论文标题
通过分析测试案例研究比较Hartree-Fock和Kohn-Sham理论中的相关组件和近似值
Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study
论文作者
论文摘要
非对称哈伯德二聚体是一个模型，允许对Hartree-fock（HF）和Kohn-Sham（KS）表示明确表达外部电位的分析功能，$ΔV$以及交互强度的分析功能，$ U $。我们使用这种独特的情况来建立对$ \ {u，ΔV\} $参数空间中两个理论的相关能量的各个贡献之间的严格比较。在对Hubbard二聚体的分析中，我们观察到HF动力学相关能量的迹象发生了变化，比较间接排斥能，并得出了“传统”相关能量的表达，即在纯粹的位点占领函数理论精神[eq eq中纠正HF估计值的校正HF估计值。 （43）]。接下来，我们测试Liu-Burke和Seidl-perdew-Levy功能的性能，它们基于其弱和强相互作用极限的扩展对相关能量进行建模，并可用于传统和KS相关能。我们的结果表明，在Hubbard Dimer设置中，尽管最初是为KS设计的，但它们通常可以更好地用于HF参考。这些结论与对各种化学数据集的这些功能的先前评估有些一致。但是，Hubbard Dimer模型允许我们显示在使用强度相互作用成分来代替HF参考的强度相互作用成分时可能发生的误差的程度，就像先前的大多数评估中所进行的那样。
The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions of the external potential, $Δv$, and of the interaction strength, $U$. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the $\{U,Δv\}$ parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the 'traditional' correlation energy, i.e. the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (43)]. Next, we test the performances of the Liu-Burke and the Seidl-Perdew-Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical data sets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.
