基于分割密度泛函理论的强电子关联
Strong Electron Correlation from Partition Density Functional Theory
AI总结：
针对 KS-DFT 在强关联电子系统中误差大的问题，提出基于分割密度泛函理论的广义重叠近似（GOA）方法，有效改进了氢链解离曲线与电子密度，且无需破坏自旋对称性。
摘要：
Kohn-Sham 密度泛函理论（KS-DFT）中交换关联（XC）泛函的标准近似在应用于强关联电子系统时，通常会导致不可接受的大误差。分割密度泛函理论（PDFT）是 KS-DFT 的一种形式上精确的重构，其中系统的基态密度和能量通过对孤立片段的自洽计算获得，并用一个分割能量表示片段间的相互作用。在此我们展示了，通过对 PDFT 中的分割能量采用一种简单近似，即广义重叠近似（GOA），可以很大程度上抑制 KS-DFT 中局部密度近似（LDA）的典型误差。我们的方法以一维强关联线性氢链的简单模型为例进行了说明。将 GOA 与片段的 LDA 结合使用时，改进了氢链的 LDA 解离曲线，并产生了与自旋无限制 LDA 可比的结果，但未破坏自旋对称性。GOA 还对 LDA 电子密度引入了修正，部分捕捉到了强关联氢链中正确的密度二聚化现象。此外，通过对分割能量进行额外修正，该近似被证明能够产生与基于密度矩阵重整化群方法的计算在定量上吻合的解离能。
英文摘要：
Standard approximations for the exchange-correlation (XC) functional in Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing the \textit{inter}-fragment interactions. Here we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the generalized overlap approximation (GOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly-correlated linear hydrogen chains. The GOA, when used in combination with the LDA for the fragments, improves the LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. GOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly-correlated hydrogen chains. Moreover, with an additional correction to the partition energy, the approximation is shown to produce dissociation energies in quantitative agreement to calculations based on the Density Matrix Renormalization Group method.
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