Franck–Condon Factors in Electronic Excitations from the Ground and Excited Vibrational States Are Different

Vibrational fine structure observed in the published
He–I
UV photoelectron spectra of H2 and N2 molecules
recorded at room temperature and under microwave excitation or at
700 °C have been reexamined and compared with calculations of
the Franck–Condon factors (FCFs) using simple harmonic oscillator
wave functions and/or those obtained using Morse potentials. In general,
FCFs are used to explain vibronic transitions of molecules observed
in the UV–vis and photoelectron spectra of diatomic and polyatomic
molecules, which can be computed using differing levels of complexity.
We advocate constructing the vibrational wave functions numerically,
rather than analytically, with the help of a program such as Excel,
Origin, or Python. In this way students can also verify the normalization
and orthogonality of the wave functions using numerical integration
routes provided within these programs. Special attention is drawn
to possible deviations of the FCFs of the vibrationally excited molecules
from those of the ground states.