In a DFT calculation, the nuclei are obliged to stand still while the electrons dance. By repositioning the nuclei and repeating the calculation many times, we can map out the electronic density everywhere in nuclear configuration space. This electronic density is a conditional probability, depending parametrically on the nuclear coordinates. But since DFT assumes the electrons are always in the Born-Oppenheimer ground state, it misses contributions from other eigenstates.
This talk will present a functional theory in which the electronic density and nuclear wave function are obtained variationally without recourse to the Born-Oppenheimer approximation. Like DFT, the theory is useful for both molecules and solids. I will survey some illustrative examples, including charge transfer in heterodiatomic molecules, nonadiabatic effects at conical intersections, vibration-induced band structure renormalization, and nonadiabatic corrections to the phonons in density functional perturbation theory.