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)

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

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