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 a-priori 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 (H₂, CO, C₆H₆) demonstrate TAGI's ability to efficiently achieve chemical accuracy.

我们为全电子Kohn-Sham密度泛函理论提出了一种称为树码加速绿色迭代（TAGI）的真实空间计算方法。TAGI基于Kohn-Sham方程的重新公式化，其中微分形式的特征值问题通过与改进的Helmholtz Green函数卷积而转换为积分形式的不动点问题。在每个自洽字段（SCF）迭代中，不动点由Green迭代计算，其中离散卷积和由GPU加速的重心拉格朗日树码有效评估。TAGI中使用的其他技术包括先验自适应网格细化，Fejér正交，奇异度减法，无梯度特征值更新以及Anderson混合，可加快SCF和Green迭代的收敛速度。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能够有效实现化学准确性。