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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 (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.

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