Time-dependent approach to the calculation of spectral functions

A time-dependent generalization of the $\exp \mathrm{}\left(S\right)\mathrm{}$ (or coupled-cluster) method of Coester and Kümmel is presented and is used for the calculation of spectral functions of (infinite) Fermi systems. This leads to an alternative formulation of the problem for noninteracting Fermions and to new approximation schemes for interacting systems. The formalism is applied to the calculation of core-level spectra of adsorbed atoms and molecules, taking the Coulomb repulsion in the adsorbate valence level into account. In the limiting cases of strong and weak adsorbate-substrate coupling we obtain agreement with the time-dependent Hartree-Fock approximation and a perturbation expansion, respectively. Due to the nonperturbative character of our treatment, it is possible for the first time to obtain results also for intermediate coupling (weak chemisorption).