Treecode-accelerated Green iteration for Kohn-Sham density functional theory
Treecode-accelerated Green iteration for Kohn-Sham density functional theory
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DOI：
10.1016/j.jcp.2020.110101
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
N. Vaughn;V. Gavini;R. Krasny
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文献类型：
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作者：
N. Vaughn;V. Gavini;R. Krasny
提出了一种全电子Kohn-Sham密度泛函理论的实空间计算方法——树码加速绿色迭代（TAGI）。TAGI是基于Kohn-Sham方程的重新表述，其中微分形式的特征值问题通过与修正的Helmholtz Green函数的卷积转化为积分形式的不动点问题。在每次自洽域（SCF）迭代中，采用Green iteration计算不动点，其中离散卷积和由gpu加速的重心拉格朗日树码有效地计算。TAGI中使用的其他技术包括优先级自适应网格优化、fej<s:1>正交、奇点减法、无梯度特征值更新和安德森混合，以加速SCF和Green迭代的收敛。几个原子（Li, Be， O）和小分子（H2， CO, C6H6）的基态能量计算证明了TAGI能够有效地实现化学精度。
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 includea-prioriadaptive 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.