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.