Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.7, p. 906

Section The hydrogen bond and the definition of the packing units

A. J. C. Wilson,a V. L. Karenb and A. Mighellb

aSt John's College, Cambridge CB2 1TP, England, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA The hydrogen bond and the definition of the packing units

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The variously shaped molecular packing units of organic crystal structures are not necessarily identical with the individual molecule. The molecule (of a shape defined by chemical bonds on the inside and van der Waals forces on the outside) can be subjected to clustering under formation of intermolecular hydrogen bonds. Although far weaker than the chemical bond, hydrogen bonds are strong enough to alter the shape of the packing units of the crystal structure significantly. This may have far-reaching consequences for the adopted packing and symmetry. An extreme example is represented by the clustering of H2O molecules, where two hydrogen bonds and two regular O—H bonds create a [\overline {4}3m] point symmetry at each O atom, and a highly symmetrical structure emerges with an infinite bond network, similar to that in quartz, SiO2. From the point of view of an individual H2O molecule, the structure is very open. In contrast, a pseudo-close-packed structure of crystalline water, assuming an effective H2O radius of 1.38 Å, would have specific density of 1.8 g cm−3.

Analogous principles apply to organic structures with hydrogen bonding. CH3OH, for example, forms hydrogen-bonded zig-zag chains in its crystal structure. Obviously, the shape of the hydrogen-bonded cluster of molecules depends on the number and orientations of the hydrogen bonds relative to the size and shape of the molecule, causing three-dimensional, planar and linear `polymers', or the formation of dimers and trimers. As in the example of water, this introduces additional symmetry elements and decreases the degree of space filling.

There is a general rule that ensures that this phenomenon is widespread. The principle of maximum hydrogen bonding states that all the H atoms in the active (polar) groups of a molecule are employed in hydrogen-bond formation (Evans, 1964[link]). Therefore, as the [{\rm O}\cdots{\rm HO}] and [{\rm O}\cdots{\rm HN}] hydrogen bonds are both energetic and common, they are also of the greatest importance in this respect. Although most pronounced in smaller molecules, the symmetry-altering influence of hydrogen bonding also applies to relatively large molecules with a lower proportion of hydrogen bonding as, for example, in long-chain carboxylic acids that are linked in pairs. In large molecules with many active groups, however, the hydrogen bonds merely become the new delimiters of the shape of the individual molecule. The perils of the symmetry-statistical treatments of the hydrogen-bonded structures are well recognized and, for some purposes, the strategy adopted is to exclude such systems from the statistical pool (Filippini & Gavezzotti, 1992[link]).


Evans, R. C. (1964). An introduction to crystal chemistry. Cambridge University Press.
Filippini, G. & Gavezzotti, A. (1992). A quantitative analysis of the relative importance of symmetry operators in organic molecular crystals. Acta Cryst. B48, 230–234.

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