and the system slips into the next minimum. This energy is actually underestimated by $\sim 25\%$ within our proposed quasi-static friction model at $E_{\mathrm{qs}}(0^\circ)=\unit[156]{meV}$ although we include contributions of the unrelaxed energy curve (see figure \[fig:2\] and equation (\[eq:F2\])). In contrast, applying the model by Zhong and Tománek [@zhong:90; @tomanek:91] to the relaxed energy curve underestimates the dissipated energy during shearing by more than 80% at $E_{\mathrm{ZT}}(0^\circ)=\unit[38]{meV}$.

For the $30^\circ$ (see figure \[fig:shear\_30\]) sliding direction the situation is different, as the shearing appears to become periodic only after the first slip with a much shorter period than in our quasi static model. Three small slips of roughly equal size happen during a sliding distance of $\sim\unit[4.2]{\AA}$ (from $l\sim\unit[2.0]{\AA}$ to $l\sim\unit[6.2]{\AA}$ in figure \[fig:shear\_30\]), which is comparable to one period in our quasi-static model of $\sim\unit[4.4]{\AA}$ where one small and one large slip occur. While the predicted slipping process is different the energetics are in excellent agreement, with $E_{\mathrm{qs}}(30^\circ)=\unit[286]{meV}$ being lost per period in our model and $E_{\mathrm{shear}}(30^\circ)=\unit[287]{meV}$ dissipated in three slips during shearing. Using the model of Zhong and Tománek underestimates the energy severely again at $E_{\mathrm{ZT}}(30^\circ)=\unit[104]{meV}$.

![A comparison between our friction model and a shearing simulation for the periodic 