Development and pilot molecular applications of the uncoupled state-specific MRCC (UC-SS-MRCC) theory

In this paper, we propose and apply an uncoupled approximation to the rigorous, size-extensive state-specific multireference coupled cluster theory (SS-MRCC), developed earlier by Mukherjee and coworkers [U.S. Mahapatra, B. Datta, D. Mukherjee, J. Chem. Phys. 110 (1999) 6171]. Both the parent formulation and the uncoupled approximant use the Jeziorski-Monkhorst Ansatz: Ω=∑μexp(Tμ)|ϕμ〉〈ϕμ| involving a different cluster operator exp(Tμ) acting on its corresponding model function ϕμ. The approximant presented in this paper builds on a preliminary formulation presented by us recently [THEOCHEM 79 (2006) 771]. The working equations of the SS-MRCC, following a set of physically motivated sufficiency conditions, are characterized by certain projection amplitudes connecting each ϕμ to each virtual function χl, which is equated to zero. These equations have two types of terms: a 'direct' term where for each ϕμ only powers of Tμ appear, and a 'coupling' term where Tν (ν ≠ μ) also figures. In the uncoupled SS-MRCC approximant (UC-SS-MRCC) we explore the possibility of avoiding the coupling term by approximating the coupling matrix element 〈χl∣exp(−Tμ)exp(Tν)∣ϕμ〉 by 〈χl|exp(-Tμ)exp(Tμ′(ν))|ϕμ〉, where Tμ′(ν)s form the subset of the components of Tμ operators which has the same excitation structure of those operators Tν that give nontrivial contributions by their actions on ϕμ. Absence of the coupling terms leads to considerable simplifications of the working equations. Pilot molecular applications of the UC-SS-MRCC theory to the singlet states of CH2 and SiH2, which possess strongly multi-reference character and to the potential energy surface of the ground state of Li2 indicate the extreme closeness of the computed energies with those from the rigorous but more involved parent SS-MRCC theory. This indicates the potentiality and the efficacy of the UC-SS-MRCC approximation.