Keesom potential

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

${\mathrm{\Phi }}_{12}(r)=4ϵ[{(\frac{\sigma }{r})}^{12}-{(\frac{\sigma }{r})}^6]-\frac{1}{3}\frac{\underset{1}{\overset{2}{\mu }}\underset{2}{\overset{2}{\mu }}}{(4\pi {ϵ}_0{)}^2{k}_{B}T{r}_{12}^6}$

where:

• ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential between two particles at a distance r;
• $\sigma$ is the diameter (length), i.e. the value of $r$ at $\mathrm{\Phi }(r)=0$ ;
• $ϵ$ : well depth (energy)
• $\mu$ is the dipole moment
• $T$ is the temperature
• $k_B$ is the Boltzmann constant
• ${ϵ}_0$ 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 $4\pi {ϵ}_0$ 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)