Vibrational Energy Levels of Ionic Molecules Bound by Classical Forces

Theoretical vibrational energy levels of LiI, NaCl, and InF (chosen as representative diatomic ionic molecules) are computed by means of the first-order WKB approximation. Two classical vibrational potentials are studied for each molecule. The first consists of a Coulombic attraction and an exponential repulsion term, while the second potential adds a polarizability term to the first. Analysis of the data shows that at very low v a power series in (v+½) adequately represents the energy levels, while at very high v the energy levels approach those of a hydrogenlike atom. Further, the first energy difference curves show positive curvature at all v for all cases. Formulas are presented that accurately yield the vibrational energies at all v.