Arbuznikov Alexei V, Kaupp Martin
Institut für Anorganische Chemie, Universität Würzburg, Germany.
J Chem Phys. 2009 Aug 28;131(8):084103. doi: 10.1063/1.3205003.
Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke's real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)].
占据轨道相关（OOD）交换关联泛函在当前密度泛函理论的发展中占据着特别突出的地位。它们的自洽实现较为复杂，因为其轨道相关部分并非显式的，而仅是电子密度的隐式泛函，并且交换关联势不能通过对密度取泛函导数直接得到。需要一个两步过程，首先要得到关于轨道的泛函导数（FDO），然后可以通过优化有效势技术将其转化为局域且可乘的势。鉴于目前正在研究的OOD泛函种类繁多，我们在此报告广义OOD泛函的FDO的通用、系统且透明的表达式，此外还报告了在原子轨道基组中的矩阵元版本。首次针对当前最复杂的OOD泛函示例之一——Becke的非动态关联实空间模型（B05泛函）[《化学物理杂志》122, 064101 (2005)] 推导并数值测试了显式FDO。
