# m-6-8 potential function

The m-6-8 potential function [1] is given by (Eq. 1)

$\Phi_{12}(r) = \frac{A}{r^m} - \frac{C_6}{r^6} -\frac{C_8}{r^8}$

where $r := |\mathbf{r}_1 - \mathbf{r}_2|$ and $\Phi_{12}(r)$ is the intermolecular pair potential between two particles or sites. $A$ is the coefficient corresponding to the repulsive term, and $C_6$ and $C_8$ are the coefficients corresponding to the attractive inverse sixth and eighth powers respectively.

This expression can be rewritten in the reduced form (Eq. 2):

$\Phi^*_{12}(r^*) = \left[ \frac{1}{m-6} \right] \left[ 6+2\gamma \right] \left( \frac{1}{r^*} \right)^m - \left[ \frac{1}{m-6} \right] \left[ m-\gamma(m-8)\right]\left( \frac{1}{r^*} \right)^6 - \frac{\gamma}{r^{*8}}$

where $\Phi^* = \Phi/\epsilon$, $r^* = r/r_m$ and $\gamma = C_8/r_m^8$. $\epsilon$ is the "well" depth, and $r_m$ is the intermolecular separation at the maximum well depth.