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A posteriori error estimation for the non-self-consistent Kohn-Sham equations

Abstract

We address the problem of bounding rigorously 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, (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.

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Article information


Submitted
27 Apr 2020
Accepted
16 Jun 2020
First published
16 Jun 2020

Faraday Discuss., 2020, Accepted Manuscript
Article type
Paper

A posteriori error estimation for the non-self-consistent Kohn-Sham equations

M. Herbst, A. Levitt and E. Cancès, Faraday Discuss., 2020, Accepted Manuscript , DOI: 10.1039/D0FD00048E

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