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 (instantaneous induced dipole-induced dipole)

$V_{ijk}= E_{0} \left[ \frac{1 %2B 3 \cos\gamma_{i} \cos\gamma_{j} \cos\gamma_{k}}{\left( r_{ij} r_{jk} r_{ik} \right)^3} \right]$

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 $V\alpha^{3}$ , 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, B. M.; Teller, E. (1943). "Interaction of the van der Waals Type Between Three Atoms". Journal of Chemical Physics 11 (6): 299. Bibcode 1943JChPh..11..299A. doi:10.1063/1.1723844.