# Keesom potential

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

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

where:

• ${\displaystyle r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|}$
• ${\displaystyle \Phi _{12}(r)}$ is the intermolecular pair potential between two particles at a distance r;
• ${\displaystyle \sigma }$ is the diameter (length), i.e. the value of ${\displaystyle r}$ at ${\displaystyle \Phi (r)=0}$ ;
• ${\displaystyle \epsilon }$ : well depth (energy)
• ${\displaystyle \mu }$ is the dipole moment
• ${\displaystyle T}$ is the temperature
• ${\displaystyle k_{B}}$ is the Boltzmann constant
• ${\displaystyle \epsilon _{0}}$ is the permitiviy of free space.

For dipoles dissolved in a dielectric medium, this equation may be generalized by including the dielectric constant of the medium within the ${\displaystyle 4\pi \epsilon _{0}}$ term.

## References

1. W. H. Keesom "On the Deduction from Boltzmann’s Entropy Principle of the Second Virial-coefficient for Material Particles (in the Limit Rigid Spheres of Central Symmetry) which Exert Central Forces Upon Each Other and For Rigid Spheres of Central Symmetry Containing an Electric Doublet at Their Centers", Communications Physical Laboratory University of Leiden Supplement, Ed. By H. Kamerlingh Onnes, Eduard Ijdo Printer, Leiden, Supplement 24b to No. 121-132 pp. 23-41, (1912)
2. 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)