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



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.