Intramolecular hydrogen bonds (X-H^...Y) arise where the X and Y atoms are in the same molecule (Figure 3).

Figure 3: Structure of 3-tert-butyl-2-hydroxy-5-methylacetophenone showing the presence of an intramolecular hydrogen bond. Hydrogen atoms attached to carbon are omitted for clarity. Adapted from M. B. Power, A. R. Barron, S. G. Bott, E. J. Bishop, K. D. Tierce and J. L. Atwood, J. Chem. Soc., Dalton Trans., 1991, 241.

If the hydrogen bond (X-H^...Y) involves X and Y being from different molecules this is an intermolecular hydrogen bond. Within the range of intermolecular hydrogen bonded compounds there are two sub-categories: those involving discrete molecular species (oligomers) and those resulting in polymeric species.

Carboxylic acids are a typical example of a discrete oligomeric species that are held together by intermolecular hydrogen bonds (Figure 4a). A wide range of structurally analogous compounds also form head-to-tail hydrogen bonded dimers (e.g., Figure 5). In a polymeric hydrogen bonded species every molecule hydrogen bonds but in a random form. As an example, liquid primary alcohols form extended hydrogen networks (Figure 4b). Such an arrangement is labile and as such it is difficult to determine definitive speciation. Liquids that form this type of hydrogen-bonded network are known as associated liquids. In the solid state the networks generally adopt a more ordered structure. For example as is seen in the structure of ice.

Figure 4: Structure of (a) the head-to-tail dimmer formed between two carboxylic acid molecules, and (b) a typical network of a primary alcohol in the liquid phase.

Figure 5: Structure of the hydrogen bonded diner of (C₆H₅)NNN(H)(C₆F₅). Adapted from J. T. Leman, J. Braddock-Wilking, A. J. Coolong, and A. R. Barron, Inorg. Chem., 1993, 32, 4324.

X-ray diffraction of single crystals is the most common structural method employed to determine the presence, effect, and strength of a hydrogen bond. Unfortunately, in order for the location of the hydrogen to be determined with some degree of accuracy, diffraction data of a high quality is needed and/or low temperature (e.g., -196 °C) data collection is required. Neutron scattering can be used where very accurate data is required because hydrogen atoms scatter neutrons better than they do X-rays. Figure 6 summarizes the key parameters that are obtained from X-ray (and neutron) diffraction experiments.

Figure 6: Structural parameters obtained from diffraction methods.

Given the electrostatic nature of a hydrogen bond between a polar X-H bond and a Lewis base it is reasonable that the X-H^...Y angle (θ) is roughly linear (i.e., 180°). However, it is not always so and non-linear interactions are known where steric or conformational restrictions limit the orientation of the X-H bond with respect to Y.

The distance between X and Y, d(X^...Y), is less than the sum of the van der Waal radii of X and Y (Table 1). This is in line with the relative strength of these interactions. As would be expected the shorter the X^...Y distance the stronger the hydrogen bond.

The bond distance to hydrogen, d(X-H), is often longer in hydrogen bonded species. For example the O-H distance for an alcohol in the absence of hydrogen bonding is typically 0.97 Å. In contrast, the value typically seen for a hydrogen-bonded analog is 1.05 Å.

Spectroscopy is a simple method of comparing hydrogen-bonded systems in particular in the solution or liquid phase.

Infra red and Raman

The X-H stretching frequency in the IR (and Raman) spectrum is dependant on the identity of X, i.e., O-H = 3610 - 3640 cm^-1 and N-H = 3400 - 3500 cm^-1. However, the ν(X-H) is shifted to lower energy (lower frequency) as a consequence of hydrogen bonding. In addition, while non-hydrogen bonded X-H stretches are sharp, the presence of hydrogen bonding results in the peak being broadened. Figure X demonstrates both these effects. The O-H stretch for dilute ⁿBuOH in CCl₄ is a sharp peak at 3650 cm^-1 due to the lack of hydrogen bonding between the two components (Figure 7a), and the presence of hydrogen bonding between ⁿBuOH and ⁿBuOH is limited by the dilution. By contrast, a dilute solution of ⁿBuOH in Et₂O results in a shift to lower frequency and a significant increase of peak width (Figure 7b) as a result of fairly strong O-H^...O bonds. Finally, a dilute solution of ⁿBuOH in NMe₃ results in a further shift to 3250 cm^-1 and a very broad peak (Figure 7c). The broadening of the peaks is due to the distribution of X-H distances within a X-H^...Y hydrogen bond.

Figure 7: Schematic representation of the O-H stretch region in the IR spectra of a dilute solution of ⁿBuOH in (a) CCl₄, (b) Et₂O, and (c) NEt₃.

NMR

The presence of hydrogen bonding results the shift to higher ppm (lower frequency) of the ¹H NMR resonance for the proton. This shift is due to the decrease in shielding of the proton. A dilute solution of ⁿBuOH in CCl₄ shows a resonance typical of a non-hydrogen bonded compound (Figure 8a), while that for ⁿBuOH in NMe₃ (Figure 8b) shows a significant low field shift. Very strong intra or intermolecular hydrogen bonded species show a very large ¹H NMR shift (e.g., Figure 8c).

Figure 8: Schematic representation of the relative shift of the OH resonance for (a) ⁿBuOH in CCl₄, (b) ⁿBuOH in NEt₃, and (c) concentrated acetic acid.

The presence of intermolecular hydrogen bonding provides additional attractive forces between molecules. Thus, properties that depend on intramolecular forces are affected.

