# 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.