THE PRIOR IN THE MAXIMUM ENTROPY METHOD. DO NON-NUCLEAR MAXIMA IN BE AND SI EXIST? R. Y. de Vries, W. J. Briels & D. Feil, Chem Phys.Lab. University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

In the past few years the maximum entropy method (MEM) has become very popular for extracting electron density distributions (EDD) from X-ray diffraction data. In the MEM formalism, the EDD is described on a very dense grid. It is believed that, in contrast to multipolar refinement, the MEM is 'model free'.

The discovery by the MEM of maxima in the EDD that are not located at a nucleus, the non-nuclear maxima, in Si and Be could be the result of this enormous flexibility. On the other hand, these non-nuclear maxima could also be an artifact of the MEM.

We have tested the MEM on data calculated from a known EDD of silicon. This EDD was calculated with the Amsterdam Density Functional-BAND program which takes the periodicity of the crystal into account. No non-nuclear maxima were observed in this density. When the MEM was applied on the structure factors calculated from this density non-nuclear maxima appeared in the Si-Si bond. This clearly demonstrates that these maxima in Si are an artifact of the MEM.

The MEM as used above strives towards an EDD displaying as few features as possible within the constraints given by the experiment. We know, however, that our EDDs are characterized by sharp atomic peaks. By including this prior knowledge in the form of the sum of the free atoms, the MEM gave an excellent reconstruction of the EDD. Applying this to the experimental data of both Si and Be did not reveal any non-nuclear maxima. These EDDs will be compared with the EDDs resulting from multipolar refinements.