插值可分密度拟合分解加速杂化密度泛函计算及其在硅缺陷中的应用
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations With Applications to Defects in Silicon
摘要：
提出了一种新的基于混合密度泛函理论的电子结构计算方法。新方法使用插值可分离密度拟合（ISDF）程序来构造一组数值辅助基向量和一个紧凑的近似矩阵组成的产品的占用轨道表示在一个大的基组，如平面波的基础。当我们在求解Kohn-Sham方程的迭代方法中将交换算子应用于占据轨道时，这种近似使我们能够将泊松解的数量从$\Or(N_{e}^2)$减少到$\Or(N_{e})$，其中$N_{e}$是待研究系统中的电子数。我们表明，ISDF程序可以在$\Or(N_{e}^3)$操作中进行，与现有方法中使用的方法相比，具有小得多的前常数。当结合最近开发的自适应压缩交换（ACE）运营商的形式主义，这减少了交换运营商需要更新的次数，所得到的ACE-ISDF方法显着降低了计算成本\REV{associated with the exchange operator}的近两个数量级相比，现有的方法为一个大型的硅系统与$1000$原子。我们证明，ACE-ISDF方法可以产生准确的能量和力的绝缘和金属系统，它是可能的，以获得收敛的混合功能计算结果的1000个原子的体硅在10分钟内2000个计算核心。我们还表明，ACE-ISDF可以扩展到8192个计算核心的4096原子体硅系统。我们使用ACE-ISDF方法几何优化1000原子硅系统与空位缺陷使用HSE 06功能和计算其电子结构。
英文摘要：
We present a new efficient way to perform hybrid density functional theory (DFT) based electronic structure calculation. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from $\Or(N_{e}^2)$ to $\Or(N_{e})$ when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn-Sham equations, where $N_{e}$ is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in $\Or(N_{e}^3)$ operations, with a much smaller pre-constant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the resulting ACE-ISDF method significantly reduces the computational cost \REV{associated with the exchange operator} by nearly two orders of magnitude compared to existing approaches for a large silicon system with $1000$ atoms. We demonstrate that the ACE-ISDF method can produce accurate energies and forces for insulating and metallic systems, and that it is possible to obtain converged hybrid functional calculation results for a 1000-atom bulk silicon within 10 minutes on 2000 computational cores. We also show that ACE-ISDF can scale to 8192 computational cores for a 4096-atom bulk silicon system. We use the ACE-ISDF method to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure.
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