Asymptotic behavior of the primitive function of different “symmetry‐adapted” perturbation schemes for the H ground state

Abstract

AbstractThe leading terms in the asymptotic 1/R expansion of the wave functions and energies of various “symmetry‐adapted” perturbation schemes for intermolecular forces, as well as for the “polarization approximation” (PA) are derived for the H ground state, both exactly (i.e., to infinite order in λ) and in the first two orders of the λ expansion. It is pointed out that only in the PA and the Hirschfelder–Silbey scheme is the formal primitive function Φ genuinely primitive, whereas Φ in the other schemes is asymmetric in a rather strange way. In this lack of genuine primitivity lies the reason why in these schemes the leading term of the 1/R expansion is only recovered to infinite order in λ and requires knowledge of the R−4 term of the wave function, provided that one uses the “internal” energy expression. Four different energy expressions are compared that behave differently in the different schemes. The results obtained here are basis independent, but the implications of the basis completeness problem are discussed as well.