3.1. CHARMM Force Field

In ABCrystal, the function to assess the crystal stability is enthalpy:

\[H = U + PV\]

Here, \(P\) is the external pressure in bar, \(V\) is the cell volume, and \(U\) is the internal potential energy described by CHARMM force field:

\[U = \sum_{I}\sum_{J<I}u_{IJ\mathbf{0}}+\frac{1}{2}\sum_{\mathbf{n}\ne\mathbf{0}}\sum_{I}\sum_{J}u_{IJ\mathbf{n}}\]

\[\begin{split}\begin{split} u_{IJ\mathbf{n}} = & \sum_{i \in I}\sum_{j \in J}\left( \frac{e^{2}}{4\pi\epsilon_{0}}\frac{q_{i}q_{j}}{r_{ij\mathbf{n}}} +4\epsilon_{ij}\left(\left(\frac{\sigma_{ij}}{r_{ij\mathbf{n}}}\right)^{12}-\left(\frac{\sigma_{{ij}}}{r_{ij\mathbf{n}}}\right)^{6}\right) \right) \\ \end{split}\end{split}\]

\[r_{ij\mathbf{n}} = \left|\mathbf{r}_i-\mathbf{r}_j+n_1\mathbf{T}_1+n_2\mathbf{T}_2+n_3\mathbf{T}_3 \right|\]

In this formula, \(I\) and \(J\) are indices for molecules; \(i\) and \(j\) are indices for atoms in molecule \(I\) and \(J\), respectively; \(N\) is the total number of molecules; \(\mathbf{T}_1,\mathbf{T}_2,\mathbf{T}_3\) are the 3 vectors describing the cell; \(\mathbf{n}\) is 3 integers \(n_1,n_2,n_3\). 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 \(\sigma\). Their units are:

Parameter	Unit
\(q\)	e
\(\epsilon\)	kJ mol -1
\(\sigma\)	Å
\(P\)	bar

For many molecules, the CHARMM parameters \(q\), \(\epsilon\), and \(\sigma\) have been provided in ABCrystal distributions misc/charmm36. 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.