1.3 Basic Strategy of DFT

A consequence of the theorems of Hohenberg and Kohn is the following procedure for finding the inhomogeneous equilibrium density $\rho$:

• Find a good, or at least a plausible, approximation for ${\rm\cal{F}}_{ex}[\rho']$, either based on the molecular interaction or from other considerations (see below).
  
  
• Minimize $\Omega_{\phi} \equiv {\rm\cal{F}}_{ex}[\rho']$ $+{\rm\cal{F}}_{id}[\rho']$ $- \int d\vec{r} u(\vec{r}) \rho(\vec{r'})$ with respect to $\rho'(\vec{r})$.

The optimal $\rho(\vec{r})$ is then the equilibrium inhomogeneous density of the system.