论文标题
在Kohn-Sham密度函数理论中加速了自洽场迭代，使用介电矩阵的低等级近似
Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low rank approximation of the dielectric matrix
论文作者
论文摘要
我们提出了一种有效的预处理技术，用于加速实际空间KOHN-SHAM密度功能理论（DFT）计算中的固定点迭代。预处理使用基于固定点迭代的残差沿适当选择的方向函数的Gâteaux衍生物的介电矩阵（LRDM）的低秩近似值。我们开发了一种计算有效的方法，以与Chebyshev过滤的子空间迭代程序一起评估这些Gâteaux衍生物，这是一种广泛用于大规模Kohn-Sham DFT计算的方法。此外，我们提出了一种基于先前SCF迭代的低级别近似值的自适应积累的LRDM预处理，并将LRDM Proventioner扩展到自旋极化的Kohn-Sham DFT计算。我们在一系列基准系统上，尺寸从$ \ sim $ \ sim $ 100-1100 ATOM（$ \ sim $ 500--20,000电子）中，在一系列基准系统上证明了LRDM预处理的鲁棒性和效率。基准系统包括金属胰岛导态 - 导向的异质材料系统的各种组合，纳米颗粒在费米能量附近具有局部$ d $轨道，带有金属掺杂剂的纳米膜和磁系统。在所有基准系统中，LRDM预处理器在20--30次迭代中都稳健地收敛。相比之下，在许多情况下，其他广泛使用的预处理显示出缓慢的收敛性，在某些情况下，固定点迭代的差异。最后，我们证明了LRDM方法所提供的计算效率，与其他预调节器相比，总地面计算的计算成本最高为3.4 $ \ times $。
We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous SCF iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from $\sim$ 100-1100 atoms ($\sim$ 500--20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized $d$ orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20--30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed point iteration in some cases. Finally, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4$\times$ reduction in computational cost for the total ground-state calculation compared to other preconditioners.
