DFT+U and DFT+U+V: Basic Concepts and Applications - Advanced Quantum ESPRESSO Tutorial 2022

Explore the fundamental concepts and applications of DFT+U and DFT+U+V in this comprehensive tutorial video from the Advanced Quantum ESPRESSO series. Delve into Density Functional Theory and its applications in studying cathode materials for Li batteries, focusing on LixCoPO4 and electron localization. Examine the Hubbard model, understand how the +U correction works in DFT, and investigate its effects on defects and Fe minerals in Earth's interior. Learn about Raman spectra calculations using DFT+U and explore electron localization in LiMnPO4. Compare DFT+U+V with hybrid functionals for band semiconductors like Si, GaAs, and Ge. Address challenges such as delocalization error, static correlation error, and potential discontinuities in extended systems. Gain insights into symmetry breaking, localization, and the linearization of energy in DFT+U calculations.

Intro
Outline
Density Functional Theory
Case study: cathode materials of Li batteries
LixCoPO4: e localization and energetics Assessing the oxidation state: total occupation of atomic d states of Co
Band vs localized pictures: the Hubbard model
DFT+U: general idea
DFT+U: correcting DFT with the Hubbard model
How does the +U correction work?
e-localization: defects
Fe minerals of the Earth's interior
Raman spectra from DFT+U
LiMnPO4: e localization and energetics
Localization and covalency: DFT+U+V
Band semiconductors: Si and GaAs
Band semiconductors: C, Si and Ge
DFT+U+V vs hybrids
Delocalization error
Static (strong) correlation error
Potential discontinuities
Localization in extended systems
DFT+U and the linearization of energy
Symmetry breaking and localization
Summary