Reappraisal of the Role of Size-Extensive Normalization for Multireference Coupled Cluster (MRCC) Theory Using General Model Space: A Valence Universal MRCC Approach

Abstract

We present a brief description of a valence-universal multireference coupled cluster (VU-MRCC) theory that can handle completely general incomplete model spaces, remaining close to the intermediate normalization (IN) condition for Ω as much as possible without violating extensivity and without the use of a post facto correction. In this formalism, the connectedness of the cluster operators as well as effective Hamiltonian and hence the extensivity of the corresponding roots is achieved by invoking appropriate decoupling conditions on the special type of wave operator Ω = {exp(S + Xcl)} satisfying the Bloch equations in the Fock-space S in an excitation operator and X is a closed operator (denoted by cl). This special type of wave-operator leads to a unique partition of the excitations from the model space into those generated by the cluster operators (open and quasi-open) and those generated by the effective Hamiltonian (closed). In this formulation, for every Xcl, there is a counterterm from {exp(S)}cl canceling each other. This leads to a connected expressions for cluster amplitudes, using the constraint Ωcl = 1. The new form of the effective Hamiltonian preserves the extensivity of the target energies. Our analysis implies that IN for Ω is a valid size-extensive normalization for certain special IMS such as the quasi-complete model space and the isolated incomplete model space.