  We present a perturbation approach rooted in time-dependent
density-functional theory to calculate electron hole (eh)-pair excitation
spectra during the non-adiabatic vibrational damping of adsorbates on metal
surfaces. Our analysis for the benchmark systems CO on Cu(100) and Pt(111)
elucidates the surprisingly strong influence of rather short electronic
coherence times. We demonstrate how in the limit of short electronic coherence
times, as implicitly assumed in prevalent quantum nuclear theories for the
vibrational lifetimes as well as electronic friction, band structure effects
are washed out. Our results suggest that more accurate lifetime or
chemicurrent-like experimental measurements could characterize the electronic
coherence.
