TEMPERATURE, AN ADDITIONAL DIMENSION IN CHEMICAL CRYSTALLOGRAPHY.
H.-B. Bürgi,
Labor für Kristallographie, Universität, Freiestr. 3,
CH-3012 BERN, Switzerland
Diffraction intensities, especially those at high scattering angle, increase with decreasing temperature. As early as 1913 Debye interpreted this in terms of a decrease of atomic vibrational amplitudes and thus of the atomic mean square displacement parameters (ADP).1 Although ADP's are determined routinely with every crystal structure analysis, they are rarely measured as a function of temperature and much less analysed for the dynamic information they contain; wrongfully so, as will be discussed below.
In 1956 Cruickshank showed how to extract amplitudes of molecular libration and translation from ADP's measured at a single temperature, but concluded that 'it is not possible to extend this kind of analysis to determine the internal vibrations of non-rigid molecules'.2 Although this view seems overly pessimistic now, there is good reason for it: the interatomic or correlation ADP's, which describe the coupling of atomic displacements, are lost in Bragg diffraction.
The information on the correlation of atomic motions can be retrieved, however, from the temperature dependence of ADP's. Measurements in the (low temperature) quantum and the (high temperature) classical regimes provide the relative and absolute atomic displacements associated with low frequency molecular vibrations on one hand, and allow a distinction between the effects of motion and positional disorder on the other. The basic idea will be illustrated for the simple case of a homonuclear diatomic molecule and generalized for application to any molecule including proteins, at least in principle.
Diffraction experiments as a function of temperature are thus a potentially rich source of information on dynamic processes and disorder phenomena in crystals. The information is relatively easy to obtain and extends the scope of crystal structure analysis.