The structure and the hydrogen bonding in the systems formed by the intramolecularly H-bonded systems, namely, maltol (3-hydroxy-2-methyl-4-pyrone), 5, 2,4,6-trinitrophenol, 6, acetylacetone enol, 7, with Lewis bases, phosgene, 8, dioxane, 9, and DMSO, 10, have been studied by density functional theory (B3LYP) and MP2 using the 6-311G* basis set. The continuum solvent effect was simulated by IEF-PCM model. The hydrogen bond analysis using the atoms in molecules (AIM) method was applied by using the MP2(full)/ 6-311++G** electron density to establish the nature of the bifurcate hydrogen bond (BHB) in these systems as well as contributory factors for its stabilization. The nature of interaction in the intermolecular H-complexes formed by compounds 5-7 with the Lewis bases 8-10 was shown to depend on the strength of the intramolecular hydrogen bond O center dot center dot center dot H and the strength of the base. The critical values of the C=O center dot center dot center dot H and N=O center dot center dot center dot H angles for which the formation of BHB is possible, have been determined.