m-6-8 potential function

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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.


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