Comparison of single and double excitation coupled cluster and configuration interaction theories: determination of structure and equilibrium propertie

doi:10.1016/0009-2614(87)80165-3

Chemical Physics Letters

Volume 139, Issue 2, 21 August 1987, Pages 134-139

https://doi.org/10.1016/0009-2614(87)80165-3 Get rights and content

Abstract

Using our recently implemented closed-shell coupled cluster singles and doubles (CCSD) model, the equilibrium structure and vibrational harmonic frequency of N₂, CO, HF and OH⁻ have been determined. This set ofdiatomics was specially chosen so as to represent the range of bonding characteristics found in small molecules. The CCSD results are compared to analogous configuration interaction (CI) predictions and are found to be most similar to CISDQ or CISDTQ. That is, CI including all singles + doubles + quadruples (CISDQ) or CISDQ+all triple excitations (CISDTQ). The agreement of CCSD with CISDQ/CISDTQ is found to be much better for the singly bonded species with the agreement for neutral HF somewhat better than for anionic OH⁻. We arrive at two major conclusions. First, higher-order effects not present in the CCSD model are less negligible for multiply bonded species and, to a smaller degree, for anionic species as well. Secondly, even for the two types of molecules discussed above, the CCSD results are closer to the CISDQ/CISDTQ predictions than are CISD values. Since CCSD is less computationally time consuming than CISDQ/CISDTQ, we suggest that the CCSD model is one of the best methods available when highly accurate ab initio predictions for chemical species strongly dominated by a single-determinant wavefunction are desired.

References (25)

T.J. Lee, R.B. Remington, Y. Yamaguchi and H.F. Schaefer III, J. Chem. Phys., submitted for...
M.F. Guest et al.
Chem. Phys. Letters
(1980)
S. Wilson et al.
Chem. Phys. Letters
(1980)
G.E. Scuseria et al.
J. Chem. Phys.
(1987)
G. Fogarasi et al.
Ann. Rev. Phys. Chem.
(1984)
G. Fogarasi et al.
B.A. Hess et al.
Chem. Rev.
(1986)
H.F. Schaefer et al.
J. Mol. Struct.
(1986)
R.B. Remington, Y. Yamaguchi, T.J. Lee and H.F. Schaefer III, J. Chem. Phys., to be...
C.W. Bauschlicher et al.
J. Chem. Phys.
(1986)
L. Brillouin
Actualities Sci. Ind.
(1934)

J. Paldus et al.

Phys. Rev.

(1972)

R. Krishnan et al.

J. Chem. Phys.

(1980)

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Chemical Physics Letters

Comparison of single and double excitation coupled cluster and configuration interaction theories: determination of structure and equilibrium propertie

Abstract

Chem. Phys. Letters

Chem. Phys. Letters

J. Chem. Phys.

Ann. Rev. Phys. Chem.

Chem. Rev.

J. Mol. Struct.

J. Chem. Phys.

Actualities Sci. Ind.

Phys. Rev.

J. Chem. Phys.

The imperfect pairing approximation

Improved potential energy curves and dissociation energies for HF, DF and TF

AB initio force constants: a cautionary tale concerning nitrogen oxides

A new implementation of the full CCSDT model for molecular electronic structure

An efficient closed-shell singles and doubles coupled-cluster method

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules