Pribram-Jones Aurora, Yang Zeng-Hui, Trail John R, Burke Kieron, Needs Richard J, Ullrich Carsten A
Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA.
Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.
J Chem Phys. 2014 May 14;140(18):18A541. doi: 10.1063/1.4872255.
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
一种从精确的激发态密度中提取系综Kohn-Sham势的新方法被应用于各种双电子体系，以探索精确系综密度泛函理论的行为。研究了分离哈特里能量的问题以及简并本征态的选择。推导了一种新的近似方法——自旋本征态哈特里-交换。已证明的精确条件包括相关能分量的符号以及激发态小权重时势的渐近行为。给出了一维扁平盒、具有大势垒以产生电荷转移激发的盒、三维谐振子阱（胡克原子）中两个电子的许多能量分量作为权重的函数，以及氦原子单重态-三重态系综、单重态-三重态-单重态系综和三重态双系综的能量分量。
