Lennard-Jones-Potential
\begin{aligned}
U_\mathrm{LJ}(r) & = 4\epsilon \left[
\left( \frac{\sigma}{r} \right)^{12}
- \left( \frac{\sigma}{r} \right)^{6}
\right] \\
F_\mathrm{LJ}(r) = -\frac{\mathrm{d} U(r)}{\mathrm{d}r} & =
\frac{4\epsilon}{\sigma} \left[
12 \left( \frac{\sigma}{r} \right)^{13}
- 6 \left( \frac{\sigma}{r} \right)^{7}
\right] \\
\end{aligned}