Dependence of the Diatomic Rotational Constant Bν on the Long-Range Internuclear Potential

Abstract

A simple expression is derived which explicitly relates the rotational constant Bν for vibrational levels near the dissociation limit D of a diatomic molecule, to the nature of the long-range interatomic potential. Assuming a long-range potential of the form V(R) = D – Cn/Rn, the expression Bν = Qn(νD – ν)[4/(n−2)] is obtained, where νD is the effective vibrational index at the dissociation limit, and Qn is a constant depending only on n, Cn, and the reduced mass. This result is slightly less accurate than an analogous recently developed relation for the vibrational level distribution near D. Its utility and accuracy are demonstrated by application to experimental data for the [Formula: see text] states of Cl2, Br2, and I2.