Local Exchange-Correlation Potentials by Density Inversion in Solids

Abstract

Following Hollins et al. [J. Phys.: Condens. Matter 29, 04LT01 (2017)], we invert the electronic ground state densities for various semiconducting and insulating solids calculated using several density functional approximations within the generalised Kohn-Sham (GKS) scheme, Hartree-Fock (HF) theory and the LDA+$U$ method, and benchmark against standard (semi-)local functionals. The band structures from the resulting local exchange-correlation (LXC) Kohn-Sham potential for these densities are then compared with the band structures of the original GKS method. We find the LXC potential obtained from the HF density systematically predicts band gaps in good agreement with experiment, even in strongly correlated transition metal monoxides (TMOs). Furthermore, we find that the HSE06 and PBE0 hybrid functionals yield similar densities and LXC potentials, and in weakly correlated systems, these potentials are similar to PBE. For LDA+$U$ densities, the LXC potential effectively reverses the flattening of bands caused by over-localisation by a large Hubbard-$U$ value, while for meta-GGAs, we find only small differences between the GKS and LXC results demonstrating that the non-locality of meta-GGAs is weak.

25 pages, 15 figures, 4 tables - Accepted version with supplementary material. Published in PRB

References in corpus (46)

• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Perspective on density functional theory
• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems
• Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach
• Understanding Band Gaps of Solids in Generalized Kohn-Sham Theory
• Spectral and Fermi surface properties from Wannier interpolation
• Understanding and reducing errors in density functional calculations
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Hubbard parameters from density-functional perturbation theory
• Regularized SCAN functional
• Koopmans' condition for density-functional theory
• More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme
• Magnetic Moment Collapse-Driven Mott Transition in MnO
• Evaluating transition-metal oxides within DFT-SCAN and SCAN+U frameworks for solar thermochemical applications
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Ions in solution: Density Corrected Density Functional Theory (DC-DFT)
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Basic Physical Properties of Cubic Boron Arsenide
• Accurate screened exchange band structures for transition metal monoxides MnO, FeO, CoO and NiO
• Numerical Methods for the Inverse Problem of Density Functional Theory
• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Systematic beyond-DFT study of binary transition metal oxides
• Koopmans-compliant spectral functionals for extended systems
• Accurate and efficient approximation to the optimized effective potential for exchange
• Precise response functions in all-electron methods: Application to the optimized-effective-potential approach
• Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation
• All-electron quasi-particle self-consistent $GW$ band structures for SrTiO${}_3$ including lattice polarization corrections in different phase
• Zero-point Renormalization of the Band Gap of Semiconductors and Insulators Using the PAW Method
• Koopmans-compliant functionals and potentials and their application to the GW100 test-set
• Understanding density driven errors for reaction barrier heights
• Constraining density functional approximations to yield self-interaction free potentials
• Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density
• Density-inversion method for the Kohn-Sham potential: role of the screening density
• Optimized Effective Potential Using The Hylleraas Variational Method
• Re-examining the electronic structure of germanium: A first-principle study
• Influence of magnetic ordering on the spectral properties of binary transition metal oxides
• Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals
• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• A local Fock-exchange potential in Kohn-Sham equations
• Improving MP2 band gaps with low-scaling approximations to EOM-CCSD
• Noncollinear DFT+$U$ and Hubbard parameters with fully-relativistic ultrasoft pseudopotentials
• Performance of the Constrained Minimization of the Total Energy in Density Functional Approximations: the Electron Repulsion Density and Potential
• A correction for the Hartree-Fock Density of States for Jellium without Screening
• Improving the exchange and correlation potential in density functional approximations through constraints