The Franck–Condon principle and the sudden approximation

The corrections to conventional Franck–Condon factors required by the assumption that an electronic transition takes place in a non-zero time t0 are investigated using a theory based on the sudden approximation. An explicit expression using a harmonic oscillator model is given for the vibrational progression k′ ← 0″, where k′, 0″ are the vibrational quantum numbers in the final and initial states respectively. The calculations for this case suggest that the effects of a non-zero t0 will be very small for most molecular electronic spectra, but for certain long progressions the corrections become more significant and may in favourable cases be detectable, thus giving an experimental basis for the concept of a non-zero t0 and an estimate of its size. Possible examples in the spectra of diatomic molecules where this effect may be found are discussed.