Size dependence of delocalized treatments of the correlation problem

Using a perfectly localized perfectly delocalizable model problem, which reduces to N identical noninteracting electron pairs, the N dependences of various perturbative corrections for the correlation problem have been established. These theoretical results for the zero interaction case are verified to a surprising accuracy in strongly delocalized problems (π polyenes), namely the invariance of the Moller–Plesset corrections under localization of the MO’s, and its proportionality to the number of electron pairs, the Epstein–Nesbet satisfactory N dependence for localized pictures and its meaningless behavior for delocalized pictures. Using delocalized MO’s the doubly excited determinants belong to two classes with respect to their interaction with the ground state SCF determinant, N3 interacting through a N−1 matrix element, the N4 others interacting through N−2 matrix elements. These phenomena may have undesirable consequences on approximate variational CI techniques. In view of the N dependence, the use of delocalized MO’s for correlation calculations seems perfectly irrelevant.