Volume 224, 2020

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

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

Associated articles

Article information

Article type
Paper
Submitted
27 Apr. 2020
Accepted
16 Jūn. 2020
First published
16 Jūn. 2020

Faraday Discuss., 2020,224, 227-246

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

M. F. Herbst, A. Levitt and E. Cancès, Faraday Discuss., 2020, 224, 227 DOI: 10.1039/D0FD00048E

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