We develop a combined coupled-cluster (CC) or equation-of-motion coupled-cluster (EOM-CC) theory and Rayleigh–Schrödinger perturbation theory on the basis of a perturbation expansion of the similarity-transformed Hamiltonian H̄=exp(−T)H exp(T). This theory generates a series of perturbative corrections to any of the complete CC or EOM-CC models and hence a hierarchy of the methods designated by CC(m)PT(n) or EOM-CC(m)PT(n). These methods systematically approach full configuration interaction (FCI) as the perturbation order (n) increases and/or as the cluster and linear excitation operators become closer to complete (m increases), while maintaining the orbital-invariance property and size extensivity of CC at any perturbation order, but not the size intensivity of EOM-CC. We implement the entire hierarchy of CC(m)PT(n) and EOM-CC(m)PT(n) into a determinantal program capable of computing their energies and wave functions for any given pair of m and n. With this program, we perform CC(m)PT(n) and EOM-CC(m)PT(n) calculations of the ground-state energies and vertical excitation energies of selected small molecules for all possible values of m and 0⩽n⩽5. When the Hartree–Fock determinant is dominant in the FCI wave function, the second-order correction to CCSD [CC(2)PT(2)] reduces the differences in the ground-state energy between CCSD and FCI by more than a factor of 10, and thereby significantly outperforms CCSD(T) or even CCSDT. The third-order correction to CCSD [CC(2)PT(3)] further diminishes the energy difference between CC(2)PT(2) and FCI and its performance parallels that of some CCSD(TQ) models. CC(m)PT(n) for the ground state with some multideterminantal character and EOM-CC(m)PT(n) for the excitation energies, however, appear to be rather slowly convergent with respect to n.

1.
F.
Coester
,
Nucl. Phys.
7
,
421
(
1958
).
2.
F.
Coester
and
H.
Kümmel
,
Nucl. Phys.
17
,
477
(
1960
).
3.
J.
Čı́žek
,
J. Chem. Phys.
45
,
4256
(
1966
).
4.
J.
Paldus
,
J.
Čı́žek
, and
I.
Shavitt
,
Phys. Rev. A
5
,
50
(
1972
).
5.
J. A.
Pople
,
R.
Krishnan
,
H. B.
Schlegel
, and
J. S.
Binkley
,
Int. J. Quantum Chem.
14
,
545
(
1978
).
6.
R. J.
Bartlett
and
G. D.
Purvis
,
Int. J. Quantum Chem.
14
,
561
(
1978
).
7.
R. J.
Bartlett
,
J. Phys. Chem.
93
,
1697
(
1989
).
8.
R. J. Bartlett, in Modern Electronic Structure Theory, Part. I, edited by D. R. Yarkony (World Scientific, Singapore, 1995), p. 1047, and references therein.
9.
G. D.
Purvis
, III
and
R. J.
Bartlett
,
J. Chem. Phys.
76
,
1910
(
1982
).
10.
J.
Noga
and
R. J.
Bartlett
,
J. Chem. Phys.
86
,
7041
(
1987
);
J.
Noga
and
R. J.
Bartlett
,
J. Chem. Phys.
89
,
3401
(
1988
) (E).
11.
G. E.
Scuseria
and
H. F.
Schaefer
, III
,
Chem. Phys. Lett.
152
,
382
(
1988
).
12.
J. D.
Watts
and
R. J.
Bartlett
,
J. Chem. Phys.
93
,
6104
(
1990
).
13.
N.
Oliphant
and
L.
Adamowicz
,
J. Chem. Phys.
95
,
6645
(
1991
).
14.
S. A.
Kucharski
and
R. J.
Bartlett
,
J. Chem. Phys.
97
,
4282
(
1992
).
15.
Y. S.
Lee
,
S. A.
Kucharski
, and
R. J.
Bartlett
,
J. Chem. Phys.
81
,
5906
(
1984
).
16.
M.
Urban
,
J.
Noga
,
S. J.
Cole
, and
R. J.
Bartlett
,
J. Chem. Phys.
83
,
4041
(
1985
).
17.
J.
Noga
,
R. J.
Bartlett
, and
M.
Urban
,
Chem. Phys. Lett.
134
,
126
(
1987
).
18.
K.
Raghavachari
,
J. Chem. Phys.
82
,
4607
(
1985
).
19.
J. A.
Pople
,
M.
Head-Gordon
, and
K.
Raghavachari
,
J. Chem. Phys.
87
,
5968
(
1987
).
20.
K.
Raghavachari
,
G. W.
Trucks
,
J. A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
21.
S. A.
Kucharski
and
R. J.
Bartlett
,
Chem. Phys. Lett.
158
,
550
(
1989
).
22.
