A posteriori error estimation for the non-self-consistent Kohn–Sham equations. (14th September 2020)

• Record Type: Journal Article
• Authors: Herbst, Michael F.; Levitt, Antoine; Cancès, Eric
• Is Part Of: Faraday discussions. Volume 224(2020)
• Page Start: 227
• Page End: 246
• Publication Date: 2020-09-14
• Subjects: Chemistry -- Periodicals; Metallurgy -- Periodicals; Electrochemistry -- Periodicals; 540
• DOI: 10.1039/d0fd00048e
• Languages: English
• ISSNs: 1359-6640

Abstract

Abstract : We address the problem of rigorously bounding the errors in the numerical solution of the Kohn–Sham equations in the pseudopotential approximation. We demonstrate our method by providing band structure diagrams of silicon annotated with the total error. 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.