# m-6-8 potential function

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

${\displaystyle \Phi _{12}(r)={\frac {A}{r^{m}}}-{\frac {C_{6}}{r^{6}}}-{\frac {C_{8}}{r^{8}}}}$

where ${\displaystyle r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|}$ and ${\displaystyle \Phi _{12}(r)}$ is the intermolecular pair potential between two particles or sites. ${\displaystyle A}$ is the coefficient corresponding to the repulsive term, and ${\displaystyle C_{6}}$ and ${\displaystyle C_{8}}$ are the coefficients corresponding to the attractive inverse sixth and eighth powers respectively.

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

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

where ${\displaystyle \Phi ^{*}=\Phi /\epsilon }$, ${\displaystyle r^{*}=r/r_{m}}$ and ${\displaystyle \gamma =C_{8}/r_{m}^{8}}$. ${\displaystyle \epsilon }$ is the "well" depth, and ${\displaystyle r_{m}}$ is the intermolecular separation at the maximum well depth.