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Hydrogen Bondshydrogen bonding: H2O---H-OH dimer

Hydrogen bonding occurs when an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one, such that it may be considered to be acting as a bond between them.


V Water dimer

V Hydrogen bonding in water (1)

V Hydrogen bonding in water (2)

V Van der Waals interactions



'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. '

IUPAC definition, 2011 [1702]     


HF2- calculated using the Restricted Hartree-Fock wave function (RHF) using the 6-31G** basis set

Hydrogen bonds are medium strength intermolecular or intramolecular forces. Hydrogen bonding [2458] occurs when an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one, such that it may be considered to be acting as a bond between them [99]. Typically hydrogen bonding occurs where the partially positively charged hydrogen atom lies between partially negatively charged oxygen and/or nitrogen atoms, but is also found elsewhere, such as between fluorine atoms in HF2- (a very strong hydrogen bond at 163 kJ ˣ mol-1, see right) and between water and the smaller halide ions F-, Cl- and Br- (for example, HO-H····Br-, [178, 1190]; a the strength of hydrogen bonding reducing as the halide radius increases), and to a much smaller extent to I- [190] and even xenon [941], (a very weak hydrogen bond at 2 kJ ˣ mol-1). Even very weak C-H····OH2 hydrogen bonds (~ 4 kJ ˣ mol-1) are being increasingly recognized [1293]. In theoretical studies, strong hydrogen bonds even occur to the hydrogen atoms in metal hydrides (for example, LiH····HF; see below right [217]). The current view of the hydrogen bond has been reviewed [1462] and comparison to halogen bonds (i.e. C-X····Z; X = Cl, Br, I; Z = O, N, S), C-H····π interactions, and C-Br····π interactions made [2248]. An exactly solvable Schrödinger equation with double-well potential has been proposed for the hydrogen bond [2940].


LiH-HF calculated using the Restricted Hartree-Fock wave function (RHF) using the 6-31G** basis setHydrogen bond strength is given by the weaker of the two interactions of the flanking atoms with the central hydrogen atom and is strongest when these interactions are equal [1653]. They are now thought to be dynamic bonds with a continuity of electron density and present where the 'bonding' is directed [2381]. Hydrogen bond strength may be estimated theoretically from the quantum theory of atoms in molecules [2191]. Hydrogen bonding is characterized by its preferred dimensions, molecular orientation, approximate linearity and changes in infrared frequency and intensity. Hydrogen bond distances are dynamic with substantial zero-point energy and vibration even at absolute zero (0 K). Hydrogen bonds are not atom-pair functions and do not just depend on the neighboring atoms but also upon the sequential nature of the total pattern of bonding.


Hydrogen bonds form the most important stabilizing interaction in nature, being important in the secondary and tertiary structure of proteins the structure of DNA and membranes, and the controlling forces of hydration. Networks of hydrogen bonds show cooperativity, with stronger interactions than expected from pairwise additivity.


Hydrogen bonding H····A distances are less than van der Waals distances, but greater than the length of covalent bonds or ionic pair separations. Hydrogen bonds are different from van der Waals dispersion interactions, but this difference is blurred in some instances. The key to the difference is that hydrogen bonding usually involves partial covalent bond formation and a mutual penetration of atoms within their van der Waals radii. The IUPAC definition is given above [1702]. The most important criteria for a hydrogen bond are: (i) the H in the X–H group is more electropositive than X and (ii) the physical forces involved in hydrogen bonding should include attractive electrostatic forces, i.e. it should not be primarily dispersive forces [1461]. Recently, it has been suggested that the definition be broadened somewhat [2381] to include its dynamic nature, such that hydrogen bonds may form due to molecular vibrations and not necessarily within the structural potential energy minimum. The strength of the attraction (bond) between the electronegative atoms (e.g. O····O is (experimentally) the same as the strength between the included hydrogen atom and the furthest electronegative atom (e.g. O-H····O). In this text both such 'bonds' are called 'hydrogen bonds'. Using first principle density functional theory simulations the overall attraction between the molecular species may be split into separate O····O and O-H····O attractions [2510].


