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Uniform electron gases

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Abstract

We show that the traditional concept of the uniform electron gas (UEG)—a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume—is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, viz. the usual one-electron density parameter ρ and a new two-electron parameter η. We outline a systematic strategy to determine a new density functional E (ρ, η) across the spectrum of possible ρ and η values.

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Notes

  1. The hookium atom consists of two electrons that repel Coulombically but are bound to the origin by a harmonic potential [61].

  2. Henceforth, all energies will be reduced energies.

  3. We note that, in low-density cases, the RHF solutions are unstable with respect to lower-energy, symmetry-broken UHF wavefunctions [49]. However, we will not consider the latter in the present study.

  4. This hypergeometric may be related to a Wigner 6j symbol [64].

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Acknowledgments

We would like to thank the Australian Research Council for funding (Grants DP0771978, DP0984806 and DP1094170) and the National Computational Infrastructure (NCI) for generous supercomputer grants.

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Authors and Affiliations

  1. Research School of Chemistry, Australian National University, Canberra, ACT, 0200, Australia

    Peter M. W. Gill & Pierre-François Loos

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  1. Peter M. W. Gill
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  2. Pierre-François Loos
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Correspondence to Peter M. W. Gill.

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Published as part of the special collection of articles celebrating the 50th anniversary of Theoretical Chemistry Accounts/Theoretica Chimica Acta.

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Gill, P.M.W., Loos, PF. Uniform electron gases. Theor Chem Acc 131, 1069 (2012). https://doi.org/10.1007/s00214-011-1069-7

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