Advantages of a Nonharmonic-Oscillator Analysis of Molecular Vibrations

It is suggested that the theory of molecular vibrations, currently based on the harmonic oscillator potential, should be reformulated in terms of the potential $V=K{\left[\frac{(x-x_e)}{x}\right]}^2$. The proposed potential is shown to possess numerous advantages, including an improved physical form, superior eigenfunctions and eigenvalues, the ability to include rotation analytically, and a set of continuum wave functions. The standard classical vibrational analyses are retained.