嵌入球形凝胶中的简单杂质：密度泛函理论与量子蒙特卡罗基准的比较
Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks
摘要：
本文研究了中心高斯杂质存在下球形胶凝体系的电子结构。我们测试如何以及由此产生的非均匀性效应超出球形凝胶再现几个近似的密度泛函理论（DFT）。Perdew阶梯的DFT泛函，即局域密度近似（LDA），广义梯度近似（GGA），元GGA和轨道相关的混合泛函的四个梯级进行比较，我们的量子蒙特卡罗（QMC）基准。我们确定了几个不同的过渡系统的基态之间的离域和本地化状态的电子占领的变化。我们检查参数空间的现实密度（$1 \le r_s\le 5$）和中等深度的高斯杂质（$Z<7$）。所选的18电子体系（具有闭壳层基态）呈现$1d \to 2s$跃迁，而30电子体系（具有开壳层基态）呈现$1f \to 2p$跃迁。对于前一个系统，过渡的准确性明显提高与元GGA和混合泛函的泛函只有很小的偏差，从QMC的复杂性。然而，对于后者的系统，我们发现更大的差异，我们的池的DFT泛函和QMC之间的潜在的过渡。我们把这一失败归因于这些泛函内的确切交换的处理。此外，我们通过创建具有球壳的系统来放大非均匀性效应，这导致DFT近似中更大的误差。
英文摘要：
We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities ($1 \le r_s\le 5$) and moderate depths of the Gaussian impurity ($Z<7$). The selected 18 electron system (with closed-shell ground state) presents $1d \to 2s$ transitions while the 30 electron system (with open-shell ground state) exhibits $1f \to 2p$ transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute this failure to treatment of the exact exchange within these functionals. Additionally, we amplify the inhomogeneity effects by creating the system with spherical shell which leads to even larger errors in DFT approximations.
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