Bound vibrational states for weakly attractive potentials

Abstract

An empirical form for the potential energy curve of a diatomic molecule which closely resembles the frequently used 6–12 potential is:

This has the advantage over the 6–12 potential that it gives simple analytic form for the ground state solution of the Schrödinger equation:

It is shown how the parameters a and λ may be fitted to the coordinates of the potential minimum, and how it may be used to define upper and lower bounds to the lowest eigenvalue of any non-empirical potential. The diatomics He₂ and Ne₂ are specifically considered.