Relativistic Spin-Polarized Density-Functional Theory: Simplified Method for Fully Relativistic Calculations

Abstract

In the relativistic spin-polarized density-functional theory the one-electron wave functions are solutions of a Dirac equation containing a symmetry-breaking term. As a consequence, the wave functions cannot be separated in an angular and a radial part. No attempt to solve exactly this equation has been done till now. In general, one looks for approximate solutions which can be determined by solving a system of two coupled radial Dirac equations. The solution of this system is not easy, and only a few non-self-consistent solid-state calculations based on it have been performed. In this paper we will discuss a method which permits to find very accurate approximate solutions of the coupled equations by solving two uncoupled Dirac equations. The new method is easy to apply, numerically more stable and less computing time consuming than the original one. Furthermore, the tests we have performed seem to indicate that the loss of accuracy introduced by the new approximation is negligible.