Electron-ion dynamics: A technique for simulating both electronic transitions and ionic motion in molecules and materials

We describe a technique for simultaneously treating the dynamics of electrons and ions. The key features are a generalized Hellmann-Feynman theorem, a standard time-dependent self-consistent-field (TDSCF) description, and use of the interaction picture to separate fast electronic oscillations from slower processes. The technique can be used in tight-binding or first-principles simulations, with either a ground-state or TDSCF Hamiltonian.