Transverse electric-dipole pair energy

The point-dipole energy is $[{\mathbf{p}}_1\cdot {\mathbf{p}}_2-3({\mathbf{p}}_1\cdot \hat{r})({\mathbf{p}}_2\cdot \hat{r})]/(4\pi {ϵ}_0{r}^3)$. If the separation is perpendicular to the first dipole, the second term vanishes. Parallel dipoles then have positive energy $p_1{p}_2/(4\pi {ϵ}_0{r}^3)$, while mutually perpendicular dipoles give zero in this approximation. Real molecular interactions can include multipoles, induction and short-range contributions beyond this point-dipole term.