[@he:99; @mueser:01], which is also recovered from thermodynamic considerations [@gao:04]. Other studies report a greater than linear [@gosvami:10], or sublinear dependence of the friction force on load [@wenning:01; @luan:05; @mo:09] where the latter is consistent with classic Hertzian contact mechanics [@hertz:1881]. Also even more complex dependencies of the friction force on the load have been reported [@eder:11; @vernes:12]. A more general overview on friction simulations on the nanoscale may be found in two recent reviews [@dong:13; @vanossi:13b]. Friction forces can also depend on the sliding direction as shown in experiments on rather complex geometries [@overney:94; @park:05], and recently by Weymouth et al. for a single atom asperity [@weymouth:13].

While the conventional method of choice for simulating atomic scale friction is classical molecular dynamics (MD), see Ref.  and references therein, *ab-initio* density-functional-theory (DFT) apporaches [@hohenberg:64; @kohn:65] have become more common during recent years [@garvey:11a; @garvey:11b; @garvey:11c; @zibilotti:11; @cahangirov:12; @lf_wang:12; @j_wang:12; @kwon:12]. This is due to advantages in accuracy and the increasing power of computers which retain the simulation time manageable. In classical MD simulations, energy becomes dissipated to a heat bath via a thermostat, a method which is in principle also possible for DFT calculations. As simulation times for *ab-initio* MD 