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}