The effect of triple excitations in coupled-cluster calculations of indirect spin-spin coupling constants is investigated in coupled-cluster singles and doubles (CCSD) calculations augmented by a perturbative treatment of triples [CCSD(T)], in calculations based on the CC3 model as well as in coupled-cluster singles, doubles, and triples (CCSDT) calculations. Though triple excitation effects are in most cases not particularly pronounced, it is demonstrated that among the approximate schemes for handling triples only the CC3 model with no orbital relaxation included (unrelaxed CC3) provides an adequate description. The otherwise successful CCSD(T) aproach appears to either significantly overestimate triple excitation effects or to yield corrections with the wrong sign in comparison to CCSDT.

1.
For a recent review of coupled-cluster methods, see, for example, J. Gauss, in Encyclopedia of Computational Chemistry, edited by P.v.R. Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, P.A. Kollmann, H.F. Schaefer, and P.R. Schreiner (Wiley, New York, 1998), p. 615.
2.
J.
Noga
and
R.J.
Bartlett
,
J. Chem. Phys.
86
,
7041
(
1987
);
G.E.
Scuseria
and
H.F.
Schaefer
,
Chem. Phys. Lett.
152
,
382
(
1988
).
3.
K.
Raghavachari
,
G.W.
Trucks
,
J.A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
4.
M.
Urban
,
J.
Noga
,
S.J.
Cole
, and
R.J.
Bartlett
,
J. Chem. Phys.
83
,
4041
(
1985
);
J.
Noga
,
R.J.
Bartlett
, and
M.
Urban
,
Chem. Phys. Lett.
134
,
126
(
1987
).
5.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
Chem. Phys. Lett.
243
,
409
(
1995
).
6.
See, for example,
T.
Helgaker
,
J.
Gauss
,
P.
Jørgensen
, and
J.
Olsen
,
J. Chem. Phys.
106
,
6430
(
1997
).
7.
T.J. Lee and G.E. Scuseria, in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, edited by S.R. Langhoff (Kluwer, Dordrecht, 1995).
8.
J.
Gauss
and
J.F.
Stanton
,
J. Chem. Phys.
104
,
2574
(
1996
).
9.
O.
Christiansen
,
P.
Jørgensen
, and
C.
Hättig
,
Int. J. Quantum Chem.
68
,
1
(
1998
).
10.
O.
Christiansen
,
J.
Gauss
, and
J.F.
Stanton
,
Chem. Phys. Lett.
292
,
437
(
1998
);
J.
Gauss
,
O.
Christiansen
, and
J.F.
Stanton
,
Chem. Phys. Lett.
296
,
117
(
1998
).
11.
It should be, however, noted that calculation of spin–spin coupling constants are possible in the context of perturbation theory using the so-called second-order polarization propagator (SOPPA) approach [
J.
Geertsen
,
J.
Oddershede
, and
G.E.
Scuseria
,
J. Chem. Phys.
87
,
3945
(
1986
)].
12.
It should be noted that the CCSDT-n models (Ref. 4) are less suitable for the calculation of molecular properties, in particular, within the unrelaxed approach. The reason is that in the derivation of the CCSDT-n models single excitations are treated as second order as appropriate for energies. Consequently, the triples equations for CCSDT-1, CCSDT-1b, and CCSDT-2 only include linear terms in the single excitations, while within the unrelaxed approach an adequate treatment of molecular properties requires inclusion of singles up to the highest possible order. For CC3, this treatment of single excitations is ensured by taking them as zeroth order. In the case of CCSDT-3, which in comparison to CC3 just includes a few additional terms, we expect—unlike for CCSDT-1, CCSDT-1b, and CCSDT-2—results similar to those obtained at the CC3 level. For the relaxed calculation of properties similar problems as encountered in the current work for CC3 can be anticipated for all CCSDT-n models.
13.
For a recent review of calculations of spin–spin coupling constants, see
T.
Helgaker
,
M.
Jaszunski
, and
K.
Ruud
,
Chem. Rev.
99
,
293
(
1999
).
14.
O.
Vahtras
,
H.
Ågren
,
P.
Jørgensen
,
H.J.Aa.
Jensen
,
S.B.
Padkjaer
, and
T.
Helgaker
,
J. Chem. Phys.
96
,
6120
(
1992
).
15.
