Coupled-cluster approaches with an approximate account of triexcitations and the optimized-inner-projection technique. II. Coupled-cluster results for cyclic-polyene model systems

Three coupled-cluster (CC) approaches that approximately account for connected triexcited clusters, namely, the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80 4371 1984; J. Chem. Phys. 81 5906 1984; J. Chem. Phys. 82 5761 1985; J. Chem. Phys. 83 4041 1985], CCD + T(CCD) perturbative estimate due to Raghavachari [J. Chem. Phys. 82 4607 1985] and Urban et al. [J. Chem. Phys. 83 4041 1985], and approximate coupled-pair theory with triples and quadruples (ACPTQ) introduced in paper I of this series [Theor. Chim. Acta (to be published)], are implemented and applied to the Pariser-Parr-Pople and Hubbard models of cyclic polyenes ${\mathrm{C}}_N{\mathrm{H}}_N$, with $N=4\mathrm{}\nu +2\mathrm{}$ and $\nu =1\mathrm{}-5$, in the whole range of the coupling constant. In actual calculations, full advantage is taken of the high symmetry of these systems and the noniterative version of the CCDT-1 model, as proposed in paper I, is used. A comparison is made with the CC approach with doubles (CCD), approximate coupled-pair theory with quadruples (ACPQ), as well as with full and various limited configuration-interaction models. The CCDT-1 and CCD+T(CCD) methods provide excellent results in the weakly correlated region, while the ACPTQ approach, in which both triply and quadruply excited clusters are accounted for, provides remarkably good results even in the region of intermediate correlation. Contrary to ACPQ, the ACPTQ method breaks down in the highly correlated region. It is shown that this is connected with an approximate way in which the triples are included. The CCDT-1 and CCD+T(CCD) methods break down not only in the highly correlated, but even in the intermediately correlated regions, similarly as the CCD approximation. Singularities that plague the CCDT-1, CCD+T(CCD) (or CCD), and ACPTQ approaches are studied in detail and are shown to be algebraic branch points.