m-6-8 potential function

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) = \frac{A}{r^m} - \frac{C_6}{r^6} -\frac{C_8}{r^8}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) } is the intermolecular pair potential between two particles or sites. $A$ is the coefficient corresponding to the repulsive term, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_6} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi^* = \Phi/\epsilon} , $r^{*}=r/r_{m}$ and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma = C_8/r_m^8} . Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon} is the "well" depth, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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)