Axilrod-Teller potential

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

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

where $r i j$ is the distance between atoms $i$ and $j$ , and $γ i$ is the angle between the vectors $\mathbf{r}_{ij}$ and $\mathbf{r}_{ik}$ . The coefficient $E 0$ is positive and of the order $V α 3$ , where $V$ is the ionization energy and $α$ 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.