Keesom potential

The Keesom potential is a Boltzmann average over the dipolar section of the Stockmayer potential, resulting in

$\Phi _{12}(r)=4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]-{\frac {1}{3}}{\frac {\mu _{1}^{2}\mu _{2}^{2}}{(4\pi \epsilon _{0})^{2}k_{B}Tr_{12}^{6}}}$

where:

• $\Phi _{12}(r)$ is the intermolecular pair potential between two particles at a distance r;
• $\sigma$ is the diameter (length), i.e. the value of $r$ at $\Phi (r)=0$ ;
• $\epsilon$ : well depth (energy)
• $\mu$ is the dipole moment
• $T$ is the temperature
• $k_{B}$ is the Boltzmann constant
• 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_0} is the permitiviy of free space.

For dipoles disolved in a dielectric medium, this equation may be generalized by including the dielectric constant of the medium within the 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 4\pi\epsilon_0} term.

References

1. Richard J. Sadus "Molecular simulation of the vapour-liquid equilibria of pure fluids and binary mixtures containing dipolar components: the effect of Keesom interactions", Molecular Physics 97 pp. 979-990 (1996)