A BAYESIAN APPROACH TO HIGH-RESOLUTION X-RAY CRYSTALLOGRAPHY: ACCURATE DENSITY STUDIES WITH PROGRAM BUSTER. Pietro Roversi, Dipartimento di Chimica Fisica ed Elettrochimica, Università di Milano, Via Golgi 19, 20133 Milano, Italy; John Irwin and Gérard Bricogne, MRC-LMB, Hills Road, CB2 2QH, Cambridge, England, UK

Implementation around the existing code BUSTER [1] of algorithms to perform accurate electron density studies from high-resolution X-ray diffraction data has been accomplished, as part of a comprehensive programme for doing crystallography within a Bayesian theory of structure determination [2]. We consider the reconstruction of an accurate electron density as an extension of the structure determination process. The program seeks the electron distribution having maximum entropy relative to a given prior, and reproducing the experimental measurements. The program is fully automated, space-group general and is operated from a user-friendly graphical interface. The maximum-entropy equations are solved by means of a robust and efficient algorithm, targeting phased structure factors values. An interface between BUSTER and the program for multipolar electron density studies VALRAY[3] allows one to define a `fragment' of atomic core density functions, and to redistribute only the valence electrons. A prior distribution for the latter can computed within VALRAY from a superposition of atomic valence density functions and is used to provide a description of the radial dependence of the atomic density, thus preventing the accumulation of density in regions far from the nuclei within the crystal.

First tests against synthetic data have confirmed the viability of the method to obtain dynamic densities for centrosymmetric structures (Si, Be, TriGlycine). Non-centrosymmetric crystals, which present the added difficulty of phase uncertainty, have also been studied. We are still investigating the dependence of the final reconstructed densities on the choices made for the prior, and comparing them with the traditional multipolar densities. There is strong evidence of the need to use a thermally smeared prior density.

[1] G. Bricogne, Acta Cryst. (1993). D49, 37-60.

[2] G. Bricogne, Acta Cryst. (1988). A44, 517-545.

[3] R.F. Stewart and M.A. Spackman. VALRAY Users Manual. (1983) Carnegie-Mellon Univ., Pittsburgh, Penn.