Finite-Size Error and Its Correction in Energy Calculations for Periodic Systems
Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube
Course Description
Overview
Explore a comprehensive lecture on finite-size error and its correction in energy calculations for periodic systems. Delve into the challenges of understanding finite-size errors in electronic structure theories and their impact on periodic systems using Monkhorst-Pack grids. Examine the rigorous analysis of finite-size errors in Hartree-Fock theory and second-order Møller-Plesset perturbation theory. Discover how energy calculations for periodic systems can be viewed as multi-dimensional integrals at the thermodynamic limit and how standard evaluation methods relate to trapezoidal quadrature rules. Investigate the complexities arising from the Coulomb kernel's singularity and the limitations of standard error analysis based on the Euler-Maclaurin formula. Learn about a unified analysis providing sharp convergence rates for finite-size errors in periodic HF and MP2 theories for insulating systems. Understand the technical advancements in obtaining sharp convergence rates for trapezoidal rules with non-smooth integrands. Explore the effectiveness of Madelung-constant correction for Fock exchange energy and the staggered mesh method for periodic Fock exchange and MP2 calculations.
Syllabus
Outline
General introduction
Electronic structure calculations
Problems
Example
External energy calculation
Exchange energy calculation
Stagger mesh method
Results
Analysis
Focus change calculation
Conclusion
Summary
Taught by
Institute for Pure & Applied Mathematics (IPAM)
Related Courses
The Quantum WorldHarvard University via edX Approximate Methods In Quantum Chemistry
Indian Institute of Technology, Kharagpur via Swayam Computational Chemistry and Classical Molecular Dynamics
NPTEL via YouTube A Mathematical Look at Electronic Structure Theory - JuliaCon 2021 Workshop
The Julia Programming Language via YouTube Breaking the Curse of Dimension in Quantum Mechanical Computations Through Analysis and Probability
Alan Turing Institute via YouTube