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Exact and local spin density approximation (LSDA) exchange energy density functionals in the Coulomb-attenuated Schrödinger equation (CASE) approximation are constructed. When expressed as asymptotic series in the attenuation parameter ω, their leading terms are identical. If a Gaussian basis set is used, the terms in the exact series (but not the LSDA series) can be evaluated analytically, i.e. without resorting to quadrature on a grid.
Gill et al. (Mon,) studied this question.