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)

$V_{ijk}=E_{0}\left[{\frac {1+3\cos \gamma _{i}\cos \gamma _{j}\cos \gamma _{k}}{\left(r_{ij}r_{jk}r_{ik}\right)^{3}}}\right]$

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.