论文标题
自适应压缩性算子的拆分表示
Split representation of adaptively compressed polarizability operator
论文作者
论文摘要
极化性操作员在密度功能扰动理论和对第一本主要电子结构理论的其他扰动处理中起着核心作用。计算极化性运算符的成本通常将缩放为$ \ Mathcal {o}（n_ {e}^4）$，其中$ n_e $是系统中的电子数。最近开发的自适应压缩性极化操作员（ACP）配方[L. Lin，Z. Xu和L. Ying，多尺度模型。模拟。 2017年，将这种复杂性降低到$ \ Mathcal {o}（n_ {e}^3）$在音调计算的上下文中，首次设置了很大的基础，并证明了其在模型问题上的有效性。在本文中，我们通过将极化性分解为静态压缩的近乎单数组件以及适应性压缩的光滑组件来提高ACP公式的性能。新的拆分表示形式维护$ \ Mathcal {O}（N_E^3）$复杂性，并加速了ACP配方的几乎所有组件，包括能量水平的Chebyshev插值，Sternheimer方程的迭代溶液，以及dyson方程的融合。为了模拟真实材料，我们讨论了如何纳入非局部假性和有限温度效应。我们使用一维模型问题在绝缘和金属状态以及其对实际分子和固体的准确性中证明了我们方法的有效性。
The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as $\mathcal{O}(N_{e}^4)$ where $N_e$ is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to $\mathcal{O}(N_{e}^3)$ in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the $\mathcal{O}(N_e^3)$ complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. We demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.
