Calculation of autocorrelation functions for electronic spectra

The autocorrelation function C(t) associated with the vibrational motion in the A²II_u state of N₂⁺ is calculated by three different methods. The classical method is based on classical trajectory calculations and provides good results except for secondary maxima appearing in the experimental autocorrelation function and resulting from interference effects. In the semiclassical method, the wavefunction is expanded in a basis of frozen gaussian functions. The secondary maxima are reproduced and the result is quite satisfactory. The superposition procedure consists in an expansion of the wavefunction in the eigenfunctions of the A state of N₂⁺ and leads to a very simple formula for the autocorrelation function C(t). The secondary maxima are accounted for and the calculated function agrees very well with experimental results.