Solving crystal structures with the symmetry minimum function

Abstract

Unravelling the Patterson function (the auto-correlation function of the crystal structure) (A.L. Patterson, Phys. Rev. 46 (1934) 372) can be the only way of solving crystal structures from neutron and incomplete diffraction data (e.g. powder data) when direct methods for phase determination fail. The negative scattering lengths of certain isotopes and the systematic loss of information caused by incomplete diffraction data invalidate the underlying statistical assumptions made in direct methods. In contrast, the Patterson function depends solely on the quality of the available diffraction data. Simpson et al. (P.G. Simpson et al., Acta Crystallogr. 18 (1965) 169) showed that solving a crystal structure with a particular superposition of origin-shifted Patterson functions, the symmetry minimum function, is advantageous over using the Patterson function alone, for single-crystal X-ray data. This paper describes the extension of the Patterson superposition approach to neutron data and powder data by (a) actively using the negative regions in the Patterson map caused by negative scattering lengths and (b) using maximum entropy Patterson maps (W.I.F. David, Nature 346 (1990) 731). Furthermore, prior chemical knowledge such as bond lengths and angles from known fragments have been included. Two successful structure solutions of a known and a previously unknown structure (M. Hofmann, J. Solid State Chem., in press) illustrate the potential of this new development.