R. J.
Bartlett
,
J. D.
Watts
,
S. A.
Kucharski
, and
J.
Noga
,
Chem. Phys. Lett.
165
,
513
(
1990
).
23.
S. A.
Kucharski
and
R. J.
Bartlett
,
Chem. Phys. Lett.
206
,
574
(
1993
).
24.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
Chem. Phys. Lett.
243
,
409
(
1995
).
25.
H.
Koch
,
O.
Christiansen
,
P.
Jørgensen
,
A. M.
Sanchez de Merás
, and
T.
Helgaker
,
J. Chem. Phys.
106
,
1808
(
1997
).
26.
S. A.
Kucharski
and
R. J.
Bartlett
,
J. Chem. Phys.
108
,
5243
(
1998
).
27.
S. A.
Kucharski
and
R. J.
Bartlett
,
J. Chem. Phys.
108
,
5255
(
1998
).
28.
S. A.
Kucharski
and
R. J.
Bartlett
,
J. Chem. Phys.
108
,
9221
(
1998
).
29.
M.
Musiał
,
S. A.
Kucharski
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
320
,
542
(
2000
).
30.
K.
Kowalski
and
P.
Piecuch
,
J. Chem. Phys.
113
,
5644
(
2000
).
31.
H. J .
Monkhorst
,
Int. J. Quantum Chem., Symp.
11
,
421
(
1977
).
32.
D.
Mukherjee
and
P. K.
Mukherjee
,
Chem. Phys.
39
,
325
(
1979
).
33.
K.
Emrich
,
Nucl. Phys. A
351
,
379
(
1981
).
34.
K.
Emrich
,
Nucl. Phys. A
351
,
397
(
1981
).
35.
H.
Nakatsuji
and
K.
Hirao
,
Int. J. Quantum Chem.
20
,
1301
(
1981
).
36.
H.
Nakatsuji
,
K.
Ohta
, and
K.
Hirao
,
J. Chem. Phys.
75
,
2952
(
1981
).
37.
E.
Dalgaard
and
H. J.
Monkhorst
,
Phys. Rev. A
28
,
1217
(
1983
).
38.
H.
Sekino
and
R. J.
Bartlett
,
Int. J. Quantum Chem., Symp.
18
,
255
(
1984
).
39.
M.
Takahashi
and
J.
Paldus
,
J. Chem. Phys.
85
,
1486
(
1986
).
40.
J.
Geertsen
,
M.
Rittby
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
164
,
57
(
1989
).
41.
J.
Koch
and
P.
Jørgensen
,
J. Chem. Phys.
93
,
3333
(
1990
).
42.
H.
Koch
,
H. J.
Aa. Jensen
,
P.
Jørgensen
, and
T.
Helgaker
,
J. Chem. Phys.
93
,
3345
(
1990
).
43.
L.
Meissner
and
R. J.
Bartlett
,
J. Chem. Phys.
94
,
6670
(
1991
).
44.
D. C.
Comeau
and
R. J.
Bartlett
,
Chem. Phys. Lett.
207
,
414
(
1993
).
45.
J. F.
Stanton
and
R. J.
Bartlett
,
J. Chem. Phys.
98
,
7029
(
1993
).
46.
R. J.
Rico
and
M.
Head-Gordon
,
Chem. Phys. Lett.
213
,
224
(
1993
).
47.
J. D.
Watts
and
R. J.
Bartlett
,
J. Chem. Phys.
101
,
3073
(
1994
).
48.
J. D.
Watts
and
R. J.
Bartlett
,
Chem. Phys. Lett.
233
,
81
(
1995
).
49.
J. D.
Watts
and
R. J.
Bartlett
,
Chem. Phys. Lett.
258
,
581
(
1996
).
50.
H.
Koch
,
O.
Christiansen
,
P.
Jørgensen
, and
J.
Olsen
,
Chem. Phys. Lett.
244
,
75
(
1995
).
51.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
J. Chem. Phys.
103
,
7429
(
1995
).
52.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
J. Chem. Phys.
105
,
1451
(
1996
).
53.
M.
Head-Gordon
,
R. J.
Rico
,
M.
Oumi
, and
T. J.
Lee
,
Chem. Phys. Lett.
219
,
21
(
1994
).
54.
M.
Head-Gordon
,
M.
Oumi
, and
D.
Maurice
,
Mol. Phys.
96
,
593
(
1999
).
55.
J. F.
Stanton
and
J.
Gauss
,
J. Chem. Phys.
103
,
1064
(
1995
).
56.
J. F.
Stanton
and
J.
Gauss
,
Theor. Chim. Acta
93
,
303
(
1996
);
J. F.
Stanton
and
J.
Gauss
,
Theor. Chim. Acta
95
,
97
(
1997
) (E).
57.
P.-O.
