Knowledge Bank

Theoretical energy levels of LiI, NaCl, and InF (chosen as representative diatomic ionic molecules.) have been calculated up to vibrational quantum number v = 10,000. Two classical vibrational potentials were studied for each molecule. The first potential consisted of the Coulombic attraction term and a nuclear repulsion term, while the second added a polarizability term to the first. The vibrational energy levels were computed with an IBM 704 program, using a first order WKB approximation. Analysis of the data shows that at very low v () a power series adequately represents the energy levels, while at very high values, of $v(v\to \infty )$ the energy levels approach H atom-like energies corresponding to a 1/r Coulombic potential. Further, the first energy difference curves show positive curvature at all v for all cases. Formulae will be presented that accurately yield the vibrational energies and first differences at all v.