Nonadiabaticity from first principles: Exact-factorization approach for solids

The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many physical phenomena, it is limited in its ability to capture meaningful features originating from nonadiabatic coupling effects. The exact factorization method, starting from the full Hamiltonian of electrons and nuclei, provides a way to systematically account for nonadiabatic effects. This formalism was recently developed into an ab initio density functional theory framework. Within this framework we develop here a perturbative approach to the electronic states in solid state materials. We derive exact-factorization-based perturbations of the Kohn-Sham states up to second order in the nuclear displacements. These nonadiabatic features in the calculated energy and wave function corrections are expressed in terms of readily available density functional perturbation theory components.