Plane Wave Expansion

The plane wave expansions introduced in the last section were for local potentials (i.e. the potential is identical for each angular momentum).

$$V^{\rm local}({\bf r}) = \sum_{\bf G} V^{\rm local}({\bf G}) \exp \! \left[ {i {\bf G} \cdot {\bf r}} \right] \enspace ,$$ (205)

Kohn-Sham orbitals

$$\Phi ({\bf r}) = {1 \over \sqrt{\Omega}} \sum_{\bf G} c_{i}({\bf G}) \exp \! \left[ {i {\bf G} \cdot {\bf r}} \right] \enspace ,$$ (206)

and the electron density

$$n ({\bf r}) = \sum_{\bf G} n({\bf G}) \exp \! \left[{i {\bf G} \cdot {\bf r}}\right] \enspace .$$ (207)