Studying hydrogen atom disorder via multiple temperature diffraction

Measurements of relative site occupancies of disordered hydrogen atoms in hydrogen bonded systems (benzoic acid dimer derivatives, for example) can be used to estimate the energy difference in intermolecular migrating hydrogen bond systems. Structural evolution as a function of temperature has been used to study the behavior of hydrogen atoms in hydrogen bonds.

Although disorder in hydrogen bonds has been observed many times by single crystal diffraction methods, temperature dependent disorder in hydrogen bonds is a relatively newly explored phenomenon. Typically in such systems, the proton occupies a single position at low temperature, but is observed to be increasingly disordered as the temperature is increased. Such hydrogen bonds correspond to the classical "double-well" hydrogen bond, with a significant difference in energy between the two energy wells. Using this model, a typical low temperature structure determination will contain only a single peak in the Fourier difference map corresponding to a hydrogen atom in a hydrogen bond, whereas at a higher temperature a disordered model may be more appropriate. This can be explained simply by the idea that at higher temperatures the system has more energy, so the profile of the potential energy well is revealed as the second hydrogen atom position becomes visible.

For the first time, temperature dependent disorder of a simple molecular compound, 4-dimethylaminobenzoic acid (4-DABA), both in its native crystal structure, and as a 2:2 molecular complex with 3,5 dinitrobenzoic acid has been studied. These compounds are ideal for a comparative study; in both the structures of the complex and the native compound the 4-DABA dimer contains slightly elongated O-H bonds, suggesting that the hydrogen atom could potentially exhibit disorder. The 3,5-DNBA dimer in the molecular complex was originally refined with a disordered hydrogen atom.

Using Fourier difference maps is more  successful than refining proton occupancies from X-ray data; refined values have a tendency to leave large holes and peaks in the Fourier difference maps lying over the partially occupied proton positions. Although hydrogen atom positions have traditionally been regarded as difficult to locate by X-ray diffraction, with modern instrumentation it is even possible to estimate the percentages of disorder present in each dimer by treating the disorder peaks as discrete cones of height h and base diameter d and calculating the volume of the cone produced. There will, however, still be significant errors attached to occupancies calculated this way. 

To be able to get the most accurate information from the Fourier difference maps, it is first necessary to collect 100% complete, high-quality data to a reasonably high Bragg angle, usually to around  0.7-0.75 Å. Imaging plate area detector systems like the RAPID II make this process easy. The dynamic range of the imaging plate means that it is a simple matter to collect both the strong low-angle reflections and the high-angle reflections at an exposure time that gives good counting statistics for the weaker high angle reflections. 

A very small amount of proton disorder is observed for 4-DABA (above) at 100K in the native structure, but this amount increases consistently with temperature. This is not the case in the co-crystal, however, although the 3,5-DNBA dimer moiety within the complex does exhibit significant disorder, even at 100K. The geometries of the two molecules of 4-DABA are remarkably similar, with the exception of a marked increase in the amount of pyramidalisation of the nitrogen atom in the molecular complex. This is most likely due to a close contact between this nitrogen and one of the highly electropositive nitrogen atoms in 3,5-DNBA. The localization of the lone pair on the pyramidal position of the nitrogen makes the extreme quinoidal form of the compound less likely, and therefore should significantly affect the ability of the 4-DABA to donate the acidic proton. The observed results bear this out; the packing interactions within the crystal structures do not greatly perturb the molecular symmetry of the 3,5-DNBA dimer or the 4-DABA dimer in the native structure, but they do significantly affect the symmetry of the 4-DABA dimer in the molecular complex.

At 100K the 3,5-DNBA dimer in the molecular complex is clearly disordered. The degree of disorder increases consistently over the nine measured temperatures, enabling an estimate of the energy difference between the two 21 configurations in this dimer to be made at 0.8 kJ mol^-1. The lower value for this energy difference compared with the native structure DABA dimer reflects the higher occupancy of the secondary proton site in the DNBA (complex) dimer across the temperature range studied.

Difference Fourier maps through atoms O1B, C7B and O2B of 3,5-DNBA in the molecular complex

Results courtesy of Andy Parkin, Lynne H Thomas and Chick C Wilson, Structural Chemistry Group,  University of Glasgow. 

Tags:  hydrogen bonding, variable temperature studies, disorder