Multiscale Modeling &Simulation, Volume 18, Issue 4, Page 1621-1663, January 2020.
In this paper, we propose and analyze a gradient flow based model for electronic structure calculations. First, based on an extended gradient flow proposed in this paper, we propose a Kohn--Sham gradient flow based model. We prove that our gradient flow based model is orthogonality preserving, the extended gradient has an exponential decay over time $t$, and the equilibrium point is a local minimizer of the Kohn--Sham energy functional. Then we propose a midpoint scheme to carry out the temporal discretization, which is proven to be orthogonality preserving, too. Based on the midpoint scheme, we design a practical orthogonality preserving iteration scheme which can deal with the propagation of the gradient flow based model and prove that the scheme produces approximations that converge to a local minimizer with some convergence rate under some reasonable assumptions. Finally, we report a number of numerical experiments that validate our theoretical results.

中文翻译：

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基于梯度流的Kohn-Sham密度泛函理论模型

2020年1月，《多尺度建模与仿真》，第18卷，第4期，第1621-1663页。
在本文中，我们提出并分析了基于梯度流的电子结构计算模型。首先，基于本文提出的扩展梯度流，我们提出了一种基于Kohn-Sham梯度流的模型。我们证明我们的基于梯度流的模型是正交的，扩展的梯度具有随时间$ t $的指数衰减，并且平衡点是Kohn-Sham能量函数的局部极小值。然后，我们提出了一个中点方案来进行时间离散化，这也被证明是保持正交性的。根据中点方案，我们设计了一种实用的正交性保留迭代方案，该方案可以处理基于梯度流的模型的传播，并证明在合理的假设下，该方案能够以一定的收敛速度产生近似收敛到局部极小值的近似值。最后，我们报告了许多数值实验，这些实验验证了我们的理论结果。