Efficient calculation of femtosecond time-resolved photoelectron spectra: method and application to the ionization of pyrazine

A computational scheme to calculate the femtosecond time-resolved photoelectron spectrum of polyatomic molecules is outlined. The method exploits (i) the fact that the calculation of the ionization yield at a particular photoelectron energy is formally equivalent to the calculation of the total transient absorption into a single excited electronic state, and (ii) a recently proposed convolution scheme (S. Hahn and G. Stock, Chem. Phys. Lett., 1998, 296, 137), which allows for an efficient calculation of the transient absorption. Obtaining the complete photoelectron spectrum from a single transient-absorption calculation, the approach circumvents the cumbersome discretization of the electron continuum. To demonstrate its capability, the method is applied to a four-mode vibronic-coupling model of pyrazine, which includes the three lowest singlet states (S-0, S-1, S-2) as well as the two lowest cation states (I-0, I-1) of pyrazine. Explicit simulations of femtosecond ionization experiments are presented for this model and compared to recent experiments. It is demonstrated that the time-resolved photoelectron spectrum directly monitors the ultrafast S-2 --> S-1 internal conversion process in pyrazine.