在数值原子轨道框架下应用空间群对称性加速混合泛函计算
Applying Space-Group Symmetry to Speed up Hybrid-Functional Calculations within the Framework of Numerical Atomic Orbitals
AI总结：
本文提出在数值原子轨道框架下利用空间群对称性加速混合密度泛函计算，通过约化k点和实空间区域分别减少Kohn-Sham方程求解数量并加速精确交换哈密顿量构建，已在ABACUS中实现并验证加速效果。
摘要：
基于在数值原子轨道基组框架内利用局域分辨恒等式（RI）技术为大规模周期体系高效实现混合密度泛函（HDFs）的工作，我们开发了一种在HDF计算的关键操作步骤中利用空间群对称性的算法，从而在两个方面带来进一步改进。第一，布里渊区中$\mathbf{k}$点的约化可以减少需要求解的Kohn-Sham方程数量。这要求在原子轨道表示中正确实现等价$\mathbf{k}$点的密度矩阵之间的旋转关系。第二，实空间区域的约化可以加速实空间中哈密顿量精确交换部分的构建。我们已在与LibRI接口的ABACUS软件中实现了该算法，并在几种具有不同对称性的晶体体系上测试了其性能。在两个方面都达到了预期的加速效果：求解Kohn-Sham方程的时间随$\mathbf{k}$点的约化成比例减少，而实空间中哈密顿量的构建则加速了数倍，加速程度取决于体系的大小和对称性。
英文摘要：
Building upon the efficient implementation of hybrid density functionals (HDFs) for large-scale periodic systems within the framework of numerical atomic orbital bases using the localized resolution of identity (RI) technique, we have developed an algorithm that exploits the space group symmetry in key operation steps of HDF calculations, leading to further improvements in two ways. First, the reduction of $\mathbf{k}$-points in the Brillouin zone can reduce the number of Kohn-Sham equations to be solved. This necessitates the correct implementation of the rotation relation between the density matrices of equivalent $\mathbf{k}$-points within the representation of atomic orbitals. Second, the reduction of the real-space sector can accelerate the construction of the exact-exchange part of the Hamiltonian in real space. We have implemented this algorithm in the ABACUS software interfaced with LibRI, and tested its performance for several types of crystal systems with different symmetries. The expected speed-up is achieved in both aspects: the time of solving the Kohn-Sham equations decreases in proportion with the reduction of $\mathbf{k}$-points, while the construction of the Hamiltonian in real space is sped up by several times, with the degree of acceleration depending on the size and symmetry of the system.
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