The Maximum Entropy Reconstruction of Patterson and Fourier Densities in Orientationally Disordered Molecular Crystals: A Systematic Test for Crystallographic Interpolation Models

Abstract

Accurate density data are the primary information required for a thermodynamic model of molecular disorder. Neutron or X-ray Bragg scattering yields truncated and noisy data sets of unphased Fourier components. In the specific case of disordered molecular crystals, the phase problem can be bypassed by means of a density interpolation model using Frenkel atoms. The fitting to the data is usually quite good, and the validity of such a parametric model follows from the stability of the recovered phases with respect to the parameters. It is well established by now that MaxEnt is the best tool to retrieve 3-dim or projected 2-dim densities from phased data.

But MaxEnt helps a great deal more. By removing most of the noise and series truncation effects, a direct analysis of 2-dim and 3-dim Patterson functions, which relate to the autocorrelation function of the sought density, yields a direct check of the density interpolation model: one can observe directly the disordered density looked for.

The points mentioned above will be illustrated on a specific example, that of disordered ammine molecules in Ni(ND ₃)₆ Br ₂.

Moreover, a possible pitfall leading to spurious line-splitting in the standard case of back transforming phased Fourier data using MaxEnt will be addressed.