An efficient reformulation of the closed-shell self-consistent electron pair theory

The closed-shell SCEP method is reformulated in terms of pairwise nonorthogonal configuration state functions with particle-hole singlet coupling. The use of a single type of external pair function instead of the usual singlet and triplet coupled pairs results in the elimination of the internal coupling coefficients in the residual vector formulas, simplifying the latter considerably. The new CI coefficients are represented as unsymmetrical quadratic matrices which are naturally adapted to the description of long-range correlation between spatially distant localized orbitals. The number of matrix multiplications required for the interorbital pair coupling terms is reduced by half. This should lead to a reduction in the total computational effort by about 30%, except for very small molecules where intraorbital correlation dominates the computation.