A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons

Zhang, Yingkai; Yang, Weitao

doi:doi:10.1063/1.476859

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Molecular model for the simultaneous orientational and translational ordering in a two-dimensional liquid

We present a molecular–statistical theory of the phase transition from the two-dimensional isotropic liquid to the phase which has the elements of the orientational and translational order combined in a single order parameter. This phase possesses the glide symmetry, similar to the herringbone order in crystals, and is related to the mesophases observed in Langmuir monolayers. The microscopic definition of the herringbone order parameter is presented and the transition temperatures from the isot...

The exchange energy functional in a weak magnetic field

A density functional theory for the Kohn–Sham exchange energy of a bounded, closed shell system in a weak, uniform, magnetic field is presented. The form obtained vanishes when the electron density is radial and, unlike the unscreened exchange energy of a locally uniform electron gas, does not diverge due to the Coulomb interaction. The role of the exchange-correlation functional in the context of magnetic response theory is also examined. © 1998 American Institute of Physics.

The difficulty of widely used density functionals in describing the dissociation behavior of some homonuclear and heteronuclear diatomic radicals is analyzed. It is shown that the self-interaction error of these functionals accounts for the problem—it is much larger for a system with a noninteger number of electrons than a system with an integer number of electrons. We find the condition for the erroneous dissociation behavior described by approximate density functionals: when the ionization energy of one dissociation partner differs from the electron affinity of the other partner by a small amount, the self-interaction error will lead to wrong dissociation limit. Systems with a noninteger number of electrons and hence the large amount of self-interaction error in approximate density functionals arise also in the transition states of some chemical reactions and in some charge-transfer complexes. In the course of analysis, we derive a scaling relation necessary for an exchange-correlation functional to be self-interaction free. © 1998 American Institute of Physics.

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KEYWORDS and PACS

Keywords

density functional theory, electron affinity, dissociation, free radicals

PACS

82.30.Lp

Decomposition reactions (pyrolysis, dissociation, and fragmentation)
31.15.E-

Density-functional theory
33.15.Ry

Ionization potentials, electron affinities, molecular core binding energy