A noniterative triples correction for the equation-of-motion coupled-cluster method with single and double substitutions (CCSD) is presented. The correction is derived by second-order perturbation treatment of the similarity-transformed CCSD Hamiltonian. The spin-conserving variant of the correction is identical to the triples correction of Piecuch and co-workers [Mol. Phys. 104, 2149 (2006)] derived within method-of-moments framework and is not size intensive. The spin-flip variant of the correction is size intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho-, meta-, and para-benzynes, 1,2,3-tridehydrobenzene, as well as C–C bond breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the correction reduced the errors against the benchmark values by about a factor of 2–3, the absolute errors being less than 0.04 eV.
REFERENCES
1.
D. J.
Rowe
, Rev. Mod. Phys.
40
, 153
(1968
).2.
K.
Emrich
, Nucl. Phys. A
351
, 379
(1981
).3.
J.
Geertsen
, M.
Rittby
, and R. J.
Bartlett
, Chem. Phys. Lett.
164
, 57
(1989
).4.
J. F.
Stanton
and R. J.
Bartlett
, J. Chem. Phys.
98
, 7029
(1993
).5.
S. V.
Levchenko
and A. I.
Krylov
, J. Chem. Phys.
120
, 175
(2004
).6.
D.
Sinha
, D.
Mukhopadhyay
, and D.
Mukherjee
, Chem. Phys. Lett.
129
, 369
(1986
).7.
S.
Pal
, M.
Rittby
, R. J.
Bartlett
, D.
Sinha
, and D.
Mukherjee
, Chem. Phys. Lett.
137
, 273
(1987
).8.
J. F.
Stanton
and J.
Gauss
, J. Chem. Phys.
101
, 8938
(1994
).9.
M.
Nooijen
and R. J.
Bartlett
, J. Chem. Phys.
102
, 3629
(1995
).10.
D.
Mukherjee
and S.
Pal
, Adv. Quantum Chem.
20
, 291
(1989
).11.
R. J.
Bartlett
and J. F.
Stanton
, Rev. Comput. Chem.
5
, 65
(1994
).12.
R. J.
Bartlett
, Int. J. Mol. Sci.
3
, 579
(2002
).13.
J. F.
Stanton
and J.
Gauss
, Adv. Chem. Phys.
125
, 101
(2003
).14.
A. I.
Krylov
, Acc. Chem. Res.
39
, 83
(2006
).15.
16.
A. I.
Krylov
, Annu. Rev. Phys. Chem.
59
, 433
(2008
).17.
18.
H.
Sekino
and R. J.
Bartlett
, Int. J. Quantum Chem., Quantum Chem. Symp.
26
, 255
(1984
).19.
H.
Koch
, H. J.
Aa Jensen
, P.
Jørgensen
, and T.
Helgaker
, J. Chem. Phys.
93
, 3345
(1990
).20.
M.
Head-Gordon
and T. J.
Lee
, in Modern Ideas in Coupled Cluster Theory
, edited by R. J.
Bartlett
(World Scientific
, Singapore
, 1997
).21.
H.
Nakatsuji
and K.
Hirao
, J. Chem. Phys.
68
, 2053
(1978
).22.
H.
Nakatsuji
, Chem. Phys. Lett.
177
, 331
(1991
).23.
H.
Koch
and P.
Jørgensen
, J. Chem. Phys.
93
, 3333
(1990
).24.
H.
Larsen
, K.
Hald
, J.
Olsen
, and P.
Jørgensen
, J. Chem. Phys.
115
, 3015
(2001
).25.
L. V.
Slipchenko
and A. I.
Krylov
, J. Chem. Phys.
117
, 4694
(2002
).26.
S.
Hirata
, M.
Nooijen
, and R. J.
Bartlett
, Chem. Phys. Lett.
326
, 255
(2000
).27.
L. V.
Slipchenko
and A. I.
Krylov
, J. Chem. Phys.
123
, 084107
(2005
).28.
M.
Kállay
and J.
Gauss
, J. Chem. Phys.
121
, 9257
(2004
).29.
K. W.
Sattelmeyer
, J. F.
Stanton
, J.
Olsen
, and J.
Gauss
, Chem. Phys. Lett.
347
, 499
(2001
).30.
S. A.
Kucharski
, M.
Włoch
, M.
Musiał
, and R. J.
Bartlett
, J. Chem. Phys.
115
, 8263
(2001
).31.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
115
, 643
(2001
).32.
M.
Kállay
and P. R.
Surjan
, J. Chem. Phys.
