论文标题
有效的全电子时间依赖性密度功能理论使用丰富的有限元基础计算
Efficient all-electron time-dependent density functional theory calculations using an enriched finite element basis
论文作者
论文摘要
我们使用混合基础（称为富集的有限元（EFE）基础），对全电子实时时间依赖性密度功能理论（TDDFT）计算提出了有效且系统收敛的方法。 EFE基础以紧凑的数值原子为中心的经典有限元基础（CFE），从原子地面DFT计算获得。特别是，我们将富集功能正交相对于经典的有限元基础，以确保良好的基础调节。我们将二阶Magnus繁殖器与自适应Krylov子空间方法结合使用，用于有效的Kohn-Sham轨道时间演化。我们依靠\ textit {先验}错误估计来指导我们选择自适应有限元网格以及在TDDFT计算中使用的时间步长。我们观察到相对于空间和时间离散化，偶极矩的最佳收敛速率接近。值得注意的是，我们在CFE基础上获得了EFE的$ 50-100 \ times $加速。我们还通过研究钠簇中的吸收光谱，绿色荧光蛋白发色团中的线性到非线性响应跃迁以及镁二聚体中较高的谐波产生来证明EFE基础对线性和非线性反应的疗效。最后，我们使用50个原子钠纳米群的基准系统，可以实现高达$ \ sim1000 $处理器的数值实现的良好并行可扩展性。
We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with compactly supported numerical atom centered basis, obtained from atomic groundstate DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on \textit{a priori} error estimates to guide our choice of an adaptive finite element mesh as well as the time-step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization. Notably, we attain a $50-100\times$ speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear response by studying the absorption spectrum in sodium clusters, the linear to nonlinear response transition in green fluorescence protein chromophore, and the higher harmonic generation in magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to $\sim1000$ processors, using a benchmark system of 50-atom sodium nanocluster.
