M-6-8 potential function

The m-6-8 potential function 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 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. 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 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):

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

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} , 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^* = 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)