Löwdin
,
J. Math. Phys.
3
,
969
(
1962
).
58.
T. D.
Crawford
and
J. F.
Stanton
,
Int. J. Quantum Chem.
70
,
601
(
1998
).
59.
M.
Nooijen
and
J. G.
Snijders
,
J. Chem. Phys.
102
,
1681
(
1995
).
60.
L.
Meissner
and
M.
Nooijen
,
J. Chem. Phys.
102
,
9604
(
1995
).
61.
S. R.
Gwaltney
,
M.
Nooijen
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
248
,
189
(
1996
).
62.
S. R.
Gwaltney
and
M.
Head-Gordon
,
Chem. Phys. Lett.
323
,
21
(
2000
).
63.
S. R.
Gwaltney
,
C. D.
Sherrill
,
M.
Head-Gordon
, and
A. I.
Krylov
,
J. Chem. Phys.
113
,
3548
(
2000
).
64.
S.
Hirata
and
R. J.
Bartlett
,
Chem. Phys. Lett.
321
,
216
(
2000
).
65.
M.
Kálley
and
P. R.
Surján
,
J. Chem. Phys.
113
,
1359
(
2000
).
66.
S.
Hirata
,
M.
Nooijen
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
326
,
255
(
2000
).
67.
J.
Olsen
,
J. Chem. Phys.
113
,
7140
(
2000
).
68.
W. D.
Laidig
,
G.
Fitzgerald
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
113
,
151
(
1985
).
69.
P. J.
Knowles
,
K.
Somasundram
,
N. C.
Handy
, and
K.
Hirao
,
Chem. Phys. Lett.
113
,
8
(
1985
).
70.
J.
Olsen
,
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
J. Chem. Phys.
105
,
5082
(
1996
).
71.
O.
Christiansen
,
J.
Olsen
,
P.
Jørgensen
,
H.
Koch
, and
P.-Å.
Malmqvist
,
Chem. Phys. Lett.
261
,
369
(
1996
).
72.
S.
Zarrabian
and
R. J.
Bartlett
,
Chem. Phys. Lett.
153
,
133
(
1988
).
73.
S.
Zarrabian
,
W. D.
Laidig
, and
R. J.
Bartlett
,
Phys. Rev. A
41
,
4711
(
1990
).
74.
S.
Zarrabian
and
J.
Paldus
,
Int. J. Quantum Chem.
38
,
761
(
1990
).
75.
S.
Hirata
,
M.
Nooijen
, and
R. J.
Bartlett
,
Chem. Phys. Lett.
328
,
459
(
2000
).
76.
E. A.
Salter
,
G. W.
Trucks
, and
R. J.
Bartlett
,
J. Chem. Phys.
90
,
1752
(
1989
).
77.
POLYMER version 1.0, S. Hirata, M. Tasumi, H. Torii, S. Iwata, M. Head-Gordon, and R. J. Bartlett, 1999.
78.
P. J.
Knowles
and
N. C.
Handy
,
Chem. Phys. Lett.
111
,
315
(
1984
).
79.
J.
Olsen
,
B. O.
Roos
,
P.
Jørgensen
, and
H. J.
Aa. Jensen
,
J. Chem. Phys.
89
,
2185
(
1988
).
80.
R. J.
Harrison
and
S.
Zarrabian
,
Chem. Phys. Lett.
158
,
393
(
1989
).
81.
K.
Hirao
and
H.
Nakatsuji
,
J. Comput. Phys.
45
,
246
(
1982
).
82.
E. R.
Davidson
,
J. Comput. Phys.
17
,
87
(
1975
).
83.
J. A.
Pople
,
H.
Krishnan
,
H. B.
Schlegel
, and
J. S.
Binkley
,
Int. J. Quantum Chem., Quantum Chem. Symp.
13
,
225
(
1979
).
84.
P.
Pulay
,
J. Chem. Phys.
78
,
5043
(
1983
).
85.
ACES II is a program product of the Quantum Theory Project, University of Florida written by J. F. Stanton, J. Gauss, J. D. Watts et al., 1998. Integral packages included are VMOL (J. Almlöf and P. R. Taylor); VPROPS (P. Taylor); ABACUS (T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, J. Olsen, and P. R. Taylor).
86.
C. A. White, J. Kong, D. R. Maurice et al., Q-CHEM, Version 1.2, Q-Chem, Inc., Pittsburgh, PA (1998).
87.
J. B.
Foresman
,
M.
Head-Gordon
,
J. A.
Pople
, and
M. J.
Frisch
,
J. Phys. Chem.
96
,
135
(
1992
);
the equivalence of EOM-CC(1)PT(2) to CIS-MP2 may become evident by realizing that P|Rk(1) does not directly contribute to Ek(2).
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