Non-adiabaticity from first principles: the exact-factorization approach for solids

TL;DR

This paper develops a first-principles perturbative approach based on the exact factorization method to systematically include non-adiabatic effects in the electronic structure calculations of solids.

Contribution

It introduces a novel perturbation scheme for Kohn-Sham states using the exact factorization framework, extending density functional perturbation theory to account for non-adiabatic couplings.

Findings

Derived second-order non-adiabatic corrections to electronic states.

Expressed non-adiabatic effects in terms of existing density functional perturbation theory components.

Provided a systematic way to include non-adiabatic effects in solid-state electronic structure calculations.

Abstract

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 non-adiabatic coupling effects. The exact factorization method, starting from the full Hamiltonian of electrons and nuclei, provides a way to systematically account for non-adiabatic effects. This formalism was recently developed into an ab initio density functional theory framework. Within this framework we here develop 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 non-adiabatic features in the calculated energy and wavefunction corrections are expressed in terms of readily available density functional perturbation theory components.