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

Abstract

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 = ∑ μ exp ( T μ ) | ϕ μ 〉 〈 ϕ μ | involving a different cluster operator exp( T μ ) acting on its corresponding model function ϕ μ . 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 ϕ μ to each virtual function χ l, which is equated to zero. These equations have two types of terms: a ‘direct’ term where for each ϕ μ only powers of T μ appear, and a ‘coupling’ term where T ν ( 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 〈 χ l∣exp(− T μ )exp( T ν )∣ ϕ μ 〉 by 〈 χ l | exp ( - T μ ) exp ( T μ ′ ( ν ) ) | ϕ μ 〉 , where T μ ′ ( ν ) s form the subset of the components of T μ operators which has the same excitation structure of those operators T ν that give nontrivial contributions by their actions on ϕ μ . 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 CH 2 and SiH 2, which possess strongly multi-reference character and to the potential energy surface of the ground state of Li 2 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.