Axilrod-Teller potential

The Axilrod-Teller potential is a three-body potential that results from a third-order perturbation correction to the attractive London dispersion interactions

:$V\_\{ijk\}=\; E\_\{0\}\; left\; [\; frac\{1\; +\; 3\; cosgamma\_\{i\}\; cosgamma\_\{j\}\; cosgamma\_\{k\{left(\; r\_\{ij\}\; r\_\{jk\}\; r\_\{ik\}\; ight)^3\}\; ight]$

where $r\_\{ij\}$ is the distance between atoms $i$ and $j$, and $gamma\_\{i\}$ is the angle between the vectors $mathbf\{r\}\_\{ij\}$ and $mathbf\{r\}\_\{ik\}$. The coefficient $E\_\{0\}$ is positive and of the order $Valpha^\{3\}$, where $V$ is the ionization energy and $alpha$ is the mean atomic polarizability; the exact value of $E\_\{0\}$ depends on the magnitudes of the dipole matrix elements and on the energies of the $p$ orbitals.

References

Axilrod BM and Teller E. (1943) "Interaction of the van der Waals Type between Three Atoms", "J. Chem. Phys.", 11, 299-300.