# OPLS

The OPLS (Optimized Potentials for Liquid Simulations) force field was developed by Prof. William L. Jorgensen at Purdue University and later at Yale University.

## Functional form

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".

## Parameterization

Several sets of OPLS parameters have been published. There is OPLS-ua (united atom), which includes hydrogen atoms next to carbon implicitly in the carbon parameters, and can be used to save simulation time. OPLS-aa (all atom) includes every atom explicitly. Later publications include parameters for other specific functional groups and types of molecules such as carbohydrates. OPLS simulations in aqueous solution typically use the TIP4P or TIP3P water model.

A distinctive feature of the OPLS parameters is that they were optimized to fit experimental properties of liquids, such as density and heat of vaporization, in addition to fitting gas-phase torsional profiles.

## Implementation

The reference implementations of the OPLS force field are the BOSS and MCPRO programs developed by Jorgensen. Other packages such as TINKER, GROMACS, PCMODEL, Abalone, Hyperchem, LAMMPS and NAMD also implement OPLS force fields.

## References

• Jorgensen WL, Tirado-Rives J (1988). "The OPLS Force Field for Proteins. Energy Minimizations for Crystals of Cyclic Peptides and Crambin". J. Am. Chem. Soc. 110 (6): 1657–1666. doi:10.1021/ja00214a001.
• Jorgensen WL, Maxwell DS, Tirado-Rives J (1996). "Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids". J. Am. Chem. Soc. 118 (45): 11225–11236. doi:10.1021/ja9621760.