Theoretical analysis demonstrates that the local spin density approximation is not strictly exact for short-wavelength fluctuations in Hooke's atom, highlighting bounds on standard assumptions.
A commonly cited reason for the success of the local spin density (LSD) approximation is that it correctly accounts for short wavelength contributions to the exchange-correlation energy. We show that this result, while true in several limits and for several approximations to these fluctuations, is not exact in general, with an analytic demonstration on a specific system (Hooke's atom). Nevertheless, we find that LSD is rather accurate for small separations.
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Burke et al. (1994) studied this question.
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