Basics of Electronic Structure Calculations

Abstract

Describing the properties of solids from first-principles theory implies solving the Schrödinger equations for a huge number of interacting electrons and nuclei. This is an impossible task even for relatively small systems. The first step to overcome this objection is given by the Born-Oppenheimer approximation. It is assumed that on the timescale of nuclear motion, the electronic subsystem is always in its stationary state. Then the motion of the nuclei is solved separately, and this gives rise to the concept of phonons. The remaining set of stationary Schrödinger equations for electrons is still too large for numerical solution. The Density Functional Theory [1, 2, 3] offers an elegant reformulation of this problem. Instead of considering many electrons in the external potential of static nuclei, non-interacting electrons in an effective potential are considered. This effective potential is a functional of the total charge density and it incorporates the effect of all the electrons and nuclei. The complexity of the initial problem is hidden in the exchange-correlation part of the potential. Solving the single-electron equations self-consistently, one obtains the equilibrium electron density and the total energy of the system.