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 open-quotes exactclose quotes 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 Li2, N2, CN, and CO molecules. 23 refs., 11 tabs