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# 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.

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