OPLS

The functional form of the OPLS force field is very similar to that of AMBER:

${\displaystyle E\left(r^{N}\right)=E_{\mathrm {bonds} }+E_{\mathrm {angles} }+E_{\mathrm {dihedrals} }+E_{\mathrm {nonbonded} }}$

${\displaystyle E_{\mathrm {bonds} }=\sum _{\mathrm {bonds} }K_{r}(r-r_{0})^{2}\,}$

${\displaystyle E_{\mathrm {angles} }=\sum _{\mathrm {angles} }k_{\theta }(\theta -\theta _{0})^{2}\,}$

${\displaystyle E_{\mathrm {dihedrals} }=\sum _{\mathrm {dihedrals} }\left({\frac {V_{1}}{2}}\left[1+\cos(\phi -\phi _{1})\right]+{\frac {V_{2}}{2}}\left[1-\cos(2\phi -\phi _{2})\right]+{\frac {V_{3}}{2}}\left[1+\cos(3\phi -\phi _{3})\right]+{\frac {V_{4}}{2}}\left[1-\cos(4\phi -\phi _{4})\right]\right)}$

${\displaystyle E_{\mathrm {nonbonded} }=\sum _{i>j}f_{ij}\left({\frac {A_{ij}}{r_{ij}^{12}}}-{\frac {C_{ij}}{r_{ij}^{6}}}+{\frac {q_{i}q_{j}e^{2}}{4\pi \epsilon _{0}r_{ij}}}\right)}$

with the combining rules ${\displaystyle A_{ij}={\sqrt {A_{ii}A_{jj}}}}$ and ${\displaystyle C_{ij}={\sqrt {C_{ii}C_{jj}}}}$.

Intramolecular nonbonded interactions ${\displaystyle E_{\mathrm {nonbonded} }}$ are counted only for atoms three or more bonds apart; 1,4 interactions are scaled down by the "fudge factor" ${\displaystyle f_{ij}=0.5}$, otherwise ${\displaystyle f_{ij}=1.0}$. All the interaction sites are centered on the atoms; there are no "lone pairs".