Hilbert space multireference coupled-cluster methods. II. A model study on H8

The performance of various coupled-cluster (CC) approaches using both single and multideterminantal references is investigated for the (quasi-)degenerate states of molecular systems, where inclusion of higher excitations (or equivalently nondynamic correlation) proves to be needed. The prototype system H8 represents an adequate model for our study, where we can vary the degree of degeneracy from a completely degenerate situation to a nondegenerate one in a continuous way. To obtain a reliable benchmark for our CC results, the full configuration interaction (FCI) and large-scale complete active space configuration interaction (CAS CI) calculations, respectively, are performed for a variety of geometries and states. The convergence of the approximate single reference CC approaches is found to be extremely sensitive to the level of degeneracies involved. In the nondegenerate case the standard CC method with single and double excitations is found to be quite satisfactory; in the (quasi-)degenerate situations, however, the inclusion of triple excitations and noniterative quadruple excitations is needed to furnish semiquantitative values of correlation energies. The alternative treatment of nondynamic correlation using a multideterminantal Hilbert space coupled-cluster (MRCC) method demonstrates the power of this approach, which provides a balanced description of both dynamic and nondynamic correlation in the degenerate region for all the investigated states of H8. Its convergence for nondegenerate situations, however, is less satisfactory, being affected by an intruder state problem.