R.Y. de Vries

Novel treatment of the experimental data in the application of the maximum-entropy method to the determination of the electron-density distribution from x-ray experiments

The maximum-entropy method (MEM) has been tested on a limited set of noisy Fourier data from a known electron-density distribution (EDD). It is shown that maximizing the entropy of the EDD under the usual condition of fitting the variance of the data set does not necessarily lead to a satisfactory error distribution of the calculated reflections. The MEM property of producing the flattest EDD consistent with the data causes the calculated values of strong reflections to deviate systematically as much as possible from their measured values. Calculated values of strong reflections are usually smaller than their measured values. The use of a novel constraint on the entropy maximization greatly improves the form of the error distribution and also the calculated EDD.

Extracting charge density distributions from diffraction data: a model study on urea

The quality of the extraction of electron density distributions by means of a multipole refinement method is investigated. Structure factors of the urea crystal have been obtained from an electron density distribution (EDD) resulting from a density function calculation with the CRYSTAL95 package. To account for the thermal motion of the atoms, the stockholder-partioned densities of the atoms have been convoluted with thermal smearing functions, which were obtained from a neutron diffraction experiment. A POP multipole refinement yielded a good fit, R = 0.6%. This disagreement factor is based on magnitudes only. Comparison with the original structure factors gave a disagreement of 0.8% owing to differences in magnitude and phase. The fitted EDD still showed all the characteristics of the interaction density. After random errors corresponding to the experimental situation were added to the structure factors, the refinement was repeated. The fit was R = 1.1%. This time the resulting interaction density was heavily deformed. Repetition with another set of random errors from the same distribution yielded a widely different interaction density distribution. The conclusion is that interaction densities cannot be obtained from X-ray diffraction data on non-centrosymmetric crystals.

Deconvolution of the two-dimensional point-spread function of area detectors using the maximum-entropy algorithm

The maximum-entropy method (MEM) has been applied for the deconvolution of the point-spread function (PSF) of two-dimensional X-ray detectors. The method is robust, model and image independent, and only depends on the correct description of the two-dimensional point-spread function and gain factor of the detector. A significant enhancement of both the spatial resolution and the contrast ratio has been obtained for two phase-contrast images recorded with an ultra-high-resolution X-ray imaging detector. The method has also been applied to a Laue diffraction image of a protein crystal, showing an important improvement in both the peak separation of closely spaced diffraction peaks and the signal-to-noise ratio of medium and weak peaks. The principle of the method is explained and examples of its application are presented.