Continuous transition between Brillouin–Wigner and Rayleigh–Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster

A continuous transition between the Rayleigh–Schrödinger and Brillouin–Wigner perturbation theories is constructed and the Bloch equation for the corresponding wave operator is derived. Subsequently it is applied to the Hilbert space multireference coupled cluster theory and used to investigate relationships between several versions of multireference coupled cluster methods. Finally, based on those continuous transitions, new size extensivity corrections for the Brillouin–Wigner coupled cluster method are suggested. Numerical tests of size-extensivity and separability of a supermolecule to closed- and open-shell fragments are also presented. Equivalence of some of the multireference coupled cluster methods with single and double excitations to full configuration interaction for two-electron systems is investigated, both theoretically and numerically.