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.