使用有限元离散的无轨道密度泛函理论的实空间公式：Al、Mg和Al-Mg金属间化合物的情况
Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al-Mg intermetallics
摘要：
我们提出了一个局部的实空间配方与密度相关的动能泛函和一个统一的变分框架计算与几何优化的内部原子的位置，以及细胞的几何构型的配置力的轨道自由DFT。建议的实空间配方，其中涉及到的静电和动能泛函的局部变分问题的扩展相互作用的重新制定辅助势场，也很容易扩展到所有的电子轨道自由密度泛函计算，采用在温暖的稠密物质计算。我们使用的本地实空间配方结合高阶有限元离散化来证明无轨道DFT的准确性和所提出的形式主义的铝镁材料系统，在那里我们获得了良好的协议与Kohn-Sham DFT计算的广泛的属性和基准计算。最后，我们调查的电子结构中的点缺陷，特别是一个单空位在Al的细胞大小的影响。我们明确地表明，细胞大小的影响，观察到的空位形成能量计算使用周期性边界条件低估了电子结构扰动的程度所造成的缺陷。相反，散装狄利克雷边界条件，只能通过建议的实空间配方，这对应于一个孤立的缺陷嵌入在散装，显示细胞大小的影响，在缺陷形成的能量是相称的电子结构中的扰动。我们的研究表明，即使是一个简单的缺陷，如铝中的空位，我们需要细胞大小的$\sim 10^3$原子的电子结构的收敛。
英文摘要：
We propose a local real-space formulation for orbital-free DFT with density dependent kinetic energy functionals and a unified variational framework for computing the configurational forces associated with geometry optimization of both internal atomic positions as well as the cell geometry. The proposed real-space formulation, which involves a reformulation of the extended interactions in electrostatic and kinetic energy functionals as local variational problems in auxiliary potential fields, also readily extends to all-electron orbital-free DFT calculations that are employed in warm dense matter calculations. We use the local real-space formulation in conjunction with higher-order finite-element discretization to demonstrate the accuracy of orbital-free DFT and the proposed formalism for the Al-Mg materials system, where we obtain good agreement with Kohn-Sham DFT calculations on a wide range of properties and benchmark calculations. Finally, we investigate the cell-size effects in the electronic structure of point defects, in particular a mono-vacancy in Al. We unambiguously demonstrate that the cell-size effects observed from vacancy formation energies computed using periodic boundary conditions underestimate the extent of the electronic structure perturbations created by the defect. On the contrary, the bulk Dirichlet boundary conditions, accessible only through the proposed real-space formulation, which correspond to an isolated defect embedded in the bulk, show cell-size effects in the defect formation energy that are commensurate with the perturbations in the electronic structure. Our studies suggest that even for a simple defect like a vacancy in Al, we require cell-sizes of $\sim 10^3$ atoms for convergence in the electronic structure.
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