W0292

The Phase Problem in Neutron Crystallography. Herbert A. Hauptman and David A. Langs, Hauptman-Woodward Medical Research Institute, Inc., 73 High St., Buffalo, NY 14203-1196.

The easy solution of the crystal structure of cyclosporin (C₆₂H₁₁₁N₁₁O₁₂•H₂O) by a modified Shake-and-Bake procedure, using experimental neutron diffraction data alone, and comparison with the structure determination of the deuterated isomorph by direct methods show that the positivity of the density function is not only not a necessary prerequisite for solving the phase problem but that positivity, contrary to general belief, is actually a hindrance instead.

The probabilistic theory of the structure invariants (Hauptman, 1976, Acta Cryst. A32, 877-882) when neutron diffraction data alone are available yields, as in the X-ray case (DeTitta et al. (1994), Acta Cryst. A50, 203-210), the formulation of the phase problem as a problem in constrained global minimization (the minimal principle). The latter, in turn, leads (again as in the X-ray case) to a modified Shake-and-Bake algorithm (Neutron Shake-and-Bake) which explicitly exploits the property of the neutron density function that, owing to the presence of the hydrogen atoms, takes on negative as well as positive values. Successful applications, when only neutron diffraction data are available, confirm the validity of this theoretical analysis and demonstrate the superior performance of Neutron Shake-and-Bake compared with existing direct methods techniques.