English

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

Computational Physics 2020-09-04 v2 Materials Science Numerical Analysis Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2004.13549,
  title  = {A posteriori error estimation for the non-self-consistent Kohn-Sham equations},
  author = {Michael F. Herbst and Antoine Levitt and Eric Cancès},
  journal= {arXiv preprint arXiv:2004.13549},
  year   = {2020}
}
R2 v1 2026-06-23T15:09:16.396Z