Lin Peize, Ren Xinguo, He Lixin
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
J Chem Theory Comput. 2021 Jan 12;17(1):222-239. doi: 10.1021/acs.jctc.0c00960. Epub 2020 Dec 13.
We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities-a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work, we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.
我们提出了一种高效的线性缩放实现方法，用于在数值原子轨道（NAO）基函数框架内为周期性系统构建（屏蔽）哈特里 - 福克交换（HFX）矩阵。我们的实现基于单位近似的局域分解，通过该方法，只需计算双中心量即可获得双电子库仑排斥积分——这一特性对NAO非常有利。通过利用基函数的局部性以及对中间三指标和两指标张量的高效预筛选，可以实现构建HFX矩阵的计算成本相对于系统大小的线性缩放。由于采用了MPI/OpenMP混合并行化策略来分配计算负载和内存存储，我们的实现具有大规模并行性。所有这些因素共同作用，使得能够对大规模周期性系统进行高效的杂化泛函计算。在这项工作中，我们描述了ABACUS代码包中实现的HFX构建的关键算法和实现细节。针对多达4096个原子的选定基准系统，展示了我们的实现在系统大小和CPU核心数量方面的性能和可扩展性。
