Electric dipole-dipole interaction

The electric dipole-dipole interaction is the orientation-dependent potential energy of two electric dipoles. For fixed point electric dipole moments ${\mathbf{p}}_1,{\mathbf{p}}_2$ separated by $\mathbf{r}=r\hat{\mathbf{r}}$ in vacuum,Here ${ϵ}_0$ is the vacuum permittivity. For extended neutral objects this is the leading interaction when their separation is large compared with their sizes and their electric dipole moments are nonzero.

To derive the expression, evaluate the first electric dipole's electric field,and use $U=-{\mathbf{p}}_2\cdot {\mathbf{E}}_1$. The potential energy of a fixed electric dipole in an applied electric field follows by expanding the two constituent charges' electrostatic potential energies. ^[ref]

For equal parallel electric dipole moments of magnitude $p$, a head-to-tail arrangement has $U=-2p^2/(4\pi {ϵ}_0{r}^3)$ and is attractive along the separation direction. Placing the same parallel electric dipoles side by side gives $U=p^2/(4\pi {ϵ}_0{r}^3)$ and a repulsive radial force. A freely rotating pair can also experience a torque; the orientation is part of the physical specification.

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.

Reduction of an effective electric dipole moment by the opposing local field of neighboring dipoles.