Hu Wei, Lin Lin, Yang Chao
Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.
Department of Mathematics, University of California , Berkeley, California 94720, United States.
J Chem Theory Comput. 2017 Nov 14;13(11):5420-5431. doi: 10.1021/acs.jctc.7b00807. Epub 2017 Oct 13.
We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. 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 [Formula: see text] to [Formula: see text] when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn-Sham equations, where N is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in [Formula: see text] operations, with a much smaller preconstant 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 associated with the exchange operator by nearly 2 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 min 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. We find that that the computed energy gap from the HSE06 functional is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations.
我们提出了一种基于混合密度泛函理论（DFT）进行电子结构计算的高效新方法。该新方法采用插值可分离密度拟合（ISDF）程序来构建一组数值辅助基向量，以及对由大基组（如平面波基组）中占据轨道乘积构成的矩阵进行紧凑近似。当我们在求解Kohn-Sham方程的迭代方法中对占据轨道应用交换算符时，这种近似使我们能够将泊松求解的次数从[公式：见原文]减少到[公式：见原文]，其中N是待研究系统中的电子数。我们表明，ISDF程序可以在[公式：见原文]次操作内完成，与现有方法中使用的方法相比，其预常数要小得多。当与最近开发的自适应压缩交换（ACE）算符形式相结合时，ACE算符需要更新的次数会减少，与现有方法相比，对于具有1000个原子的大硅系统，所得的ACE-ISDF方法将与交换算符相关的计算成本显著降低了近2个数量级。我们证明，ACE-ISDF方法可以为绝缘和金属系统产生准确的能量和力，并且在2000个计算核心上，有可能在10分钟内获得1000个原子的体硅的收敛混合泛函计算结果。我们还表明，对于4096个原子的体硅系统，ACE-ISDF可以扩展到8192个计算核心。我们使用ACE-ISDF方法，采用HSE06泛函对具有空位缺陷的1000个原子的硅系统进行几何优化，并计算其电子结构。我们发现，与DFT计算中的半局部泛函产生的结果相比，HSE06泛函计算得到的能隙更接近实验值。
