  The quantum hydrodynamic theory is a promising method for describing
microscopic details of macroscopic systems. The hydrodynamic equation can be
directly obtained from a single particle Kohn-Sham equation that includes the
contribution of an external vector potential. This derivation allows to
straightforwardly incorporate in the hydrodynamic equation an
exchange-correlation viscoelastic term, so that broadening of collective
excitation can be taken into account, as well as a correction to the plasmon
dispersion. The result is an accurate self-consistent and computationally
efficient hydrodynamic description of the free electron gas. A very accurate
agreement with full quantum calculations is shown.
