Analytic mathematical models for the static spin ($G_{-}$) and density ($G_{+}$) local field factors for the uniform electron gas (UEG) as functions of wave vector and density are presented. These models closely fit recent quantum Monte Carlo (QMC) data and satisfy exact asymptotic limits. A simple functional form for $G_{-}$ is developed; the same functional form parametrized for $G_{+}$ yields an improvement over previous work. The QMC-computed $G_{\pm }$ are consistent with a rapid crossover between theoretically derived small-$q$ and large-$q$ expansions of $G_{\pm }$. These expansions are completely determined by $r_{\mathrm{s}}$, the UEG correlation energy per electron, and the UEG on-top pair distribution function. We demonstrate their utility by computing uniform electron gas correlation energies over a range of densities. These models, which hold over an extremely wide range of densities, are recommended for use in practical time-dependent density functional theory calculations of simple metallic systems. A revised model of the spin susceptibility enhancement is developed that fits QMC data, and does not show a ferromagnetic instability at low density.

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• Dielectric properties
• Electronic structure
• Metals
• Density functional theory development
• Linear response theory
• Quantum Monte Carlo