论文标题
Kohn-Sham密度功能理论的Treecode加速绿色迭代
Treecode-accelerated Green Iteration for Kohn-Sham Density Functional Theory
论文作者
论文摘要
我们提出了一种真实空间计算方法，称为全电子Kohn-Sham密度功能理论，称为Treecode加速绿色迭代（TAGI）。 Tagi基于Kohn-Sham方程的重新制定，其中通过与修改的Helmholtz Green的函数卷积，以差异形式以差异形式的特征值问题转换为固定点问题。在每个自洽场（SCF）迭代中，固定点是通过绿色迭代计算的，其中离散的卷积总和由GPU加速的Barycentric Lagrange Treecode有效地评估。 Tagi中使用的其他技术包括自适应网状精炼，Fejér正交，奇异性减法，无梯度的特征值更新以及Anderson混合以加速SCF和绿色迭代的收敛。几个原子（LI，BE，O）和小分子（H $ _2 $，CO，C $ _6 $ H $ _6 $）的基态能量计算证明了Tagi有效达到化学精度的能力。
We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on a reformulation of the Kohn-Sham equations in which the eigenvalue problem in differential form is converted into a fixed-point problem in integral form by convolution with the modified Helmholtz Green's function. In each self-consistent field (SCF) iteration, the fixed-points are computed by Green Iteration, where the discrete convolution sums are efficiently evaluated by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in TAGI include adaptive mesh refinement, Fejér quadrature, singularity subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate convergence of the SCF and Green Iterations. Ground state energy computations of several atoms (Li, Be, O) and small molecules (H$_2$, CO, C$_6$H$_6$) demonstrate TAGI's ability to efficiently achieve chemical accuracy.
