Error Bounds for Properties in Planewave Electronic Structure Calculations

Explore error bounds for properties in planewave electronic structure calculations in this 39-minute conference talk presented by Genevieve Dusson at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Delve into accurate and computable error bounds for quantities of interest in electronic structure calculations, with a focus on estimating errors in ground state density matrices and interatomic forces. Examine the analysis of residuals from solved equations and their efficient approximation using computable terms. Gain insights into the perfect error bound, guaranteed bounds, and the main challenges in applying these concepts to Density Functional Theory (DFT). Investigate the formulation of the DFT ground state problem, discretization with planewaves, and first-order optimality conditions. Study linearization in the asymptotic regime, numerical results for force estimation in Silicon, and improved error bounds. Enhance your understanding of large-scale certified numerical methods in quantum mechanics through this comprehensive presentation.