113
, 1359
(2000
).33.
S.
Hirata
, J. Chem. Phys.
121
, 51
(2004
).34.
J. D.
Watts
and R. J.
Bartlett
, J. Chem. Phys.
101
, 3073
(1994
).35.
J.
Noga
, R. J.
Bartlett
, and M.
Urban
, Chem. Phys. Lett.
134
, 126
(1987
).36.
J. D.
Watts
and R. J.
Bartlett
, Chem. Phys. Lett.
233
, 81
(1995
).37.
J. D.
Watts
and R. J.
Bartlett
, Chem. Phys. Lett.
258
, 581
(1996
).38.
H.
Koch
, O.
Christiansen
, P.
Jørgensen
, and J.
Olsen
, Chem. Phys. Lett.
244
, 75
(1995
).39.
O.
Christiansen
, H.
Koch
, and P.
Jorgensen
, J. Chem. Phys.
103
, 7429
(1995
).40.
O.
Christiansen
, H.
Koch
, and P.
Jorgensen
, J. Chem. Phys.
105
, 1451
(1996
).41.
C. E.
Smith
, R. A.
King
, and T. D.
Crawford
, J. Chem. Phys.
122
, 054110
(2005
).42.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
113
, 18
(2000
).43.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
115
, 2966
(2001
).44.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
120
, 1715
(2004
).45.
46.
P.
Piecuch
and M.
Włoch
, J. Chem. Phys.
123
, 224105
(2005
).47.
M.
Włoch
, M. D.
Lodriguito
, P.
Piecuch
, and J. R.
Gour
, Mol. Phys.
104
, 2149
(2006
).48.
T. D.
Crawford
and J. F.
Stanton
, Int. J. Quantum Chem.
70
, 601
(1998
).49.
S. A.
Kucharski
and R. J.
Bartlett
, J. Chem. Phys.
108
, 5243
(1998
).50.
S. R.
Gwaltney
, C. D.
Sherrill
, M.
Head-Gordon
, and A. I.
Krylov
, J. Chem. Phys.
113
, 3548
(2000
).51.
S. R.
Gwaltney
and M.
Head-Gordon
, J. Chem. Phys.
115
, 2014
(2001
).52.
A. G.
Taube
and R. J.
Bartlett
, J. Chem. Phys.
128
, 044110
(2008
).53.
A. G.
Taube
and R. J.
Bartlett
, J. Chem. Phys.
128
, 044111
(2008
).54.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, Chem. Phys. Lett.
157
, 479
(1989
).55.
J. D.
Watts
, J. F.
Stanton
, and R. J.
Bartlett
, Chem. Phys. Lett.
178
, 471
(1991
).56.
J. F.
Stanton
and J.
Gauss
, Theor. Chim. Acta
93
, 303
(1996
).57.
S.
Hirata
, M.
Nooijen
, I.
Grabowski
, and R. J.
Bartlett
, J. Chem. Phys.
114
, 3919
(2001
).58.
J. D.
Watts
, S. R.
Gwaltney
, and R. J.
Bartlett
, J. Chem. Phys.
105
, 6979
(1996
).59.
A. I.
Krylov
, C. D.
Sherrill
, and M.
Head-Gordon
, J. Chem. Phys.
113
, 6509
(2000
).60.
S. V.
Levchenko
, T.
Wang
, and A. I.
Krylov
, J. Chem. Phys.
122
, 224106
(2005
).61.
Size extensivity of EOM-CC often causes confusion. For the two noninteracting fragments A and B, there are three different types of the EOM target states: (i) The EOM excited states of A and B being in the ground state; (ii) the EOM states of B and A is in the ground state; and (iii) simultaneous excitations on A and B. Whereas the EOM excitation energies of states (i) and (ii) are exactly the same as the EOM excitation energies of the individual fragments, the excitation energies of (iii) are not the sum of the corresponding excitation energies of A and B. Thus, only the energies of states from (i) and (ii) are size extensive, provided that the reference wave function is size extensive as well. For example, the EOM-EE-CCSD total energies of the lowest excited states of Be and Ne, which are apart, are equal to the EOM total energies of the corresponding Be state plus the CCSD energy of Ne. However, excitation energies of the states in which both Be and Ne are excited (i.e., doubly excited states of the combined system) are not the sum of the respective EOM-EE energies of the monomers and are, therefore, not size extensive. Thus, size extensivity of EOM is weaker than that of CC (e.g., the total CCSD energy of Be–Ne is the sum of the CCSD energies of the atoms), but stronger that that of the truncated CI (e.g., CISD excited states of Be are affected by the Ne atom away). To emphasize this difference, the term size intensivity is commonly employed. The important point is that the quality of the EOM treatment does not degrade with the molecular size, provided that the excited states are localized on chromophore groups, as, for example, in the series. Moreover, EOM-EE describes well those electronic states of bichromophores (or polychromophers), which are linear combinations of single excitations of the chromophores, e.g., excimer states in the benzene dimer or ionized states in the benzene dimer cation. See also discussion in Ref. 16.