Liquids with significant hydrogen bonding exhibit higher boiling points, higher viscosity, and higher heat of vaporization (ΔH_v) as compared to analogous compounds without extensive hydrogen bonding. For solids the presence of hydrogen bonding results in an increase in the melting point of the solid and an increase in the associated heat of fusion (ΔH_f).

The archetypal case for the effect of hydrogen bonding is the melting and boiling points of the hydrides of the Group 16 elements, i.e., H₂E. For a series of analogous compounds with the same molecular structure it would be expected that the boiling points would be related to the molecular mass. However, as can be seen from Table 2, the melting and boiling points of water are anomalously higher than those of its heavier analogs. In fact from Figure 9 it is clear that just considering H₂S, H₂Se, and H₂Te, the expected trend is observed, and it is similar to that for the Group 14 hydrides (CH₄, SiH₄, etc). Therefore, water must have additional intermolecular forces as compared to its heavier homologs. This observation is consistent with the strong hydrogen bonding in water, and the very weak if nonexistent hydrogen bonding in the sulfur, selenium, and tellurium analogs.

Figure 9: Plot of boiling point as a function of molecular weight for the hydrides of the Group 14 (EH₄) and 16 (H₂E) elements.

A similar but not as pronounced trend is observed for the Group 15 hydrides, where ammonia’s higher values are associated with the presence of significant hydrogen bonding (Table 3).

The types of hydrogen bond can also have a significant effect on the physical properties of a compound. For example, the cis isomer of hydroxybenzaldehyde melts at 1 °C, while the trans isomer has melting and boiling points of 112 °C. Both compounds exhibit strong hydrogen bonding in the solid state, however, as may be seen from Figure 10a, cis-hydroxybenzaldehyde (salicylaldehyde) has a configuration that allows strong intramolecular hydrogen bonding, which precludes any intermolecular hydrogen bonding. The melting point of cis-hydroxybenzaldehyde is going to be controlled by the van der Waal forces between adjacent molecules. In contrast, since intramolecular hydrogen bonding is precluded in the trans isomer (Figure 10b) it can form strong intermolecular hydrogen bonds in the solid state, and thus, it is these that define the melting point. The boiling points are controlled in a similar manner.

Figure 10: Structures of (a) salicylaldehyde and (b) trans-hydroxybenzaldehyde.

Melting and boiling are not the only physical properties that are affected by hydrogen bonding. Solubility can also be affected. Consider two isomers of C₄H₁₀O: ⁿBuOH and Et₂O. The n-butanol is much more soluble in water than diethyl ether. The reason for this is that while both compounds can hydrogen bond to water, those between ⁿBuOH and water are much stronger than those between Et₂O and water, and thus, dissolution of ⁿBuOH in water does not disrupt the very strong hydrogen bonding in water as much as Et₂O does.

The acidity of a protic species can be affected by the presence of hydrogen bonding. For example, consider the di-carboxylic acid derivatives of ethylene (fumaric acid). Each of the carboxylic acid groups has sequential equilibria that may be defined by the pK values, Equation 1. Table 4 lists the pK values for the cis and trans isomers. The acidity of the first and second carboxylic group for the trans isomer is similar, the difference being due to the increased charge on the molecule. In contrast, the second proton in the cis isomer is much less acidic than the first proton: why? A consideration of the structure of the mono anion of the cis isomer (Figure 11) shows that a very strong intramolecular hydrogen bond is formed once the first proton is removed. This hydrogen bond makes the second acidic proton much more difficult to remove and thus lowers the acidity of the proton.

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Figure 11: Structure of cis-[O₂C-HC=CH-CO₂H]^-.

In the solid state, molecules that can form hydrogen bonds will tend to arrange themselves so as to maximize the formation of linear hydrogen bonds. The structure of ice is a typical example, where each water molecule’s hydrogen bonds to four other molecules creating a diamond-like lattice (Figure 12). However, ice isn’t the only compound whose solid state structure is defined by its hydrogen bonding. Cyanuric acid forms six strong intermolecular hydrogen bonds to three other molecules in the plane of the heterocyclic ring and thus creates a graphite-like structure (Figure 13).

Figure 12: The diamond-like structure formed in ice by hydrogen bonding.

Figure 13: The hydrogen bonding of cyanuric acid.

The presence of hydrogen bonding can stabilize certain conformations over others that in the absence of hydrogen bonding would be more favored. For example, based on steric considerations H₂NCH₂CH₂C(O)H would be expected to adopt a staggered conformation as is typical for compounds with free rotation about a C-C bond. However, due to the presence of a strong intramolecular hydrogen bond it adopts a sterically disfavored eclipsed conformation (Figure 14).

Figure 14: Stable conformation of H₂NCH₂CH₂C(O)H.

This conformational stabilization is even more important in biopolymers such as peptides. If we assume that a peptide chain (Figure 15) made from a sequence of amino acids would not adopt any eclipsed conformations on steric grounds, and that the amide group (H-N-C=O) is near planar due to delocalization, then there will be 3² possible conformations per nitrogen in the peptide chain, i.e., three each for the C-C and C-N bonds (Figure 15). Assuming a modest peptide has 50 amino acids, there will be 3^2x50 potential conformations of the polymer chain, i.e., over 5 x 10⁴⁷ conformations. However, in reality there are limits to the number of conformations observed since particular ones are stabilized by intramolecular hydrogen bonds. The most important of these are the α-helix (Figure 16) and β-sheet structures.

Figure 15: A section of a peptide polymer chain showing the possible rotational freedom of the C-C and C-N bonds.

Figure 16: A representation of a peptide α-helix structure showing the stabilizing hydrogen bonds.