Using the theory of atoms in molecules (ALM), the intermolecular interactions, including hydrogen bonds (HBs) and the new intermolecular bonds (O-O) found recently in ice IX, ice II, ice VI, ice VII and ice VIII, can be described and classified by the topological properties of the charge density rho(r(b)) at the (3, - 1) bond critical points (BCPs) where the gradient of rho(r) vanishes. For 27 representative HBs and 27 representative O-O interactions, we show that the kinetic energy density G(r(b)) and the potential energy density V(r(b)) at the BCP depend exponentially on the HE and O-O distances, respectively. We also show and quantify the long-suspected result that HBs in ice Ih have some degree of covalent character, and moreover that this covalent character of the HBs persists for all of the HBs in all of the studied phases except ice VIII.