The conventional approach to electronic absorption spectroscopy is cast in the energy, rather than in the time domain. The conventional formula for the vibronic (vibrational + electronic) absorption spectrum is:
where
is the incident light frequency and
is the frequency of the initial state. The coefficients of the
δ-function in the sum are called
Franck-Condon factors, and reflect the overlap of the initial state with the excited state
at energy
Formally, eq. (1) gives a 'stick' spectrum. The absorption cross-section can also be written in terms of the Fourier transform of a wavepacket autocorrelation function:
where we have defined
and
and where
