ERRORS IN MAXIMUM-ENTROPY CHARGE-DENSITY DISTRIBUTIONS OBTAINED FROM DIFFRACTION DATA

A scheme to estimate errors in maximum-entropy-method (MEM) charge-den sity distributions via Monte Carlo simulations is presented. Knowledge of the errors in the density allows evaluation of the reliability of fine features in MEM electron densities. As a test example, the errors in the MEM electron-density distribution of metallic beryllium are ex amined based on calculations using both uniform and non-uniform prior distributions. The study shows that the MEM introduces systematic bias in the density and that the bias is closely related to the fact that after a MEM optimization most of the chi(2) value is carried by a few low-order reflections. An iterative procedure to estimate the bias is presented and this allows a correction of the MEM density to be perfor med. The systematic bias is in some regions an order of magnitude larg er than the random error in the density. The bias-corrected MEM densit y has a more uniform residual distribution than the uncorrected densit y. The topological features of the electron-density distribution in me tallic beryllium are discussed based on the bias-corrected MEM densiti es.