  Knowledge of the properties of the exchange-correlation functional in the
form $\frac 1\lambda v_{xc}([\rho _\lambda ],\frac{{\bf r}}\lambda )$, where
$\rho _\lambda ({\bf r})=$ $\lambda ^3\rho (\lambda {\bf r}),$ is important
when expressing the exchange-correlation energy as a line integral $%
E_{xc}[\rho ]=\int_0^1d\lambda \int d{\bf r}\frac 1\lambda v_{xc}([\rho
_\lambda ],\frac{{\bf r}}\lambda )\left[ 3\rho ({\bf r})+{\bf r.\nabla }\rho
({\bf r})\right] $ (van Leeuwen and Baerends, Phys. Rev. A {\bf 51}, 170
(1995)). With this in mind, it is shown that in the low density limit $%
\lim_{\lambda \rightarrow 0}\int \rho ({\bf r})\nabla ^2\frac 1\lambda
v_{xc}([\rho _\lambda ],\frac{{\bf r}}\lambda )\ d^3r\leq 4\pi \int \rho (%
{\bf r})^2d^3r.$ This inequality is violated in the local-density
approximation.