62.
Y.
Shao
, L. F.
Molnar
, Y.
Jung
, J.
Kussmann
, C.
Ochsenfeld
, S.
Brown
, A. T. B.
Gilbert
, L. V.
Slipchenko
, S. V.
Levchenko
, D. P.
O’Neil
, R. A.
Distasio
, Jr., R. C.
Lochan
, T.
Wang
, G. J. O.
Beran
, N. A.
Besley
, J. M.
Herbert
, C. Y.
Lin
, T.
Van Voorhis
, S. H.
Chien
, A.
Sodt
, R. P.
Steele
, V. A.
Rassolov
, P.
Maslen
, P. P.
Korambath
, R. D.
Adamson
, B.
Austin
, J.
Baker
, E. F. C.
Bird
, H.
Daschel
, R. J.
Doerksen
, A.
Drew
, B. D.
Dunietz
, A. D.
Dutoi
, T. R.
Furlani
, S. R.
Gwaltney
, A.
Heyden
, S.
Hirata
, C. -P.
Hsu
, G. S.
Kedziora
, R. Z.
Khalliulin
, P.
Klunziger
, A. M.
Lee
, W. Z.
Liang
, I.
Lotan
, N.
Nair
, B.
Peters
, E. I.
Proynov
, P. A.
Pieniazek
, Y. M.
Rhee
, J.
Ritchie
, E.
Rosta
, C. D.
Sherrill
, A. C.
Simmonett
, J. E.
Subotnik
, H. L.
Woodcock
III, W.
Zhang
, A. T.
Bell
, A. K.
Chakraborty
, D. M.
Chipman
, F. J.
Keil
, A.
Warshel
, W. J.
Herhe
, H. F.
Schaefer
III, J.
Kong
, A. I.
Krylov
, P. M. W.
Gill
, and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
8
, 3172
(2006
).63.
A.
Golubeva
, A. V.
Nemukhin
, L.
Harding
, S. J.
Klippenstein
, and A. I.
Krylov
, J. Phys. Chem. A
111
, 13264
(2007
).64.
C. D.
Sherrill
, M. L.
Leininger
, T. J.
Van Huis
, and H. F.
Schaefer
III, J. Chem. Phys.
108
, 1040
(1998
).65.
J. C.
Stefens
, Y.
Yamaguchi
, C. D.
Sherrill
, and H. F.
Schaefer
III, J. Phys. Chem.
102
, 3999
(1998
).66.
S.
Huzinaga
, J. Chem. Phys.
42
, 1293
(1965
).67.
T. H.
Dunning
, J. Chem. Phys.
55
, 716
(1971
).68.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
).69.
A. I.
Krylov
, Chem. Phys. Lett.
338
, 375
(2001
).70.
Y.
Shao
, M.
Head-Gordon
, and A. I.
Krylov
, J. Chem. Phys.
118
, 4807
(2003
).71.
L.
Koziol
, M.
Winkler
, K. N.
Houk
, S.
Venkataramani
, W.
Sander
, and A. I.
Krylov
, J. Phys. Chem. A
111
, 5071
(2007
).72.
See EPAPS Document No. E-JCPSA6-129-001843 for the molecular structures and total energies. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
73.
A. I.
Krylov
, C. D.
Sherrill
, and M.
Head-Gordon
(unpublished).74.
T. L.
Windus
and J. A.
Pople
, Int. J. Quantum Chem.
56
, 485
(1995
).75.
S.
Gibson
, J.
Greene
, and J.
Berkowitz
, J. Chem. Phys.
83
, 4319
(1985
).76.
P. G.
Wenthold
, J.
Hu
, and R. R.
Squires
, J. Am. Chem. Soc.
118
, 11865
(1996
).77.
P. G.
Wenthold
, R. R.
Squires
, and W. C.
Lineberger
, J. Am. Chem. Soc.
120
, 5279
(1998
).© 2008 American Institute of Physics.
2008
American Institute of Physics
You do not currently have access to this content.
