The behaviors of the electrons in binary complexes formed from HF, H2O, and NH3 as well as in the complex formed between HF and CH4 are analyzed at the single electron level in order to characterize the nature of intermolecular bonding in dimers that may contain hydrogen bonds. The analysis uses the quantitative measures of the degree to which a single electron is shared between two points zeta and zeta＇, the sharing index I(zeta; zeta＇), and the underlying sharing amplitude [zeta; zeta＇], as well as the derived quantities, bond indices, self-sharing indices, delocalization indices, and volume-point sharing indices. The bond indices, together with the delocalization indices and the self-sharing indices, give a gross dissection of the sharing of an electron between the volumes associated with atoms and between molecules. These indices give a preliminary indication of the variety of the strengths of sharing in the complexes, but they do not necessarily distinguish between bonding and antibonding sharing. It is the sharing amplitude which indicates the wide variety of types of intermolecular sharing in the complexes, the sharing ranging from covalent to antibonding in the complexes studied. By comparing the sharing in two conformations of the complexes between two given molecules, such as the complexes HOH-NH3 and H2NH-OH2 involving water and ammonia, the difference between the sharing in complexes in which the bonding is, according to the acid-base nature of the moieties, conducive to proton transfer (the natural order) and in which the bonding is not conducive to proton transfer (the unnatural order) can be determined. In general the intermolecular sharing is found to be larger in the conformation conducive to proton transfer, with the sharing amplitude with the fixed point on the bridge proton clearly indicating that in the natural conformation a covalent bond (although weak in some cases) is formed to the proton acceptor in contrast to the unnatural conformation in which the sharing amplitude indicates a non- or antibonded behavior to the proton acceptor. The electron shared from the proton acceptor is also found to be more delocalized over the bridge proton and the proton donor in the natural conformation than in the unnatural conformation. We propose that the term "hydrogen bond" should be restricted to those bonds which involve a bridge proton between the moieties forming the complex and for which the sharing amplitude from the bridge proton to the proton acceptor has the characteristics of a covalent bond. We suggest that the other complexes, which are locally stable, should not be considered to be hydrogen-bonded, The weakest covalent intermolecular sharing is found in FH-FH while the strongest is in FH-NH3, the value of the intermolecular sharing in the latter being almost the same as between the fluorine and the bridge proton in the complex. The weakest antibonding tin terms of sharing) is found in H3CH-FH, and the strongest antibonding in the NH3 dimers.