Comparison of Different Polarization Schemes in Open‐shell Relativistic Density Functional Calculations

Abstract

AbstractIt is well established that, in addition to the electron density, the spin density has to be used as a basic variable in open‐shell nonrelativistic density functional calculations. This scheme can easily be extended to scalar relativistic density functional theory, since spin symmetry is retained. However, when spin‐orbit coupling is taken into account, an ambiguity arises on how to define a proper “spin density” in four‐ and two‐component open‐shell relativistic density functional calculations, because spin is no longer a good quantum number. In this context, three conceptually different polarization schemes, viz. Kramers‐unrestricted, collinear, and noncollinear, have been proposed. Systematic comparisons are necessary to reveal their performance. Based on four‐component relativistic density functional calculations performed with the BDF program package for the whole p‐block elements, it is shown that the collinear approach should not be used, since it does not provide any conceptual or computational advantages. The Kramers‐unrestricted scheme should instead be used as a replacement. For cases where the magnitude of spin‐orbit coupling is either very small or very large, the Kramers‐unrestricted and noncollinear approaches are very similar to each other. For other cases where there is a strong interplay between exchange and spin‐orbit coupling, they may differ by 0.1 to 0.2 eV. This can be ascribed either to symmetry breaking in the noncollinear approach or to account for more exchange in the Kramers‐unrestricted scheme. For systems with more than one open subshell, the Kramers‐unrestricted scheme is favored due to its maintenance of symmetry (equivalence) and computational ease.