Many remarkable properties of liquid water originate from the ability of its molecules to form hydrogen bonds, each of which emerges as a combination of electrostatic, polarization, dispersion, and donor-acceptor or covalent interactions. In this work, ab initio molecular dynamics was tailored to isolate and switch off the covalent component of interactions between water molecules in simulations. Comparison of simulations with and without covalency shows that a small amount of intermolecular electron density transfer has a profound effect on the structure and dynamics of the hydrogen-bond network and thus on observable properties of room-temperature liquid water.