Dispersion dipoles for coupled Drude oscillators

We present the dispersion-induced dipole moments of coupled Drude oscillators obtained from two approaches. The first approach evaluates the dipole moment using the second-order Rayleigh-Schrödinger perturbation theory wave function allowing for dipole-dipole and dipole-quadrupole coupling. The second approach, based on response theory, employs an integral of the dipole-dipole polarizability of one oscillator and the dipole-dipole-quadrupole hyperpolarizability of the other oscillator over imaginary frequencies. The resulting dispersion dipoles exhibit an R^-7 dependence on the separation between the two oscillators and are connected to the leading-order C₆/R⁶ dispersion energy through the electrostatic Hellmann-Feynman theorem.