Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France.
J Chem Phys. 2019 Mar 7;150(9):094106. doi: 10.1063/1.5084312.
Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is the DFT analog of state-averaged wavefunction-based (SA-WF) methods. In GOK-DFT, the SA (so-called ensemble) exchange-correlation (xc) energy is described by a single functional of the density which, for a fixed density, depends on the weights assigned to each state in the ensemble. We show that if a many-weight-dependent xc functional is employed, then it becomes possible to extract, in principle exactly, all individual energy levels from a single GOK-DFT calculation, exactly like in a SA-WF calculation. More precisely, starting from the Kohn-Sham energies, a global Levy-Zahariev-type shift as well as a state-specific (ensemble-based) xc derivative correction must be applied in order to reach the energy level of interest. We illustrate with the asymmetric Hubbard dimer the importance and substantial weight dependence of both corrections. A comparison with more standard extraction procedures, which rely on a sequence of ensemble calculations, is made at the ensemble exact exchange level of approximation.
Gross-Oliveira-Kohn 密度泛函理论（GOK-DFT）用于系综是基于状态平均波函数（SA-WF）方法的密度泛函理论的模拟。在 GOK-DFT 中，SA（所谓的系综）交换关联（xc）能量由密度的单个泛函描述，对于固定的密度，该泛函取决于系综中分配给每个状态的权重。我们表明，如果采用许多权重相关的 xc 泛函，则从单个 GOK-DFT 计算中提取所有单个能级在原则上是可能的，就像在 SA-WF 计算中一样。更准确地说，从 Kohn-Sham 能量开始，必须应用全局 Levy-Zahariev 类型的位移以及特定于状态的（基于系综的）xc 导数校正，以达到感兴趣的能级。我们用不对称 Hubbard 二聚体说明了这两种校正的重要性和实质性的权重依赖性。在系综精确交换近似的水平上，与更标准的提取程序（依赖于一系列系综计算）进行了比较。
