Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the excitation energies. In the present article, we discuss the construction of first-rung (i.e., local) weight-dependent exchange-correlation density-functional approximations for two-electron atomic and molecular systems (He and H$_2$) specifically designed for the computation of double excitations within GOK-DFT. In the spirit of optimally-tuned range-separated hybrid functionals, a two-step system-dependent procedure is proposed to obtain accurate energies associated with double excitations.
We report a local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density-functional theory for ensembles (eDFT). This density-functional approximation for ensembles is specially designed for the computation of single and double excitations within Gross--Oliveira--Kohn (GOK) DFT (i.e., eDFT for neutral excitations), and can be seen as a natural extension of the ubiquitous local-density approximation in the context of ensembles. The resulting density-functional approximation, based on both finite…
We derive the second-order approximation (PT2) to the ensemble correlation energy functional by applying the Görling-Levy perturbation theory on the ensemble density-functional theory (EDFT). Its performance is checked by calculating excitation energies with the direct ensemble correction method in 1D model systems and 3D atoms using numerically exact Kohn-Sham orbitals and potentials. Comparing with the exchange-only approximation, the inclusion of the ensemble PT2 correlation improves the excitation energies in 1D model systems in most cases, including double excitations and charge-transfer …
By studying the lowest excitations of an exactly solvable one-dimensional molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using thee exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to stro…
Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued 'Hartree-exchange' ensemble density functional, $E_{Hx}[n]$, in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that $E_{Hx}[n]$ is straightforwardly expressible using block eigenvalues of a simple matrix [equation (14)]. …
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results like, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational eval…
The recent use of a new ensemble in density functional theory (DFT) to yield direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments suggest that direct corrections at the exchange level should not be sufficient. We show that in principle, EDFT with direct corrections can yield accurate doubles and explain the error in naive formal arguments about TDDFT. Exact calculations and analytic results on a simple model…
Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
包层密度泛函理论（eDFT）是含时DFT（TD-DFT）的一种与时间无关的精确替代方法，用于计算激发能。尽管其形式上的简单性和优势相比，TD-DFT（多个激发，例如，可以很容易地考虑在一个合奏），eDFT是不标准的，这基本上是由于缺乏可靠的近似交换相关（xc）泛函合奏。继Smith等人[Phys. Rev. B 93，245131（2016）]之后，我们在这项工作中提出为非平凡的不对称Hubbard二聚体构建一个精确的eDFT，从而更深入地了解各种相关机制中系综xc能量的权重依赖性。为了这个目的，一个精确的解析表达式依赖于重量的系综交换能已被导出。利用勒让德-芬切尔变换计算了互补精确系综关联能。有趣的功能，如在系综xc势在强关联极限的不连续性已被合理化的广义绝热连接形式主义。最后，研究了基态密度泛函近似引起的泛函驱动误差。在严格对称的情况下，或在弱关联制度，结合系综精确交换与基态关联泛函给出相对准确的系综能量。然而，当在强关联区域接近等系综时，这种近似导致具有负斜率的高度弯曲的系综能量，这是非物理的。在这种情况下，使用基态交换和相关泛函给出了更好的结果。事实上，在某些密度域中，几乎可以恢复精确的系综能量。密度驱动误差的分析留待以后的工作。
Charged excitations made neutral: N-centered ensemble density functional theory of Fukui functions
Laboratoire de Chimie Quantique, Institut de Chimie, CNRS / Université de Strasbourg（斯特拉斯堡大学化学研究所量子化学实验室）；University of Strasbourg Institute for Advanced Study（斯特拉斯堡大学高等研究院）
We present a detailed analysis of several time-dependent DFT (TD-DFT) methods, including conventional hybrid functionals and two types of non-empirically tuned range-separated functionals, for predicting a diverse set of electronic excitations in DNA nucleobase monomers and dimers. This large and extensive set of excitations comprises a total of 50 different transitions (for each tested DFT functional) that includes several n $\rightarrow$ π and π $\rightarrow$ π* valence excitations, long-range charge-transfer excitations, and extended Rydberg transitions (complete with benchmark calculations…
