One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation

Abstract

One-electron self-interaction and an incorrect asymptotic behavior of the Kohn-Sham exchange-correlation potential are among the most prominent limitations of many present-day density functionals. However, a one-electron self-interaction-free energy does not necessarily lead to the correct long-range potential. This is here shown explicitly for local hybrid functionals. Furthermore, carefully studying the ratio of the von Weizsäcker kinetic energy density to the (positive) Kohn-Sham kinetic energy density, ${\tau }_{\mathrm{W}}/\tau$, reveals that this ratio, which frequently serves as an iso-orbital indicator and is used to eliminate one-electron self-interaction effects in meta-generalized-gradient approximations and local hybrid functionals, can fail to approach its expected value in the vicinity of orbital nodal planes. This perspective article suggests that the nature and consequences of one-electron self-interaction and some of the strategies for its correction need to be reconsidered.

12 pages, 8 figures

References in corpus (4)

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• Electrical response of molecular systems: the power of self-interaction corrected Kohn-Sham theory
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• Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue
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• Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density
• Local self-interaction correction method with a simple scaling factor
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• First-principles derivation and properties of density-functional average-atom models
• Approximations to the exact exchange potential: KLI versus semilocal
• Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis
• Implementation of Perdew-Zunger self-interaction correction in real space using Fermi-Löwdin orbitals
• Ionization Potentials and Fundamental Gaps in Atomic Systems from the Ensemble-DFT Approach
• Review of the finite difference Hartree-Fock method for atoms and diatomic molecules, and its implementation in the x2dhf program
• Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration