The linear monohydroxy alcohols are strongly hydrogen bonded liquids that have been considered as homologues of water. Here we report ab initio molecular dynamics simulations of the liquid alcohols, methanol to pentanol, and from the joint radial-angular probability distribution of the intermolecular O--O distances and HO--O angles determine the geometrical parameters that define the hydrogen bond in these systems. The key feature of the hydrogen bond in the liquid alcohols, irrespective of the size of the alkyl group, is the strong orientation dependence with the donor-acceptor HO--O angle being close to zero, similar to that observed in liquid water. Hydrogen bond formation is consequently considered as the passage from a state where donor-acceptor pairs show no preferred orientation to one where they are almost linear. The potential of mean force, the reversible work associated with this process, was computed from the pair probability density distributions obtained from the simulations and that for a hypothetical state where donor-acceptors are randomly oriented. We find that the magnitude of the free energy for hydrogen bond formation is maximum for ethanol and show that this arises from a larger electrostatic contribution to hydrogen bond formation in ethanol as compared to the other alcohols.