![]() Unlike covalent bonds, which vary in strength within a factor of ~4 (30–120 kcal mol −1), hydrogen bonds are much less constrained in their geometry and physical properties, and they vary in strength by a factor of at least 20-fold (2–40 kcal mol −1). By mid-twentieth century, the weak conventional hydrogen bonds were reasonably well understood and widely accepted. Hydrogen bonds were controversial throughout the twentieth century. Frey, in Encyclopedia of Biological Chemistry (Second Edition), 2013 The Nature of Hydrogen Bonds The hydrogen bonding between ions and water is the principal mechanism of the hydration processes. For F −⋯H 2O the hydrogen-bonded O-H distance increases by about 0.1 Â from its equilibrium-isolated monomer value of 0.96 Â, and this size of elongation is typical for ionic systems. Thus, the F-H distance is increased from 0.93 Â to 1.30 Â upon the dimer formation. The H-F bond in F −⋯HF is of the same length as the F −⋯H hydrogen bond (i.e., the complex is centrosymmetric). Strong hydrogen bonds result in a significant distortion of the monomer's structure. Furthermore, the H⋯F − distance of about 1.3 Â is closer to distances typical for chemical bonds (about 1 Â) than to H⋯Y hydrogen bond distances (about 2 Â). In the case of the last complex, the bond is so strong that this complex could also be classified as a chemically bonded one. Examples include Cl −⋯H 2O, F −⋯H 2O, H 3O + ⋯H 2O, and F −⋯HF with interaction energies of about 15, 30, 35, and 40 kcal/mol, respectively. The strong hydrogen bonds involve ionic species. Other well-known dimers in this group involve carboxylic acids, base pairs of nucleic acids, and typical hydrogen bonds forming within or between proteins. Water dimer or hydrogen fluoride dimer are typical examples for this group. Most of hydrogen-bonded complexes of interest form the group of moderate hydrogen bonds. ![]() The weakest hydrogen bonds considered in the literature are about 0.5 kcal/mol. Also, the hydrogen bonds where X-H attaches to a π bond on the acceptor belong to this group (examples of such bonds are given in Fig. The weak hydrogen bonds involve less polar X-H groups in proton donors, like C-H or P-H groups, or less polar acceptors, like the N 2 molecule in the N 2⋯HF complex discussed above. Usually three classes are distinguished: weak, moderate, and strong bonds, with energetic boundaries at about 2 and 15 kcal/mol. This finding is verified by estimating cooperativity along the dissociation path of H-bonds in the infinite chains, using two empirical parameters that account for polarizability, together with DFT association energies and molecular dipoles of solely monomers and dimers.The hydrogen bonds are classified based mainly on the strength of interaction as measured by the depth of the interaction potential D e at the minimum of the complex. in a linear chain of H-bonds, quantum effects do not contribute to the H-bond non-additivity. Nevertheless, the effective point-dipoles are fully determined once a single H-bond is formed, indicating that quantum effects involved in H-bonding are circumscribed to nearest-neighbor interactions only i.e. It is found that the magnitude of these effective point-dipoles is a consequence of mutual polarization and additional effects beyond a polarizable point-dipole model. The latter is corroborated by comparing the H-bond cooperativity in infinitely-long H-bonded hydrogen cyanide, 4-pyridone and formamide chains, assessed using density functional theory (DFT), against the strengthening of the dipole–dipole interaction upon the formation of an infinite chain of effective point-dipoles. It is shown that H-bond cooperativity originates solely from classical electrostatics. The origin of non-additivity in hydrogen bonds (H-bonds), usually termed as H-bond cooperativity, is investigated in H-bonded linear chains.
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