On the approximation of potential‐energy functions for two‐center systems

Abstract

Let E(R) be a potential‐energy function for a neutral or ionic diatom in the Born‐Oppenheimer approximation. Then the approximation of E(R) for 0 < R < ∞ starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F(R) = R2E(R) derive from an eigenvalue problem which depends linearly on R. The nature of the curves F(R) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable. Show more