Hydrogen bonds allow the transfer of protons between the bonded electronegative atoms, such as

H-O-H····OH2 = HO- ····H-+O2


The van der Waals dispersive attraction b in water has been estimated as high as about 5.5 kJ ˣ mol-1 [548] based on isoelectronic molecules at optimal separation, but is likely to be repulsive within a hydrogen bond due to the close contact (see for example, [736]). Separating the hydrogen bond components, as below, helps our understanding, although in reality these components are combined.

Hydrogen bond contributions
++ electrostatic attraction
long range interaction (< 30 Å) based on point charges, or on dipoles plus quadrupoles, and so on. They may be considered as varying with distance-1.
++ polarization attraction
due to net attractive effects between charges and electron clouds (< 8 Å), which may increase cooperatively dependent on the local environment. They may be considered as varying with distance-4. This net attractive effect may contain a small repulsive element due to slightly increased electron cloud overlap.
+   covalency attraction
highly directional and increases on hydrogen bonded cyclic cluster formation. It is very dependent on the spatial arrangement of the molecules within the local environment (< 6 Å). Hydrogen bonds in many molecules, such as DNA, have been shown to possess considerable covalent character [1867].
+   dispersive attraction
interaction (< 6 Å) due to coordinated effects of neighboring electron clouds. They may be considered as varying with distance-6.
--  electron repulsion
very short range interaction (< 4 Å) due to electron cloud overlap. They may be considered as varying with distance-12. This keeps the electronegative atoms apart with very high pressures required to bring them closer. Without the attractive elements of the hydrogen bond the O atoms of neighboring water molecules would be kept about 3.2 - 3.4 Å apart.


The strength of hydrogen bonds (X-H····Y) depends on the donor (donating the hydrogen atom; X) and acceptor (accepting that hydrogen atom; Y) atoms [2511]; the stronger the electron donating power (i.e. the acceptor, the base), the stronger the hydrogen bond, e.g. (CH3)3N: > (CH3)2HN: >(CH3)H2N: > H3N: . Also the stronger the proton donor (the acid), the stronger the hydrogen bond, unless the proton is totally donated onto the base when the roles of donor and acceptor are reversed (X- ····H-+Y ). Most hydrogen bonds have a binding energy in the range 8–80 kJ ˣ mol-1. In similar structures, the donor order is O-H > N-H >> C-H and the acceptor order is N > 0 > S; thus,

O−H····N > O−H····O > N−H····N > N−H····O >> C-H····O

although there are exceptions to this, due to the neighboring bonding.


In a X–H····Y hydrogen bond, there is characteristic proton deshielding of the central H atom and spin–spin couplings between X and Y.


In conclusion, hydrogen bonds (1) have direction, (2) generally are weak compared with covalent bonds but strong compared with thermal energies, and (3) allow proton transfer between atoms.

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a Hydrogen bonding is often represented by the use of a dotted line ····. [Back]

A typical van der Waals interaction b The van der Waals interaction

All atoms repel each other at close range but attract each other at less close range. These attractive forces are known as 'Van der Waals forces' (named after Dutch scientist Johannes Diderik van der Waals) are much weaker than covalent bonds, ionic interactions, and most hydrogen bonds and thermal motions may disrupt them. They are caused by correlations in the fluctuating electronic polarizations of the atoms/molecules. They depend on their relative orientation but have no directional characteristic. The van der Waals interaction potential depends on ~ r−6 , where r is the distance between the centers of the atoms, or ~ L−2, where L is the distance between planar surfaces. Thus, they are short-range forces and disappear rapidly with distance. They vary little with temperature. The very strong short-range repulsive force, varying ~ r−12 , sets the minimum distance to be found between atoms due to the mutual repulsion of the electron clouds. Although an individual van der Waals interaction is small, some circumstances bring many interactions which are additive; such as on the central molecule in a clathrate or between macromolecules. [Back]



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