The reduced linear equation method in coupled cluster theory.

A numerical procedure for efficiently solving large systems of linear equations is presented. The approach, termed the reduced linear equation (RLE) method, is illustrated by solving the systems of linear equations that arise in linearized versions of coupled-cluster theory. The nonlinear coupled-cluster equations are also treated with the RLE by assuming an approximate linearization of the nonlinear terms. Very efficient convergence for linear systems and good convergence for nonlinear equations are found for a number of examples that manifest some degeneracy. These include the Be atom, H2 at large separation, and the N2 molecule. The RLE method is compared to the conventional iterative procedure and to Padé approximants. The relationship between the projection method and least square methods for reducing systems of equations is discussed.