标题： 应用空间群对称性以加速数值原子轨道框架内的杂化泛函计算 显示英文标题

标题： Applying Space-Group Symmetry to Speed up Hybrid-Functional Calculations within the Framework of Numerical Atomic Orbitals

摘要： 在利用局域化积分技术（RI）在数值原子轨道基组框架下对大规模周期性系统进行混合密度泛函（HDFs）高效实现的基础上，我们开发了一种算法，该算法在HDF计算的关键操作步骤中利用了空间群对称性，从而在两个方面进一步提高了性能。 首先，布里渊区中$\mathbf{k}$-点的减少可以减少需要求解的科恩-沙姆方程的数量。这需要在原子轨道表示中正确实现等效$\mathbf{k}$-点之间密度矩阵的旋转关系。 其次，实空间区域的减少可以加速实空间中哈密顿量的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，并针对具有不同对称性的多种晶体系统测试了其性能。 预期的加速效果在两个方面都得到了实现：求解科恩-沙姆方程的时间随着$\mathbf{k}$-点的减少而成比例降低，而实空间中哈密顿量的构建速度则加快了几倍，加速程度取决于系统的大小和对称性。 显示英文摘要

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.