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.
https://hal.archives-ouvertes.fr/hal-02557871 Contributor : Michael HerbstConnect in order to contact the contributor Submitted on : Wednesday, April 29, 2020 - 9:01:31 AM Last modification on : Friday, February 4, 2022 - 3:12:53 AM
Michael F. Herbst, Antoine Levitt, Eric Cancès. A posteriori error estimation for the non-self-consistent Kohn-Sham equations. Faraday Discussions, Royal Society of Chemistry, 2020, 224, pp.227-246. ⟨10.1039/D0FD00048E⟩. ⟨hal-02557871⟩