m-6-8 potential function

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

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

where $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$ and ${\mathrm{\Phi }}_{12}(r)$ 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):

$\underset{12}{\overset{*}{\mathrm{\Phi }}}(r^{*})=[\frac{1}{m-6}][6+2\gamma ]{(\frac{1}{r^{*}})}^m-[\frac{1}{m-6}][m-\gamma (m-8)]{(\frac{1}{r^{*}})}^6-\frac{\gamma }{r^{*8}}$

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

References

Related reading

• R. E. Caligaris and A. E. Rodriguez "On the m‐6–8 Potential Function", Journal of Chemical Physics 56 pp. 4715-4716 (1972)