Development And Applications Of Non-Perturbative Approximants To The State-Specific Multi-Reference Coupled Cluster Theory: The Two Distinct Variants

Abstract

In this chapter, two useful non-perturbative approximants to the state specific multi-reference coupled cluster theory (SS-MRCC) of Mukherjee et al. are developed and pilot numerical applications are presented. The parent formulation is rigorously size-extensive and the use of a complete active space leads to a size-consistent theory as well when localized orbitals are used. The redundancy of cluster amplitudes, which is customary when the Jeziorski-Monkhorst wave-operator is used in a state-specific theory is bypassed by employing strict requirements of size-extensivity of energy and the avoidance of intruders, thus rendering the parent SS-MRCC theory rigorously size-extensive as well as intruder-free when the desired state is well separated from virtual functions. In the working equations, the cluster amplitudes for the operators acting on the different model functions are coupled. In addition, the state-specific nature of the formalism leads to a lot of redundant cluster amplitudes. The equations are thus rather complex with both coupling terms and requiring sufficiency conditions to eliminate redundancy. The two approximants discussed in this chapter are designed to reduce the complexity of the working equations mentioned above via well-defined non-perturbative approximations in two different ways. In the first variant, to be called the uncoupled state-specific MRCC(UC-SS-MRCC), we use an analogue of the anonymous parentage approximation in the coupling term, which leads to considerable simplification of the working equations, yet with very little deterioration of the quality of the computed energy. In the second one, named internally contracted inactive excitations in SS-MRCC(ICI-SS-MRCC), the cluster amplitudes for all the inactive double excitations are regarded as independent of the model functions. Since the all-inactive double excitation amplitudes are the most numerous, this variant leads to a dramatic reduction in the total number of cluster amplitudes. The ICI-SS-MRCC, unlike analogous theories, such as IC-MRCISD or CASPT2, uses relaxed coefficients for the model functions and at the same time employs projection manifolds for the virtuals obtained from inactiven hole-n particle (nh-np) excitations on the relaxed multi-reference combinations. Our pilot numerical applications on a few important test cases indicate that the ICI-SS-MRCC performs remarkably well, closely paralleling the performance of the full-blown SS-MRCC.