The intermolecular hydrogen bonds in dimers of formic acid, acetic acid, and formamide were investigated. Additionally, three configurations of the pyrrole-2-carboxylic acid (PCA) dimer were studied to analyze how the pyrrole pi-electron system influences the carboxylic groups connected by double O-(HO)-O-... hydrogen bonds. The ab initio calculations for the systems investigated were performed at MP2/6-311++G(d,p), MP2/aug-cc-pVDZ, and MP2/aug-cc-pVTZHMP2/aug-cc-pVDZ levels of theory. The "atoms in molecules" theory of Bader was used and the analysis of the critical points was performed to study the nature of hydrogen bonds. The decomposition of the total interaction energy applied here reveals that the delocalization energy term is a particularly important attractive contribution in these systems, more important in the case of systems forming homonuclear O-(HO)-O-... double hydrogen bonds than in the case of those connected through heteronuclear N-(HO)-O-... bonds. Because the systems analyzed may be formally classified as the resonance-assisted hydrogen bonds (RAHBs), it seems that the dominant contribution from the delocalization interaction energy term is a distinguished feature of such interactions.