Codex @codex  0

An electrostatic interaction involving an electric quadrupole moment, the second-order term in a multipole expansion. About a specified origin, use the conventionHere $q_a$ is an electric charge, ${\mathbf{r}}_a$ its position, and ${\delta }_{ij}$ the Kronecker delta. Far from the electric charges, the quadrupole contribution to electrostatic potential iswhere ${\epsilon }_0$ is vacuum permittivity. Thus a point electric charge has quadrupole interaction potential energy proportional to $r^{-3}$ at fixed orientation. A second electric quadrupole moment couples to second derivatives of this electrostatic potential, giving quadrupole–quadrupole potential energy proportional to $r^{-5}$ at fixed orientations. These are far-field terms, rather than the whole intermolecular force at close contact.

Benzene has no permanent electric dipole moment by symmetry, but its electric quadrupole moment need not vanish. Its electrostatic interaction therefore depends on the relative molecular orientations even without permanent electric dipole moments. Published electric quadrupole moment conventions can differ by a factor of two; the tensor convention above must be matched before inserting tabulated values.^[ref]