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Exact ensemble density functional theory for excited states in a model system: Investigating the weight dependence of the correlation energy

机译：模型系统中激发态的精确集成密度泛函理论：研究相关能量的重量依赖性

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Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple excitations, for example, can be easily taken into account in an ensemble), eDFT is not standard, which is essentially due to the lack of reliable approximate exchange-correlation (xc) functionals for ensembles. Following Smith etal. [Phys. Rev. B 93,245131 (2016)], we propose in this work to construct an exact eDFT for the nontrivial asymmetric Hubbard dimer, thus providing more insight into the weight dependence of the ensemble xc energy in various correlation regimes. For that purpose, an exact analytical expression for the weight-dependent ensemble exchange energy has been derived. The complementary exact ensemble correlation energy has been computed by means of Legendre-Fenchel transforms. Interesting features like discontinuities in the ensemble xc potential in the strongly correlated limit have been rationalized by means of a generalized adiabatic connection formalism. Finally, functional-driven errors induced by ground-state density-functional approximations have been studied. In the strictly symmetric case or in the weakly correlated regime, combining ensemble exact exchange with ground-state correlation functionals gives better ensemble energies than when calculated with the ground-state exchange-correlation functional. However, when approaching the asymmetric equiensemble in the strongly correlated regime, the former approximation leads to highly curved ensemble energies with negative slope which is unphysical. Using both ground-state exchange and correlation functionals gives much better results in that case. In fact, exact ensemble energies are almost recovered in some density domains. The analysis of density-driven errors is left for future work.
机译：集合密度泛函理论（eDFT）是时间无关DFT（TD-DFT）的精确时间无关替代品，用于计算激发能。尽管与TD-DFT相比它具有形式上的简单性和优势（例如，可以很容易地将多个激发考虑为一个整体），但是eDFT并不是标准的，这主要是由于缺乏可靠的近似交换相关性（xc ）的功能。继史密斯等人。 [物理Rev. B 93,245131（2016）]，我们在这项工作中建议为非平凡的不对称Hubbard二聚体构建精确的eDFT，从而在各种相关机制中提供对合束xc能量的重量依赖性的更多见解。为此，已经得出了重量依赖的整体交换能量的精确分析表达式。互补精确集合相关能量已经通过勒让德-芬舍尔变换来计算。有趣的特征（如在强相关极限中的合奏xc势中的不连续性）已通过广义绝热连接形式主义进行了合理化。最后，研究了由基态密度-函数逼近引起的函数驱动误差。在严格对称的情况下或在弱相关的情况下，将集成精确交换与基态相关函数结合起来可以得到比用基态交换相关函数计算时更好的集成能量。但是，当在强相关状态下接近不对称等能量时，前一种近似会导致具有负斜率的高度弯曲的集合能量，这是非物理的。在这种情况下，同时使用基态交换和相关功能会得到更好的结果。实际上，在某些密度域中几乎可以回收精确的集合能量。密度驱动误差的分析留给以后的工作。

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  • 来源
    《Physical review》 |2017年第3期|035120.1-035120.17|共17页
  • 作者

    Killian Deur; Laurent Mazouin; Emmanuel Fromager;

  • 作者单位

    Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Universite de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France;

    Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Universite de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France;

    Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Universite de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France;

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