Pastorczak Ewa, Pernal Katarzyna
Institute of Applied Radiation Chemistry, Faculty of Chemistry, Lodz University of Technology, ul. Wroblewskiego 15, 93-590 Lodz, Poland.
Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.
J Chem Phys. 2014 May 14;140(18):18A514. doi: 10.1063/1.4866998.
Ensemble density functional theory (DFT) offers a way of predicting excited-states energies of atomic and molecular systems without referring to a density response function. Despite a significant theoretical work, practical applications of the proposed approximations have been scarce and they do not allow for a fair judgement of the potential usefulness of ensemble DFT with available functionals. In the paper, we investigate two forms of ensemble density functionals formulated within ensemble DFT framework: the Gross, Oliveira, and Kohn (GOK) functional proposed by Gross et al. [Phys. Rev. A 37, 2809 (1988)] alongside the orbital-dependent eDFT form of the functional introduced by Nagy [J. Phys. B 34, 2363 (2001)] (the acronym eDFT proposed in analogy to eHF--ensemble Hartree-Fock method). Local and semi-local ground-state density functionals are employed in both approaches. Approximate ensemble density functionals contain not only spurious self-interaction but also the so-called ghost-interaction which has no counterpart in the ground-state DFT. We propose how to correct the GOK functional for both kinds of interactions in approximations that go beyond the exact-exchange functional. Numerical applications lead to a conclusion that functionals free of the ghost-interaction by construction, i.e., eDFT, yield much more reliable results than approximate self- and ghost-interaction-corrected GOK functional. Additionally, local density functional corrected for self-interaction employed in the eDFT framework yields excitations energies of the accuracy comparable to that of the uncorrected semi-local eDFT functional.
系综密度泛函理论（DFT）提供了一种预测原子和分子体系激发态能量的方法，而无需涉及密度响应函数。尽管有大量的理论工作，但所提出的近似方法的实际应用却很少，而且它们无法对现有泛函的系综DFT的潜在有用性做出公正的判断。在本文中，我们研究了在系综DFT框架内制定的两种系综密度泛函形式：格罗斯等人提出的格罗斯、奥利维拉和科恩（GOK）泛函[《物理评论A》37, 2809 (1988)]以及纳吉引入的泛函的轨道相关eDFT形式[《物理杂志B》34, 2363 (2001)]（该首字母缩写eDFT是类比eHF——系综哈特里-福克方法提出的）。两种方法都采用了局域和半局域基态密度泛函。近似系综密度泛函不仅包含虚假的自相互作用，还包含所谓的幽灵相互作用，而在基态DFT中没有与之对应的相互作用。我们提出了如何在超越精确交换泛函的近似中对GOK泛函的这两种相互作用进行修正。数值应用得出的结论是，通过构建而不含幽灵相互作用的泛函，即eDFT，比近似的自相互作用和幽灵相互作用修正的GOK泛函产生的结果可靠得多。此外，在eDFT框架中采用的经自相互作用修正的局域密度泛函产生的激发能精度与未修正的半局域eDFT泛函相当。
