The article discusses various approximations used in electronic structure calculations, particularly focusing on the local-density approximation (LDA) and its relativistic extensions. The LDA approximates the many-electron problem by solving single-particle equations using the self-consistent field method. The total energy is minimized, taking into account kinetic, Coulomb, electron-nucleus, and exchange-correlation energies.
The local-spin-density approximation (LSD) generalizes the LDA by treating the spin-degree of freedom nontrivially. The relativistic local-density approximation (RLDA) is obtained by substituting the relativistic kinetic-energy operator for the non-relativistic counterpart and using relativistic corrections to the local-density functional.
The article also introduces the scalar-relativistic local-density approximation (ScRLDA), a simplified version of the RLDA that neglects spin-orbit splitting while including other relativistic effects. The ScRLDA is characterized by a single radial equation involving the parameter M, which depends on the fine structure constant α and the eigenvalue ε.
Overall, the article provides a detailed mathematical description of various approximations used in electronic structure calculations, with a focus on the LDA and its relativistic extensions. The approximations aim to simplify the many-electron problem while capturing essential relativistic effects.
Keywords: density, relativistic, local-density, approximation, electron
