极展开和选择反演加速基于原子轨道的电子结构计算
Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
摘要：
我们描述了如何应用最近开发的极点展开和选择反转（PEXSI）技术的Kohn-Sham密度泛函理论（DFT）的电子结构计算的基础上原子轨道离散化。在不使用Kohn-Sham哈密顿量的本征值和本征向量的情况下，给出了计算电荷密度、总能量、Helmholtz自由能和原子力（包括Hellman-Feynman力和Pulay力）的解析表达式.我们还展示了如何更新的化学势，而不使用Kohn-Sham本征值。使用PEXSI的优点是它具有比与矩阵对角化过程相关联的计算复杂度低得多的计算复杂度。我们证明了性能增益通过比较PEXSI的时间与绝缘和金属纳米管上的对角化。对于这些准一维系统，PEXSI的复杂性与原子数成线性关系。在我们的计算实验中，当纳米管中的原子数量大于几百个时，可以观察到这种线性缩放。PEXSI的挂钟时间和内存需求都很适中。这使得它甚至可以执行Kohn-Sham DFT计算10,000原子纳米管与所选择的反演算法的顺序实施。我们还进行了精确的几何优化计算截断（8，0）氮化硼纳米管系统包含1024个原子。数值结果表明，使用PEXSI不会导致损失的精度要求在一个实际的DFT计算。
英文摘要：
We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation.
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