A new approximation method for electron systems

Using a time-dependent generalisation of the Hohenberg-Kohn-Sham formalism the energy functional is shown to be calculable by an iteration technique. The proposed method yields approximations for the particle density and the dynamic density response function of the interacting electron system; excited energy states and non-stationary time-dependent problems can also be investigated. As an example for practicability of the formalism a simple approximation for the 1s2s states of the helium atom is presented.