State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms

Abstract

The traditional multi-reference coupled cluster (MRCC) methods are based on effective hamiltonian formalism and often suffer from the problem of intruders. A state-specific MRCC approach, focusing on only one state, offers the attractive possibility of avoiding intruders while at the same time incorporating the nondynamical correlation in a size-extensive manner. In this paper we discuss two alternative paradigms which allow us to achieve this goal. The first, to be called the decontracted description, we deliberately retain certain linearly dependent cluster amplitudes and allow the combining coefficients of the reference determinants to be updated to their values for the exact function. The presence of the linearly dependent cluster amplitudes requires imposition of suitable sufficiency conditions, which are invoked in a manner which naturally ensures size-extensivity. In the second approach, to be called the contracted description, we would generate a cluster expansion with respect to the entire reference function consisting of a combination of reference determinants and retain only the linearly independent cluster-amplitudes in the cluster expansion. For an efficient implementation of the formalism, we shall introduce the notion of extended normal ordering and an analogue of Wick's theorem which uses the entire reference function as the multi-determinantal analogue of the vacuum. This necessarily imposes the restriction that the combining coefficients appearing in the reference function have to remain frozen in the equations for the cluster amplitudes. Relaxation of the coefficients can be acheived only after the cluster-amplitudes with the current coefficients are solved.