The hydrogen bond (HB) is the subject of various studies since it is important in numerous chemical, physical and biological processes.i,ii,iii,iv One of first definitions of the hydrogen bond was given by Pauling v who stated that “under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms, instead of only one, so that it may be considered to be acting as a bond between them. This is called the hydrogen bond”. This interaction may be designated as X-H…Y, where X-H is the proton donating bond while Y is the proton acceptor. Pauling pointed out that X and Y atoms should be characterized by the high electronegativity, that the Y proton acceptor should posses at least one free electron pair and that the hydrogen bond is the electrostatic interaction.

Numerous characteristics and properties of the hydrogen bond have been presented. One can mention the elongation of the X-H bond as a result of hydrogen bond formation and a concomitant decrease of the X-H stretch vibration frequency.1 This shift to lower frequencies is called a red shift and being experimentally detectable in gas, liquid and solid phase was treated as the strong evidence of the hydrogen bond formation. The X-H…Y angle close to 1800 and the H…Y distance smaller than the corresponding sum of van der Waals radii are also attributed to the hydrogen bond However the subsequent studies have shown that there are interactions similar or related to the hydrogen bond which posses few of its characteristics but usually not all. The statement of the high electronegativity of X and Y atoms was contested since the C-H…O, C-H…N and C-H…S interactions were analyzed and classified as the hydrogen bonds;6,vii even the existence of the C-H…C hydrogen bond was discussed.viii

The dihydrogen bond (DHB) is the special type of the hydrogen bond where the role of the proton acceptor plays another hydrogen atom which is negatively charged.ix,x The X-H…Y interactions where the complexation leads to the shortening of the X-H bond and the accompanying increase of the X-H stretch vibration frequency (blue shift) were also analyzed.xi Thus one of the previously pointed out evidences of the existence of the hydrogen bond, the elongation of the proton donating bond, often treated as its signature was also contested.

The X-H…π interactions were analyzed and it was pointed out that they often posses characteristics of the hydrogen bond.3,xii,xiii Thus the existence of one-center proton acceptor possessing at least one free electron pair is also denied as the feature attributed to the hydrogen bond since π-electrons delocalized between two or more atoms are the proton acceptor for the X-H…π interactions.

The recent definition of Arunan and co-workers,xiv covers a diversity of interactions often classified as the hydrogen bonds. It is as follows: “the hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X–H in which X is more electronegative than H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation”. This definition only slightly differs from the older one of Pimentel and McClellan xv however it contains additional lists of criteria, characteristics and footnotes which refer to systems classified in numerous studies as the hydrogen bonds. For example it is stated that “the acceptor is an electron rich region such as, but not limited to, a lone pair of Y or π-bonded pair of Y-Z”. In such a sense the X-H…π interaction is in agreement with this explanation.

New experimental techniques and theoretical methods which allow to analyze inter- and intramolecular interactions were introduced in last decades. One can mention the Quantum Theory of Atoms in Molecules (QTAIM) xvi,xvii which is a powerful tool to analyze the electron density of any molecular system and so on the properties of interactions in terms of the characteristics of the electron density. The Natural Bond Orbitals (NBO) method is another tool to analyze different interactions.xviii,xix The hydrogen bond formation, in terms of the NBO method, may be considered as the combination of two processes.xx The hyperconjugative interaction connected with the charge transfer from the Y-lone pair to the σ*(X-H) antibonding orbital. This is connected with the increase of the occupation of that orbital and it leads to the elongation of the X-H bond. The second process is connected with the increase in s-character of X hybrid orbital in the X-H bond and it is responsible for the shortening of the X-H bond. If the second effect outweighs the first one thus the blue shift of the X-H stretch vibration frequency is observed, in the other case the more common red shift hydrogen bond exists.

On a basis of NBO analyses and findings the following definition was proposed recently by Weinhold and Klein.xxiHydrogen bond: A fractional chemical bond of coordinative A–H…B Lewis acid–base type, associated with the partial intermolecular A–H…:B  A:…H–B resonance (3-center/4-electron proton-sharing) commonly originating in the nB  σ*AHdonor–acceptor interaction between the lone pair nBof the Lewis base and the hydride antibond σ*AHof the Lewis acid.xxii

Two kinds of interactions are analyzed here; the dihydrogen bond which was also previously considered as the X-H…σ interaction xxiii and the interaction where molecular hydrogen acts as the Lewis base, designated later as X-H…σ(H2).

i  Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures, Springer-Verlag: Berlin, 1991.

ii  Scheiner, S. Hydrogen Bonding: A Theoretical Perspective, Oxford University Press: New York, 1997.

