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