Dynamical Born effective charges

We extend the definition of the Born effective charge to the dynamical regime. This is equal to the Fourier transform of the total electronic current divided by the Fourier transform of the velocity of a particular nucleus. The usual static Born effective charges are recovered in the zero-frequency limit. We calculate these charges for a selection of materials using time-dependent density functional theory in an all-electron code where the nuclei move along a chosen trajectory. A rich response function emerges with prominent resonance peaks. The finite value for the Born effective charge of metals is also reproduced. The dynamical Born effective charges are thus a natural choice of observable for probing the fundamental nonadiabatic coupling of electrons and nuclei.