are very short and thermostating is difficult due to a rapid heating of the electronic system, it is desirable to formulate a different way to describe dissipative sliding and to predict coefficients of friction within DFT. This may be done by computing potential energy landscapes and fitting the resulting energy barriers to mechanical models, for example the well known Prandtl-Tomlinson model [@prandtl:28; @tomlinson:29]. Another approach was suggested by Zhong and Tománek, who, in their “maximum-friction microscope” model, assume a complete dissipation of the potential energy into phonons and electronic excitations for each slip [@zhong:90; @tomanek:91].

Considering all these different concepts and methods, we attempt to formulate the problem of dry sliding friction on the basis of parameter-free (*ab-initio*) calculations, which rely only on the quantum-mechanical interactions of the sliding bodies. To this end we propose energy dissipation via the relaxations in the sliding materials themselves as calculated *ab-initio*. We will show that the concept allows to analyse arbitrary sliding directions and sliding paths up to $\mu m$ scale in length with a single initial set of DFT calculations. This permits us to gain insight into the different behavior of periodic and aperiodic (defined below) sliding directions by bridging four orders 