Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique

Abstract

A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.