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.

References in corpus (4)

• Separable Dual Space Gaussian Pseudo-potentials
• Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
• Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals
• A posteriori error estimator for adaptive local basis functions to solve Kohn-Sham density functional theory

Cited by in corpus (6)

• The long road to calibrated prediction uncertainty in computational chemistry
• An overview of a posteriori error estimation and post-processingmethods for nonlinear eigenvalue problems
• Numerical stability and efficiency of response property calculations in density functional theory
• Practical error bounds for properties in plane-wave electronic structure calculations
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory
• Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals