Foundations of the ionization potential condition for localized electron removal in density functional theory

Abstract

Optimal tuning of functional parameters in density functional theory approximations, based on enforcing the ionization potential theorem, has emerged as the method of choice for the non-empirical prediction of the electronic structure of finite systems. This method has recently been extended to the bulk limit, based on an ansatz that generalizes the ionization potential theorem to the removal of an electron from a localized Wannier orbital. This Wannier-localization based optimal tuning method has been shown to be highly successful for a wide range of periodic systems, accurately predicting electronic and optical properties. However, a rigorous theoretical justification for its foundational ansatz has been lacking. Here, we establish an ionization potential condition for the removal of a localized electron, by extending the piecewise linearity and Janak's theorems in density functional theory. We also provide numerical evidence supporting our theory.

References in corpus (25)

• Maximally localized Wannier functions: Theory and applications
• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• NWChem: Past, Present, and Future
• Fractional charge perspective on the band-gap in density-functional theory
• Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method
• Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors
• Koopmans' condition for density-functional theory
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional
• Koopmans-compliant functionals and their performance against reference molecular data
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Koopmans-compliant spectral functionals for extended systems
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• Deviations from piecewise linearity in the solid-state limit with approximate density functionals
• An Optimally-Tuned Starting Point for Single-Shot $GW$ Calculations of Solids
• koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals
• Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals
• Optical absorption spectra of metal oxides from time-dependent density functional theory and many-body perturbation theory based on optimally-tuned hybrid functionals
• Localized orbital scaling correction for periodic systems
• A DFT+U type functional derived to explicitly address the flat plane condition
• The reliability of hybrid functionals for accurate fundamental and optical gap prediction of bulk solids and surfaces
• Electronic structure and optical properties of halide double perovskites from a Wannier-localized optimally-tuned screened range-separated hybrid functional
• Flat-plane based double-counting free and parameter free many-body DFT+U