Abstract
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.