Multireference Coupled-Cluster Theory: The Internally Contracted Route

Abstract

Transferring the success of the coupled-cluster expansion for single-determinant references to multireference cases remains a challenge. The main dilemma is a proper merge of the exponential ansatz, required for extensivity of the correlation energy, with a linear ansatz, required for an unbiased treatment of near-degenerate state interactions. We argue that the state interaction aspect is important and that therefore the Bloch equations are the necessary starting point for all true multireference coupled-cluster theories. Considering the aspect of spin-adaptation and orbital invariance, we arrive at internally contracted expansions, which indeed have a number of appealing formal properties, but also incur a tremendous increase in the complexity of the resulting working equations. The most striking property of internally contracted expansions is probably that a simple transformation of the reference space turns the multistate equations into state-specific equations without introducing further approximations. We discuss the present shortcomings and perspectives of the internally contracted multireference coupled-cluster theory and discuss issues like the completeness of the equations, alternative expansions using normal ordering, and perspectives for large active spaces and large molecules.