Violation of a local form of the Lieb-Oxford bound

J. G. Vilhena, E. Räsänen, L. Lehtovaara, M. A. L. Marques

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    Abstract

    In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents a rigorous lower limit for the indirect Coulomb interaction energy. Here we employ exact-exchange calculations for the G2 test set to show that the local form of the bound is violated in an extensive range of both the dimensionless gradient and the average electron density. Hence, the results demonstrate the severity in the usage of the local form of the bound in functional development. On the other hand, our results suggest alternative ways to construct accurate density functionals for the exchange energy.

    Original languageEnglish
    Article number052514
    Number of pages5
    JournalPhysical Review A
    Volume85
    Issue number5
    DOIs
    Publication statusPublished - 29 May 2012
    Publication typeA1 Journal article-refereed

    Keywords

    • GENERALIZED GRADIENT APPROXIMATION
    • EXCHANGE-CORRELATION-ENERGY
    • DENSITY-FUNCTIONAL THEORY
    • OCTOPUS
    • ATOMS
    • TOOL

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