On microscopical derivation of Lorentz-Lorenz formula

Lorentz-Lorenz formula may be derived microscopically by the analytical inversion of the dielectric matrix (DM) in the limit of tightly bound electrons. Exchange and correlation effects are to be taken into account and atomic polarisability is to be defined correctly in terms of the atomic susceptibility instead of the polarization operator. A wrong definition was the origin of usual contradictions between microscopical calculations and classical formula. The inversion of the DM diminishes dielectric constant in comparison with the diagonal element of DM but this procedure takes into account only a part of the local field effects caused by rapidly oscillating fields. Another part is connected with exchange interaction and increases the diagonal element of DM in comparison with dielectric constant without any local field effects, hence all local field effects do increase the dielectric constant.