Ionization Potentials and Fundamental Gaps in Atomic Systems from the Ensemble-DFT Approach

Abstract

Calculations in Kohn-Sham density functional theory crucially rely on high-quality approximations for the exchange-correlation (xc) functional. Standard local and semi-local approximations fail to predict the ionization potential (IP) and the fundamental gap, departing from the Kohn-Sham orbital energies, due to the deviation of the total energy from piecewise-linearity and the absence of the derivative discontinuity. The ensemble generalization procedure introduced in Phys. Rev. Lett. 110, 126403 (2013) restores, to a large extent, these features in any approximate xc functional and improves its ability to predict the IP and the fundamental gap with negligible additional computational effort. In this work we perform an extensive study of atoms and first ions across the Periodic Table, generalizing the local spin-density and the Perdew-Burke-Ernzerhof approximations. By applying the ensemble generalization to a variety of systems, with s-, p- and d-character, we assess the accuracy of the method and identify important trends. In particular, we find that the accuracy of our approach heavily depends on the character of the frontier orbitals: when d-orbitals are involved, the performance is far less accurate. Possible sources of error are discussed and ways for further improvement are outlined.

arXiv comment21 pages, 9 figures

References in corpus (32)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Perspective on density functional theory
• Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach
• Understanding Band Gaps of Solids in Generalized Kohn-Sham 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
• More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Koopmans-compliant functionals and their performance against reference molecular data
• The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms
• A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues
• Hole Localization in Molecular Crystals From Hybrid Density Functional Theory
• One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
• Comparison between exact and semilocal exchange potentials: An all-electron study for solids
• Koopmans-compliant functionals and potentials and their application to the GW100 test-set
• A new generalized Kohn-Sham method for fundamental band-gaps in solids
• Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density functional theory using the ensemble-generalization approach
• Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue
• Localized orbital scaling correction for periodic systems
• Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations
• Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density
• Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities
• Higher Ionization Energies of Atoms in Density Functional Theory