IS THE LOCAL-DENSITY APPROXIMATION EXACT FOR SHORT-WAVELENGTH FLUCTUATIONS

A commonly cited reason for the success of the local spin density (LSD ) approximation is that it correctly accounts for short wavelength con tributions to the exchange-correlation energy. We show that this resul t, while true in several limits and for several approximations to thes e fluctuations, is not exact in general, with an analytic demonstratio n on a specific system (Hooke's atom). Nevertheless, we find that LSD is rather accurate for small separations.