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.

Intro
Computing properties of materials systems
Outline
Density Functional Theory
Modelling crystalline systems
Errors arising in the course of the calculation
The perfect error bound
Abstract formulation
Guaranteed bounds
Main difficulties for applications to DFT
Formulation of the DFT ground state problem
Discretization with planewaves
First-order optimality conditions
Orthogonal projectors vs orbitals
Second-order geometry
Linearization in the asymptotic regime
Linearization : Numerical results
Choosing an adequate norm
Results: Force estimation for Silicon
Frequency splitting
Improved error bound
New estimation on the forces
Conclusion