We report converged quantum statistical mechanical simulations of liquid water with the Thole-type Model (version 2.1), Flexible, polarizable (TTM2.1-F) interaction potential for water. Simulations of total length of 600 ps with a 0.05 fs time step for a periodic unit cell of 256 molecules with up to 32 replicas per atom suggest that the quantum effects contribute 1.01+/-0.02 kcal/mol to the liquid enthalpy of formation at 298.15 K. They furthermore demonstrate for the first time a quantitative agreement with experiment for the heights and broadening of the intramolecular OH and HH peaks in the radial distribution functions.