Relativistic current- and spin-density functional theory and its application to f-electron systems

对于f电子为巡游电子并具有磁性的f电子化合物，计算其电子结构时，除了考虑相对论效应外，还必须考虑自旋极化和轨道电流引起的磁效应。对于外电磁场中的相互作用电子系统，将维尼亚莱和拉索尔特（1987）的非相对论性电流和自旋密度泛函理论推广到相对论性电流和自旋密度泛函理论。本文证明了推广的Hohenberg-Kohn定理成立，导出了Kohn-Sham-Dirac型单粒子方程，并以电荷密度和磁化强度密度为基本变量，导出了适用于孤立原子或离子的单粒子方程。在单粒子方程中，磁相互作用以类似于塞曼项的形式表示，其中自旋和轨道角动量与有效磁场耦合。轨道电流的影响通过自旋-轨道相互作用隐含地包括在内，并且通过自旋和轨道角动量与有效磁场耦合的塞曼项明确地包括在内。有效磁场由交换能和相关能泛函相对于磁化强度密度的变化给出，磁化强度密度由自旋和轨道角动量密度组成，并且应该自洽地确定。将单粒子方程应用于镧系三价离子的原子结构计算，发现总自旋和轨道角动量很好地服从Hund定则，这一新的理论方案为定量计算f电子体系的电子结构提供了良好的基础.

In order to calculate the electronic structure for f-electron compounds, in which the f electrons are itinerant and responsible to magnetism, it is necessary to take into account the magnetic effects that originate from the spin polarization and the orbital current besides relativistic effects. For a system of interacting electrons in an external electromagnetic field, a non-relativistic current- and spin-density functional theory of Vignale and Rasolt (1987) is generalized to a relativistic current- and spin-density functional theory. A generalized Hohenberg-Kohn theorem is shown to hold, and a single-particle equation of the Kohn-Sham-Dirac type is derived.By choosing the charge density and the magnetization density as the two basic variables, a single-particle equation is derived in a form suitable to an isolated atom or ion. In the single-particle equation, the magnetic interaction is expressed in a form similar to the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field. The effect of the orbital current is included implicitly through the spin-orbit interaction and explicitly through the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field. The effective magnetic field is given by the variation of the exchange and correlation energy functional with respect to the magnetization density that consists of the spin and the orbital angular momentum density, and should be determined self-consistently. The single-particle equation is applied to an atomic structure calculation for the trivalent ions of the lanthanide series, and the total spin and the orbital angular momenta are found to obey Hund's rules well.This new theoretical scheme provides a good basis for a quantitative calculation of the electronic structure for the f-electron systems.