{\it Ab-inito} liquid water with hybrid functionals and dispersion interactions*

We report {\it ab-initio} molecular dynamics simulations of liquid water using the hybrid PBE0 functional plus self-consistent dispersion forces based on the scheme of Ref.\footnote{A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. {\bf 102}, 073005 (2009).} Simulations were performed at T=300K and at T=330K to approximately account for nuclear quantum effect on the oxygen-oxygen(O-O) RDF, as suggested by previous path integral simulations. Focusing on O-O RDF, we find that the combined effect of the hybrid functional and of the dispersion interactions significantly improves the agreement of the simulated structure with experiment.