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

为了计算f电子化合物的电子结构，其中f电子是流动的，对磁性负责，除了相对论效应外，还需要考虑自旋极化和轨道电流产生的磁效应。对于外部电磁场中相互作用的电子系统，Vignale和Rasolt（1987）的非相对论性电流和自旋密度泛函理论被推广为相对论性电流和自旋密度泛函理论。证明了广义Hohenberg-Kohn定理成立，并导出了Kohn-Sham-Dirac型单粒子方程。选取电荷密度和磁化密度作为两个基本变量，推导出适合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。轨道电流的影响隐含地包含在自旋-轨道相互作用中，明确地包含在自旋和轨道角动量与有效磁场耦合的塞曼项中。有效磁场由自旋和轨道角动量密度组成的磁化密度的交换能和相关能泛函的变化给出，并应自洽确定。将单粒子方程应用于镧系系三价离子的原子结构计算，发现总自旋和轨道角动量都很好地服从洪德规则。这一新的理论方案为定量计算f电子系统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.