iii  Desiraju, G.R.; Steiner T. The weak hydrogen bond in structural chemistry and biology; Oxford University Press Inc., New York, 1999.
iv  Hydrogen Bonding – New Insights, Ed. Grabowski, S.J. Vol.3 of the series: Challenges and Advances in Computational Chemistry and Physics, Ed. Leszczynski, J. Springer, Dordrecht, 2006.
v  Pauling L. The Nature of the Chemical Bond, Cornell University Press, Ithaca, New York, 3rd edition, 1960.
vi Taylor, R.; Kennard, O. Crystallographic Evidence for the Existence of C-H…O, C-H…N, and C-H…Cl Hydrogen Bonds. J.Am.Chem.Soc. 1982, 104, 5063-5070.
vii Suttor, D. J. Evidence for the Existence of C-H…O Hydrogen Bonds in Crystals. J. Chem. Soc.1963, 1105-1110.
viii Mueller-Westerhoff, U.T.; Nazzal, A.; Proessdorf, W. First evidence for the existence of intramolecular carbon-hydrogen-carbon hydrogen bonds: carboanions of [1.1]ferrocenophane, 1-methyl-[1.1]ferrocenophane, and 1,12-dimethyl-[1.1]ferrocenophane. J.Am.Chem.Soc. 1982, 103, 7678-7681.
ix  Wessel, J.; Lee, Jr., J. C.; Peris, E.; Yap, G. P. A.; Fortin, J. B.; Ricci, J. S.; Sini, G.; Albinati, A.; Koetzle, T. F.; Eisenstein, O.; Rheingold, A. L.; Crabtree, R. H. An Unconventional Intermolecular Three-Center N-H…H2Re Hydrogen Bond in Crystalline [ReH5(PPh3)3]-indole-C6H6. Angew. Chem. Int. Ed. Engl. 1995, 34, 2507-2509.
Crabtree R. H.; Siegbahn, P. E .M.; Eisenstein, O.; Rheingold, A. L.; Koetzle, T. F. A New Intermolecular Interaction: Unconventional Hydrogen Bonds with Element-Hydride Bonds as Proton Acceptor. Acc. Chem. Res. 1996, 29, 348-354.
xi Hobza, P.; Havlas, Z. Blue-Shifting Hydrogen Bonds. Chem. Rev. 2000, 100, 4253-4264.
xii Nishio, M.; Hirota, M.; Umezawa, Y. The CH/ Interaction, Evidence, Nature, and Consequences, Wiley-VCH, New York, 1998.
xiii Takahashi, O.; Kohno, Y.; Nishio, M. Relevance of Weak Hydrogen Bonds in the Conformation of Organic Compounds and Bioconjugates: Evidence from Recent Experimental Data and High-Level ab Initio MO Calculations. Chem.Rev. 2010, 110, 6049-6076.
xiv Arunan, E.; Desiraju, G. R.; Klein, R. A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D. C.; Crabtree, R. H.; Dannenberg, J. J.; Hobza, P.; Kjaergaard, H.G.; Legon, A.C.; Mennucci, B.; Nesbitt, D.J. Definition of the hydrogen bond. Pure. Appl. Chem.2011, 83, 1637-1641.
xv G.C.Pimentel, A.L.McClellan, The Hydrogen Bond, W.H.Freeman and Company, San Francisco and London, 1960.
xvi Bader, R.F.W. Atoms in molecules. Acc.Chem.Res. 1985, 18, 9-15.
xvii  Bader, R.F. W. Atoms in Molecules, A Quantum Theory; Oxford University Press, Oxford, 1990.
xviii Weinhold, F.; Landis, C. Valency and Bonding, A Natural Bond Orbital Donor – Acceptor Perspective. Cambridge University Press 2005.
xix Reed, A.E.; Curtiss, L.A.; Weinhold, F. Intermolecular Interactions from a natural bond orbital, donor-acceptor viewpoint. Chem.Rev. 1988, 88, 899-926.
xx Alabugin, I.V.; Manoharan, M.; Peabody, S.; Weinhold, F. Electronic Basis of Improper Hydrogen Bonding:  A Subtle Balance of Hyperconjugation and Rehybridization. J.Am.Chem.Soc. 2003, 125, 5973-5987.
xxi Weinhold, F.; Klein, R. What is a hydrogen bond? Mutually consistent theoretical and experimental criteria for characterizing H-bonding interactions. Mol.Phys. 2012, 110, 565-579.
xxii  In this definition the A-H…B designation is applied for the hydrogen bond interaction, in this Account the term X-H…Y is used.
xxiii Wim T. Klooster, Thomas F. Koetzle, Per E. M. Siegbahn, Thomas B. Richardson, and Robert H. Crabtree, Study of the N-H…H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction. J.Am.Chem.Soc. 1999, 121, 6337-6343.