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Journal Articles Faraday Discussions Year : 2020

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.

Dates and versions

hal-02557871 , version 1 (29-04-2020)

Identifiers

Cite

Michael F. Herbst, Antoine Levitt, Eric Cancès. A posteriori error estimation for the non-self-consistent Kohn-Sham equations. Faraday Discussions, 2020, 224, pp.227-246. ⟨10.1039/D0FD00048E⟩. ⟨hal-02557871⟩
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