Triple excitation effects in coupled-cluster calculations of indirect spin–spin coupling constants

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.

J.

 

Noga

and

R.J.

 

Bartlett

,  , ();

G.E.

Scuseria

and

H.F.

Schaefer

, , ().

K.

Raghavachari

,

G.W.

Trucks

,

J.A.

Pople

, and

M.

Head-Gordon

, , ().

M.

 

Urban

,

J.

 

Noga

,

S.J.

 

Cole

, and

R.J.

 

Bartlett

,  , ();

J.

Noga

,

R.J.

Bartlett

, and

M.

Urban

, , ().

O.

Christiansen

,

H.

Koch

, and

P.

Jørgensen

, , ().

See, for example,

T.

Helgaker

,

J.

Gauss

,

P.

Jørgensen

, and

J.

Olsen

, , ().

T.J. Lee and G.E. Scuseria, in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, edited by S.R. Langhoff (Kluwer, Dordrecht, 1995).

J.

Gauss

and

J.F.

Stanton

, , ().

O.

Christiansen

,

P.

Jørgensen

, and

C.

Hättig

, , ().

O.

 

Christiansen

,

J.

 

Gauss

, and

J.F.

 

Stanton

,  , ();

J.

Gauss

,

O.

Christiansen

, and

J.F.

Stanton

, , ().

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

, , ()].

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.

For a recent review of calculations of spin–spin coupling constants, see

T.

Helgaker

,

M.

Jaszunski

, and

K.

Ruud

, , ().

O.

Vahtras

,

H.

Ågren

,

P.

Jørgensen

,

H.J.Aa.

Jensen

,

S.B.

Padkjaer

, and

T.

Helgaker

, , ().

S.A.

 

Perera

,

H.

 

Sekino

, and

R.J.

 

Bartlett

,  , ();

S.A.

Perera

,

M.

Nooijen

, and

R.J.

Bartlett

, , ().

V.

 

Sychrovsky

,

J.

 

Gräfenstein

, and

D.

 

Cremer

,  , ();

T.

Helgaker

,

M.

Watson

, and

N.C.

Handy

, , ().

E.A.

Salter

,

H.

Sekino

, and

R.J.

Bartlett

, , ().

J.

 

Gauss

and

J.F.

 

Stanton

,  , ();

P.G.

Szalay

,

J.

Gauss

, and

J.F.

Stanton

, , ().

J.

Gauss

and

J.F.

Stanton

, , ().

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.

A.

Schäfer

,

H.

Horn

, and

R.

Ahlrichs

, , (); 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.

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.F.

Stanton

,

J.

Gauss

,

J.D.

Watts

,

W.J.

Lauderdale

, and

R.J.

Bartlett

, , ().

O.

Christiansen

,

C.

Hättig

, and

J.

Gauss

, , ().

H.

Larsen

,

J.

Olsen

,

C.

Hättig

,

P.

Jørgensen

,

O.

Christiansen

, and

J.

Gauss

, , ().

A.A. Auer and J. Gauss, (unpublished).

S.M.

Bass

,

R.L.

DeLeon

, and

J.S.

Muenter

, , ().

N.M.

Sergeyev

,

N.D.

Sergeyeva

,

Y.A.

Strelenko

, and

W.T.

Raynes

, , ().

J.R.

Holmes

,

D.

Kivelson

, and

W.C.

Drinkard

, , ().

R.E.

Wasylishen

,

J.O.

Friedrich

, and

S.

Mooibroek

, , ().

J.O.

Friedrich

and

R. E.

Wasylishen

, , ().

G.

Dombi

,

P.

Diehl

,

J.

Lounila

, and

R.

Wasser

, , ().