Restoration of the Derivative Discontinuity in Kohn-Sham Density Functional Theory: An Efficient Scheme for Energy Gap Correction

Abstract

From the perspective of perturbation theory, we propose a systematic procedure for the evaluation of the derivative discontinuity (DD) of the exchange-correlation energy functional in Kohn-Sham density functional theory (KS-DFT), wherein the exact DD can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate DD. While the zeroth-order theory yields a vanishing DD, the first-order correction to the DD can be expressed as an explicit universal functional of the ground-state density and the KS lowest unoccupied molecular orbital density, allowing the direct evaluation of the DD in the standard KS method without extra computational cost. The fundamental gap can be predicted by adding the estimated DD to the KS gap. This scheme is shown to be accurate in the prediction of the fundamental gaps for a wide variety of atoms and molecules.

arXiv commentaccepted for publication in Phys. Rev. Lett., 24 pages, 2 figures, supplemental material included

References in corpus (7)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• 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
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Density functional theory with fractional orbital occupations
• Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections
• Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential

Cited by in corpus (22)

• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• The derivative discontinuity of the exchange-correlation functional
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Thermally-assisted-occupation density functional theory with generalized-gradient approximations
• Assessment of Density Functional Methods for Exciton Binding Energies and Related Optoelectronic Properties
• Semilocal exchange-correlation potentials for solid-state calculations: Current status and future directions
• Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Deviations from piecewise linearity in the solid-state limit with approximate density functionals
• Assessment of density functional methods with correct asymptotic behavior
• Identification of the Mott insulating CDW state in 1T-TaS${}_2$
• Limitations of the DFT-1/2 method for covalent semiconductors and transition-metal oxides
• Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections
• Unity of Kohn-Sham Density Functional Theory and Reduced Density Matrix Functional Theory
• Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue
• Learning the energy curvature versus particle number in approximate density functionals
• Electronic and Optical Properties of the Narrowest Armchair Graphene Nanoribbons Studied by Density Functional Methods
• Van der Waals interactions in rare-gas dimers: The role of interparticle interactions
• Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals
• Assessment of the LFAs-PBE exchange-correlation potential for high-order harmonic generation of aligned H2+ molecules
• Fundamental gaps of quantum dots on the cheap
• Transferability of self-energy correction in tight-binding basis constructed from first principles