Development and applications of a relaxation-inducing cluster expansion theory for treating strong relaxation and differential correlation effects

We present in this paper a multi-reference coupled cluster (MRCC) formulati on for energy differences which treats orbital relaxation and correlation e ffects on the same footing, by invoking a novel cluster ansatz of the valen ce portion of the wave operator Omega(V). Unlike in the traditional normal- ordered exponential representation of Omega(V) our new relaxation-inducing ansatz, represented symbolically as E-r(S), allows contractions between the spectator lines and also certain other special contractions. By an extensi ve theoretical analysis, taking as an example the case of one-hole model sp ace (the IP problem), we demonstrate that our ansatz incorporates in a mani festly spin-free form the orbital relaxation to all orders. The traditional Thouless-type of exponential transformation via one-body excitations can i nduce the same effect, as is done in the valence-specific or the quasi-vale nce-specific MRCC formalisms, but they have to be done in the spin-orbital basis - making the spin adaptation of the problem a complicated exercise. I n contrast, we use a spin-free representation of the cluster operators righ t from start, but expand the rank of the cluster operators by involving spe ctator orbitals to distinguish the various spin possibilities. the combinat orial factors entering the contracted power series in E-r(S) are chosen in such a way that they correspond to what we would have obtained if we had us ed a Thouless-like transformation to induce the orbital relaxation. Our wor king equations generally have only finite powers of the cluster operators S , resulting in a very compact formulation of the relaxation problem. Pilot numerical applications for the IP computations of HF and H2O in the core, t he inner valence and the outer valence regions show very good performance o f the method vis-a-vis those obtained using the traditional normal ordered ansatz for Omega(V). The improvement in the core IP value is particularly i mpressive. although even for the valence regions there is an overall improv ement of the IP values.