Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules

Abstract

We use the Morse and the Deng-Fan potentials to treat the X-H stretching motion in small molecules. The Deng-Fan potential is qualitatively similar to the Morse potential but has the correct asymptotic behaviour as the internuclear distance approaches 0. We use the Deng-Fan potential to calculate transition frequencies and intensities of overtones of X-H stretching vibrations. Parameters for the Morse oscillator can readily be found from a Birge-Sponer fit of experimental transition frequencies. We describe a procedure to find the parameters for the Deng-Fan oscillator. We compare the potentials, wavefunctions, and matrix elements of the Morse and the Deng-Fan oscillator models. In the examples considered the Deng-Fan potential does not predict observed energy levels and intensities significantly better than the Morse potential despite its correct asymptotic behaviour.