S.A.
Perera
,
H.
Sekino
, and
R.J.
Bartlett
,
J. Chem. Phys.
101
,
2186
(
1994
);
S.A.
Perera
,
M.
Nooijen
, and
R.J.
Bartlett
,
J. Chem. Phys.
104
,
3290
(
1996
).
16.
V.
Sychrovsky
,
J.
Gräfenstein
, and
D.
Cremer
,
J. Chem. Phys.
113
,
3530
(
2000
);
T.
Helgaker
,
M.
Watson
, and
N.C.
Handy
,
J. Chem. Phys.
113
,
9402
(
2000
).
17.
E.A.
Salter
,
H.
Sekino
, and
R.J.
Bartlett
,
J. Chem. Phys.
87
,
502
(
1987
).
18.
J.
Gauss
and
J.F.
Stanton
,
Chem. Phys. Lett.
70
,
276
(
1997
);
P.G.
Szalay
,
J.
Gauss
, and
J.F.
Stanton
,
Theor. Chem. Acc.
100
,
5
(
1998
).
19.
J.
Gauss
and
J.F.
Stanton
,
Phys. Chem. Chem. Phys.
2
,
2047
(
2000
).
20.
In the finite-difference scheme, second derivatives were obtained numerically using the following formula: d2E/dx dx=(E(+x,+y)+E(−x,−y)−E(+x,−y)−E(−x,+y))/4ΔxΔy with E(±x,±y) as the energies in the presence of the perturbations ±x and ±y, respectively, and Δx and Δy as the perturbation strength. For the latter, values of 0.0002 a.u. have been chosen in case of FC perturbations and 0.0001 a.u. in case of SD perturbations. The accuracy of the finite-difference results have been checked at the CCSD level by comparison with results from the corresponding analytic second derivative calculations.
21.
A.
Schäfer
,
H.
Horn
, and
R.
Ahlrichs
,
J. Chem. Phys.
97
,
257
(
1992
); the qz2p basis consists of a 11s7p2d/7s2p primitive set contracted to 6s4p2d/4s2p and the pz3d2 f basis of a 13s8p3d2 f/8s3p2d set contracted to 8s5p3d2 f/5s3p2d. All calculations have been carried out with spherical Gaussians and with all electrons correlated.
22.
The used experimental geometries have been taken from the compilation given by Bak et al. [
K.L.
Bak
,
J.
Gauss
,
P.
Jørgensen
,
J.
Olsen
,
T.
Helgaker
, and
J.F.
Stanton
,
J. Chem. Phys.
114
,
6548
(
2001
)].
23.
J.F.
Stanton
,
J.
Gauss
,
J.D.
Watts
,
W.J.
Lauderdale
, and
R.J.
Bartlett
,
Int. J. Quantum Chem., Quantum Chem. Symp.
26
,
879
(
1992
).
24.
O.
Christiansen
,
C.
Hättig
, and
J.
Gauss
,
J. Chem. Phys.
109
,
4745
(
1998
).
25.
H.
Larsen
,
J.
Olsen
,
C.
Hättig
,
P.
Jørgensen
,
O.
Christiansen
, and
J.
Gauss
,
J. Chem. Phys.
111
,
1917
(
1999
).
26.
A.A. Auer and J. Gauss, (unpublished).
27.
S.M.
Bass
,
R.L.
DeLeon
, and
J.S.
Muenter
,
J. Chem. Phys.
86
,
4305
(
1987
).
28.
N.M.
Sergeyev
,
N.D.
Sergeyeva
,
Y.A.
Strelenko
, and
W.T.
Raynes
,
Chem. Phys. Lett.
277
,
142
(
1997
).
29.
J.R.
Holmes
,
D.
Kivelson
, and
W.C.
Drinkard
,
J. Chem. Phys.
37
,
150
(
1962
).
30.
R.E.
Wasylishen
,
J.O.
Friedrich
, and
S.
Mooibroek
,
J. Chem. Phys.
83
,
548
(
1985
).
31.
J.O.
Friedrich
and
R. E.
Wasylishen
,
J. Chem. Phys.
83
,
3707
(
1985
).
32.
G.
Dombi
,
P.
Diehl
,
J.
Lounila
, and
R.
Wasser
,
Org. Magn. Reson.
22
,
573
(
1984
).
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