
E. F.
Valeev
and T. D.
Crawford
, J. Chem. Phys.
128
, 244113
(2008
).26.
M.
Torheyden
and E. F.
Valeev
, Phys. Chem. Chem. Phys.
10
, 3410
(2008
).27.
D.
Bokhan
, S.
Ten-no
, and J.
Noga
, Phys. Chem. Chem. Phys.
10
, 3320
(2008
).28.
A.
Köhn
, G. W.
Richings
, and D. P.
Tew
, J. Chem. Phys.
129
, 201103
(2008
).29.
G.
Knizia
, T. B.
Adler
, and H.-J.
Werner
, J. Chem. Phys.
130
, 054104
(2009
).30.
T.
Shiozaki
, M.
Kamiya
, S.
Hirata
, and E. F.
Valeev
, J. Chem. Phys.
130
, 054101
(2009
).31.
D.
Bokhan
, S.
Bernadotte
, and S.
Ten-no
, Chem. Phys. Lett.
469
, 214
(2009
).32.
F. A.
Bischoff
, S.
Wolfsegger
, D. P.
Tew
, and W.
Klopper
, Mol. Phys.
107
, 963
(2009
).33.
C.
Hättig
, D. P.
Tew
, and A.
Köhn
, J. Chem. Phys.
132
, 231102
(2010
).34.
H.-J.
Werner
, G.
Knizia
, and F. R.
Manby
, Mol. Phys.
109
, 407
(2011
).35.
T.
Shiozaki
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
134
, 034113
(2011
).36.
H.-J.
Werner
, T. B.
Adler
, G.
Knizia
, and F. R.
Manby
, in Recent Progress in Coupled Cluster Methods
, edited by P.
Cársky
, J.
Paldus
, and J.
Pittner
(Springer
, 2010
).37.
D. P.
Tew
, C.
Hättig
, R. A.
Bachorz
, and W.
Klopper
, in Recent Progress in Coupled Cluster Methods
, edited by P.
Cársky
, J.
Paldus
, and J.
Pittner
(Springer
, 2010
).38.
C.
Hättig
, W.
Klopper
, A.
Köhn
, and D. P.
Tew
, Chem. Rev.
112
, 4
(2012
).39.
E.
Kordel
, C.
Villani
, and W.
Klopper
, J. Chem. Phys.
122
, 214306
(2005
).40.
E.
Kordel
, C.
Villani
, and W.
Klopper
, Mol. Phys.
105
, 2565
(2007
).41.
S.
Höfener
and W.
Klopper
, Mol. Phys.
108
, 1783
(2010
).42.
S.
Höfener
, C.
Hättig
, and W.
Klopper
, Z. Phys. Chem.
224
, 695
(2010
).43.
J. M.
Zhang
, J. A.
Calvin
, and E. F.
Valeev
, Mol. Phys.
114
, 2894
(2016
).44.
H.-J.
Werner
, P. J.
Knowles
, G.
Knizia
, F. R.
Manby
, and M.
Schütz
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 242
(2011
).45.
K. R.
Shamasundar
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
135
, 054101
(2011
).46.
W.
Győrffy
, T.
Shiozaki
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
138
, 104104
(2013
).47.
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.48.
K. E.
Yousaf
and K. A.
Peterson
, J. Chem. Phys.
129
, 184108
(2008
).49.
M.
Schütz
, H.-J.
Werner
, R.
Lindh
, and F. R.
Manby
, J. Chem. Phys.
121
, 737
(2004
).50.
T.
Kato
, Commun. Pure Appl. Math.
10
, 151
(1957
).51.
R. T.
Pack
and W.
Byers Brown
, J. Chem. Phys.
45
, 556
(1966
).52.
S.
Ten-no
and F. R.
Manby
, J. Chem. Phys.
119
, 5358
(2003
).53.
F. R.
Manby
, J. Chem. Phys.
119
, 4607
(2003
).54.
R. A.
Kendall
, T. H.
Dunning
, and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).55.
T.
Dunning
, Jr., K. A.
Peterson
, and A.
Wilson
, J. Chem. Phys.
114
, 9244
(2001
).56.
F.
Weigend
, Phys. Chem. Chem. Phys.
4
, 4285
(2002
).57.
F.
Weigend
, A.
Köhn
, and C.
Hättig
, J. Chem. Phys.
116
, 3175
(2002
).58.
T.
Helgaker
, W.
Klopper
, H.
Koch
, and J.
Noga
, J. Chem. Phys.
106
, 9639
(1997
).59.
K. L.
Bak
, P.
Jørgensen
, J.
Olsen
, T.
Helgaker
, and W.
Klopper
, J. Chem. Phys.
112
, 9229
(2000
).60.
J. G.
Hill
, K. A.
Peterson
, G.
Knizia
, and H. J.
Werner
, J. Chem. Phys.
131
, 194105
(2009
).61.
A.
Karton
and J.
Martin
, Theor. Chem. Acc.
115
, 330
(2006
).62.
C.
Puzzarini
, J. Phys. Chem. A
113
, 14530
(2009
).63.
H.-J.
Werner
, T. B.
Adler
, G.
Knizia
, and F. R.
Manby
, in Recent Progress in Coupled Cluster Methods
, edited by P.
Cársky
, J.
Paldus
, and J.
Pittner
(Springer
, Dordrecht, Heidelberg, London, New York
, 2010
), pp. 573
–619
.64.
H.-J.
Werner
, G.
Knizia
, T. B.
Adler
, and O.
Marchetti
, Z. Phys. Chem.
224
, 493
(2010
).65.
J.
Yang
and C.
Hättig
, J. Chem. Phys.
131
, 074102
(2009
).66.
M.
Hanauer
and A.
Köhn
, J. Chem. Phys.
131
, 124118
(2009
).67.
J.
Yang
and C.
Hättig
, Z. Phys. Chem.
224
, 383
(2010
).© 2017 Author(s).
2017
Author(s)
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