Coupled‐Cluster approaches with an approximate account of triply and quadruply excited clusters: Implementation of the orthogonally spin‐adapted CCD + ST ( CCD ), CCSD + T ( CCSD ), and ACPQ + ST ( ACPQ ) formalisms

The orthogonally spin‐adapted ( OSA ) coupled‐pair ( CCD ) methods with an approximate account of triply and quadruply excited clusters are considered. We focus on the CCD + ST ( CCD ) perturbative estimate of the singly and triply excited clusters due to Raghavachari [J. Chem. Phys. 82 , 4607 (1985)] and its ACPQ + ST ( ACPQ ) analog proposed by Paldus and Piecuch [Int. J. Quantum Chem. 42 , 135 (1992)]. The latter approach combines the perturbative treatment of singles and triples with an approximate CCD theory corrected for connected quadruply excited clusters ( ACPQ ). We also consider the OSA version of the CCSD + T ( CCSD ) method (coupled‐cluster [ CC ] approach with singly and doubly excited clusters and noniterative perturbative account of triply excited clusters) introduced by Urban et al. {J. Chem. Phys. 83 , 4041 (1985)}. The explicit OSA expressions for the previously neglected {P. Piecuch and J. Paldus, Theor. Chim. Acta 78 , 65 (1990)} S ( CCD ) and S ( ACPQ ) terms are derived using diagrammatic methods of many‐body perturbation theory and graphical methods of spin algebras. The CCD + ST ( CCD ), CCSD + T ( CCSD ), and ACPQ + ST ( ACPQ ) formalisms have been implemented and the general purpose ab initio programs have been written using a newly developed procedure for improving the convergence of the reduced linear equation method {P. Piecuch and L. Adamowicz, J. Chem. Phys. 100 , 5857 (1994)}. Results of the pilot calculations for few nondegenerate and quasi‐degenerate systems are presented and compared with the full configuration interaction data. © 1995 John Wiley & Sons, Inc.