In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham local density approximation (LDA) models with pseudopotentials, relying on Cancès et al. (2020, Post-processing of the plane-wave approximation of Schrödinger equations. Part I: linear operators. IMA Journal of Numerical Analysis, draa044) for the proofs of such estimates in the case of linear Schrödinger equations. As in Cancès et al. (2016, A perturbation-method-based post-processing for the plane-wave discretization of Kohn–Sham models. J. Comput. Phys., 307, 446–459), where these a priori results were announced and tested numerically, we use a periodic setting and the problem is discretized with plane waves (Fourier series). This post-processing method consists of performing a full computation in a coarse plane-wave basis and then to compute corrections based on the first-order perturbation theory in a fine basis, which numerically only requires the computation of the residuals of the ground-state orbitals in the fine basis. We show that this procedure asymptotically improves the accuracy of two quantities of interest: the ground-state density matrix, i.e. the orthogonal projector on the lowest |$N$| eigenvectors, and the ground-state energy.

中文翻译：

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Schrödinger方程的平面波逼近的后处理。第二部分：Kohn–Sham模型

在本文中，我们基于Cancès等人的方法，对基于伪势的非线性Kohn-Sham局部密度近似（LDA）模型的平面波近似的基于摄动的后处理方法提供了先验估计。（2020，对Schrödinger方程的平面波逼近进行后处理。第一部分：线性算子。IMA数值分析杂志，draa044），用于线性Schrödinger方程的估计。如在Cancès等人中。（2016，A-基于扰动法的后处理为科恩深水机型。的平面波离散J. COMPUT。物理学。，307，446-459），其中，这些先验宣布了结果并进行了数值测试，我们使用了周期性设置，并且通过平面波（傅里叶级数）将问题离散化了。这种后处理方法包括在粗糙的平面波基础上执行完整的计算，然后在精细的基础上基于一阶微扰理论来计算校正，这在数值上仅需要计算基态的残差即可。轨道在精细的基础上。我们表明，该过程渐近提高了两个感兴趣的量的精度：基态密度矩阵，即最低| $ N $ |处的正交投影仪。特征向量和基态能量。