Convexity and translational invariance constraint on the exchange-correlation functional

Daniel Joubert, Mel Levy

Knowledge of the properties of the exchange-correlation functional in the form $\frac{1}{\lambda }{v}_{xc}([{\rho }_{\lambda }],\frac{\mathbf{r}}{\lambda })$, where ${\rho }_{\lambda }(\mathbf{r})=$ ${\lambda }^3\rho (\lambda \mathbf{r}),$ is important when expr…