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The phase problem in neutron crystallography

Acta Cryst. (2003). A59, 250–254

[Cyclosporin] Initial E map of the cyclosporin structure solved by Neutron Shake-and-Bake. The initial r.m.s. phase error is 37°. The hydrogen sites are displayed in negative (red) density while the C, N, O skeleton is displayed in positive (blue) density.

The crystallographic phase problem is formulated as a problem in constrained global minimization. In contrast to traditional direct-methods techniques using X-ray diffraction, this formulation does not require that the density function be positive everywhere. Instead, suitable generalization of the well known Shake-and-Bake formalism, here called Neutron Shake-and-Bake, exploits prior knowledge that the density function, as called for in the neutron diffraction case, is now permitted to assume negative, as well as positive, values. The initial application is made to the solution by Neutron Shake-and-Bake of the 199 atom (113 hydrogen atoms plus 86 nonhydrogen atoms) cyclosporin structure using experimental neutron diffraction data alone. Comparing the relative ease of this structure determination with the far greater challenge posed by the deuterated cyclosporin isomorph, in which the density function is positive everywhere, shows that, in sharp contrast to the prevailing view, the positivity of the density function not only does not facilitate, but actually substantially hinders, the phase determination process.

H. A. Hauptman and D. A. Langs