Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems.

Abstract

We present an approximate treatment of spin-extended coupled-cluster (ECC) based on the spin-projection of the broken-symmetry coupled-cluster (CC) ansatz. ECC completely eliminates the spin-contamination of unrestricted CC and is therefore expected to provide better descriptions of dynamical and static correlation effects, but introduces two distinct problems. The first issue is the emergence of non-terminating amplitude equations, which are caused by the de-excitation effects inherent in symmetry projection operators. In this study, we take a minimalist approach and truncate the Taylor series of the exponential ansatz at a certain order such that the approximation safely recovers the traditional CC without spin-projection. The second issue is that the nonlinear equations of ECC become underdetermined, although consistent, yielding an infinitude of solutions. This problem arises because of the redundancies in the excitation manifold, as is common in other multi-reference approaches. We remove the linear dependencies in ECC by employing an orthogonal projection manifold. We also propose an efficient solver for our method, in which the components are usually sparse but not diagonal-dominant. It is shown that our approach is rigorously orbital-invariant and provides more accurate results than its configuration interaction and linearized CC analogues for chemical systems.