# 4.1. CHARMM Force Field

The potential energy of clusters in rigidmol assumes the following form:

$\begin{split}\begin{split} U_{\mathrm{CHARMM}} = & \sum_{I=1}^{N}\sum_{I<J}^{N}\sum_{i_{I} \in I}\sum_{j_{J} \in J}\left( \frac{e^{2}}{4\pi\epsilon_{0}}\frac{q_{i_{I}}q_{j_{J}}}{r_{i_{I}j_{J}}} +4\epsilon_{i_{I}j_{J}}\left(\left(\frac{\sigma_{i_{I}j_{J}}}{r_{i_{I}j_{J}}}\right)^{12}-\left(\frac{\sigma_{{i_{I}j_{J}}}}{r_{i_{I}j_{J}}}\right)^{6}\right) \right)+ \\ & \sum_{I=1}^{N}\sum_{i_{I} \in I}\left(q_{i_I}e F z_{i_I} \right) \\ \end{split}\end{split}$

In this formula, $$I$$ and $$J$$ are indices for molecules; $$i_I$$ and $$j_J$$ are indices for atoms in molecule $$I$$ and $$J$$, respectively; $$N$$ is the total number of molecules. The first term describes the intermolecular Coulomb and Lennard-Jones interactions; the second term describes the interactions between molecules and external static electric field. For a molecule, you have to provide CHARMM parameters: charge $$q$$, Lennard-Jones well depth $$\epsilon$$ and width $$\sigma$$. You may also need to provide electric field strength $$F$$ if it is not zero. Their units are:

Parameter

Unit

$$q$$

e

$$\epsilon$$

kJ mol -1

$$\sigma$$

Å

$$F$$

V Å -1

For many molecules, the CHARMM parameters $$q$$, $$\epsilon$$, and $$\sigma$$ have been provided in ABCluster distributions. You can directly use these parameter files.

Tip

These CHARMM parameter files are provided in: misc/charmm36. For example, the parameter file for water $$\mathrm{H}_2\mathrm{O}$$ and potassium cation $$\mathrm{K}^{+}$$ is tip4p.xyz and k.xyz, respectively.