Vibrational levels and Franck–Condon factors of diatomic molecules via Morse potentials in a box

This work deals with two shortcomings in the use of Morse potentials to describe energy spectra and transitions of diatomic molecules: (1) Morse's well‐known “exact” solution for purely vibrational states includes the unphysical region – ∞ < r < 0 of the internuclear separation, and (2) Franck‐Condon factors are evaluated in harmonic and anharmonic approximations to the Morse potentials. The method of confining the molecule in a spherical box is developed to obtain (1) purely vibrational energy spectra and eigenvectors of Morse potentials in the physical region 0 ⩽ r < ∞, and (2) the corresponding Franck‐Condon factors without any additional approximations. The method is applied to Li 2 , N 2 , CN, and CO molecules. © 1995 John Wiley & Sons, Inc.