Alternative definition of excitation amplitudes in Multi-Reference state-specific Coupled Cluster

Abstract

A central difficulty of state-specific Multi-Reference Coupled Cluster (MR-CC) formalisms concerns the definition of the amplitudes of the single and double excitation operators appearing in the exponential wave operator. If the reference space is a complete active space (CAS) the number of these amplitudes is larger than the number of singly and doubly excited determinants on which one may project the eigenequation, and one must impose additional conditions. The present work first defines a state-specific reference-independent operator $\hat{\tilde{T}}^m$ which acting on the CAS component of the wave function $|\Psi_0^m \rangle$ maximizes the overlap between $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ and the eigenvector of the CAS-SD CI matrix $|\Psi_{\rm CAS-SD}^m \rangle$. This operator may be used to generate approximate coefficients of the Triples and Quadruples, and a dressing of the CAS-SD CI matrix, according to the intermediate Hamiltonian formalism. The process may be iterated to convergence. As a refinement towards a strict Coupled Cluster formalism, one may exploit reference-independent amplitudes provided by $(1+\hat{\tilde{T}}^m)|\Psi_0^m \rangle$ to define a reference-dependent operator $\hat{T}^m$ by fitting the eigenvector of the (dressed) CAS-SD CI matrix. The two variants, which are internally uncontracted, give rather similar results. The new MR-CC version has been tested on the ground state potential energy curves of 6 molecules (up to triple-bond breaking) and a two excited states. The non-parallelism error with respect to the Full-CI curves is of the order of 1 m$E_{\rm h}$.