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A posteriori error estimation for the non-self-consistent Kohn-Sham equations.
Faraday Discussions ( IF 3.3 ) Pub Date : 2020-06-16 , DOI: 10.1039/d0fd00048e
Michael F Herbst 1 , Antoine Levitt , Eric Cancès
Affiliation  

We address the problem of rigorously bounding the errors in the numerical solution of the Kohn–Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, and (iii) the propagation of rounding errors in floating-point arithmetic. In this contribution, we compute fully-guaranteed bounds on the solution of the non-self-consistent equations in the pseudopotential approximation in a plane-wave basis set. We demonstrate our methodology by providing band structure diagrams of silicon annotated with error bars indicating the combined error.

中文翻译:

非自洽Kohn-Sham方程的后验误差估计。

由于(i)基集的有限性,(ii)迭代过程中的收敛阈值,以及(iii)舍入误差的传播,我们解决了严格限制Kohn-Sham方程数值解中的误差的问题在浮点运算中。在此贡献中,我们在平面波基集中的伪势逼近中,计算了非自洽方程解的完全保证边界。我们通过提供带误差线的硅条带结构图来说明我们的方法,误差线指示组合误差。
更新日期:2020-06-16
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