The variation with the intermolecular distance of features in hydrogen bond (HB) dimers dependent on the electron density rho (r) are studied in four complexes representative of weak/medium HB interactions. Topological properties, energy densities and integrated atomic properties are obtained with rho (r) of dimers at B3LYP/6-311++G(d,p) optimized structures obtained upon fully relaxing the geometry of monomers. The dependence of A-H . . .B bond properties on intermolecular R(H . . .B) distances allows to characterize the nature of the interaction as monomers move nearer from infinite separation. At long distances the interaction is only electrostatic while for separations about 1 Angstrom larger than the equilibrium distance R-eq, quantum effects arising from rho (r) begin to dominate. In the immediate neighborhood of R-eq the interaction is mainly led by the stabilization of the H-donor due in turn to energy lowerings in A and B atoms associated to polarization effects. The mutual penetration of electron densities of donor and acceptor monomers provokes a considerable reduction of atomic volumes for H and B atoms which reveals in the form of redistribution rather than transfer of charge. This range of distances exhibits noncovalent bond features but shortly after, when monomers approximate a few tenths of Angstrom below R-eq, characteristics typical of covalent interactions begin to appear while the rate of change of all the rho (r)-dependent properties increases rapidly.