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

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Abstract

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.

Graphical abstract: A posteriori error estimation for the non-self-consistent Kohn–Sham equations

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Article information


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

Faraday Discuss., 2020, Advance Article
Article type
Paper

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

M. F. Herbst, A. Levitt and E. Cancès, Faraday Discuss., 2020, Advance Article , DOI: 10.1039/D0FD00048E

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