THE SOLUTION AND REFINEMENT OF STRUCTURES WITH X-RAY DIFFRACTION DATA FROM TWINNED CRYSTALS. Geoffrey B. Jameson, Department of Chemistry, Massey University, Palmerston North, New Zealand

Precise and accurate crystal structures, including proteins, can be obtained from X-ray diffraction data gathered from twinned crystals. In a twinned crystal, the intensity of each reflection or a subclass of reflections may be represented as I(hkl) = x*I(hkl) + (1-x)*I(h'k'l'), where x is the fractional amount of the major component and where the twin law that relates indices hkl and h'k'l' in a systematic manner can be summarized in matrix form. When x is greater that 0.65, the structure usually may be solved and refined without major difficulty. Since the minor component essentially amounts to a random noise on the diffaction intensity data of the major component, the final positional parameters, while often lacking the precision that would be expected from the extent of data collected, do not contain serious systematic error. Poorly behaved thermal parameters can be expected when the extent of twinning is severe (0.5<x0.75). The values of the discrepancy indices R1(on F, observed data) and, especially, wR2 (on F^2, all data) can be aesthetically displeasing to referees, even when the extent of twinning is small (0.85<x). Several least-squares programs, for example SHELXL93 (G.M. Sheldrick) and CRYSTALS (D.J. Watkin), offer the user the capability to enter a twin law, to flag twin-affected data, and to refine the twin component x (or twin components, if more than two twin components exist). In addition, the refined value of the twin component is used to "detwin" the data for subsequent electron density Fourier syntheses.

Even as x approaches 0.5, direct methods may still reveal an interpretable, albeit noisy, electron density map, since phases more so than amplitudes determine the form of electron density maps. Vector (Patterson) maps contain images related by the the twin law. There appear to be no circumstances where least-squares refinements should be made with detwinned data, since the process of detwinning unavoidably introduces considerable noise into what might have been an excellent data set. Various examples will be used to illustrate strategies for the identification of twinning (pre- and post-data collection), derivation of the twin law, and solution and optimal refinement of structures.