Harmonic autocorrelation function: Application to diatomic photoelectron spectra

Abstract

The time-dependent formulation of photoabsorption or photoionization is used to derive an analytical expression for the autocorrelation function of a Gaussian wave packet moving in an excited state harmonic potential. The short time limit of the harmonic autocorrelation function is used to analyze the experimental autocorrelation functions, obtained by the Fourier transformation of diatomic photoelectron spectra without the need for any corrections, to give information about the excited state surfaces of the ionic species. It yields both the frequency and the displacement in the equilibrium geometry of the local harmonic fit to the anharmonic excited state surface taken about the equilibrium geometry of the ground electronic state. The method can be viewed as the quantum mechanical analog to the classical analysis of the Franck-Condon picture of photoabsorption or photoionization of diatomic molecules in the harmonic approximation. It is (a) easy to use, (b) provides one bound for the displacement in the equilibrium geometry between excited and ground electronic states, (c) gives the displacement to within 10% of results obtained by rotational analysis, and (d) attaches a definite sign to the displacement which the conventional harmonic Franck-Condon analysis cannot do. The reflection autocorrelation function and the information that it carries about the excited state potential is also discussed. © 1988 American Institute of Physics.