Abstract The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented into the all-electron, numeric atom-centered orbitals electronic structure package FHI-aims. It is found that the bottleneck for large scale applications is the computation of the response density matrix, which scales as O ( N 3 ) . Here for the response properties with respect to the homogeneous electric field, we present an efficient parallel linear scaling algorithm for the response density matrix calculation. Our scheme is based on the second-order trace-correcting purification and the parallel sparse matrix–matrix multiplication algorithms. The new scheme reduces the formal scaling from O ( N 3 ) to O ( N ) , and shows good parallel scalability over tens of thousands of cores. As demonstrated by extensive validation, we achieve a rapid computation of accurate polarizabilities using DFPT. Finally, the computational efficiency of this scheme has been illustrated by making the scaling tests and scalability tests on massively parallel computer systems.

中文翻译：

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全电子实空间密度泛函微扰理论中响应密度矩阵的高效并行线性标度方法

摘要 用于计算与原子位移和均匀电场扰动有关的响应特性的实空间密度泛函扰动理论 (DFPT) 最近已被开发并实施到全电子、数字原子中心轨道电子结构中。包 FHI 目标。发现大规模应用的瓶颈是响应密度矩阵的计算，其缩放为 O ( N 3 ) 。这里对于关于均匀电场的响应特性，我们提出了一种用于响应密度矩阵计算的高效并行线性缩放算法。我们的方案基于二阶迹校正纯化和并行稀疏矩阵-矩阵乘法算法。新方案将形式缩放从 O ( N 3 ) 减少到 O ( N ) ，并在数万个内核上显示出良好的并行可扩展性。正如广泛验证所证明的那样，我们使用 DFPT 实现了准确极化率的快速计算。最后，通过在大规模并行计算机系统上进行缩放测试和可扩展性测试，说明了该方案的计算效率。