  Molecular adsorbates on metal surfaces exchange energy with substrate phonons
and low-lying electron-hole pair excitations. In the limit of weak coupling,
electron-hole pair excitations can be seen as exerting frictional forces on
adsorbates that enhance energy transfer and facilitate vibrational relaxation
or hot-electron mediated chemistry. We have recently reported on the relevance
of tensorial properties of electronic friction [Phys. Rev. Lett. 116, 217601
(2016)] in dynamics at surfaces. Here we present the underlying implementation
of tensorial electronic friction based on Kohn-Sham Density Functional Theory
for condensed phase and cluster systems. Using local atomic-orbital basis sets,
we calculate nonadiabatic coupling matrix elements and evaluate the full
electronic friction tensor in the classical limit. Our approach is numerically
stable and robust as shown by a detailed convergence analysis. We furthermore
benchmark the accuracy of our approach by calculation of vibrational relaxation
rates and lifetimes for a number of diatomic molecules at metal surfaces. We
find friction-induced mode-coupling between neighboring CO adsorbates on
Cu(100) in a c(2x2) overlayer to be important to understand experimental
findings.
