Finite-Size Error and Its Correction in Energy Calculations for Periodic Systems

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.