  While there are a number of models that tackle the problem of calculating
friction forces on the atomic level, providing a completely parameter-free
approach remains a challenge. Here we present a quasi-static model to obtain an
approximation to the nanofrictional response of dry, wearless systems based on
quantum mechanical all-electron calculations. We propose a mechanism to allow
dissipative sliding, which relies on atomic relaxations. We define two
different ways of calculating the mean nanofriction force, both leading to an
exponential friction-versus-load behavior for all sliding directions. Since our
approach does not impose any limits on lengths and directions of the sliding
paths, we investigate arbitrary sliding directions for an fcc Cu(111) interface
and detect two periodic paths which form the upper and lower bound of
nanofriction. For long aperiodic paths the friction force convergences to a
value in between these limits. For low loads we retrieve the Derjaguin
generalization of Amontons-Coulomb kinetic friction law which appears to be
valid all the way down to the nanoscale. We observe a non-vanishing
Derjaguin-offset even for atomically flat surfaces in dry contact.
