  We develop a novel approach to the coupled motion of electrons and ions that
focuses on the dynamics of the electronic subsystem. Usually the description of
electron dynamics involves an electronic Schr\"odinger equation where the
nuclear degrees of freedom appear as parameters or as classical trajectories.
Here we derive the exact Schr\"odinger equation for the subsystem of electrons,
staying within a full quantum treatment of the nuclei. This exact Schr\"odinger
equation features a time-dependent potential energy surface for electrons
(e-TDPES). We demonstrate that this exact e-TDPES differs significantly from
the electrostatic potential produced by classical or quantum nuclei.
