On the representation of long-range potentials by a [1, 0] Padé approximant

Abstract

The utility of the [1, 0] Padé approximant in the determination of long-range interaction constants is investigated using the recently calculated Rydberg-Klein-Rees potentials for the B³Π_Ou ⁺ states of I₂, Br₂ and Cl₂. The conditions under which the [1, 0] Padé approximant is a valid representation of the long-range potential outside the electron-overlap region are studied in detail, using as model systems the B states of I₂, Br₂ and Cl₂, and the X¹Σg⁺, B¹Σu⁺ and B′¹Σu⁺ states of H₂. In general, the validity of the representation depends on the nature of the potential, and is governed by

if the long-range potential can be adequately represented by a maximum number of three terms (n, m, m1) in the inverse-power expansion.