Errors in maximum-entropy charge-density distributions obtained from diffraction data

A scheme to estimate errors in maximum-entropy-method (MEM) charge-density 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 examined 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 performed. The systematic bias is in some regions an order of magnitude larger than the random error in the density. The bias-corrected MEM density has a more uniform residual distribution than the uncorrected density. The topological features of the electron-density distribution in metallic beryllium are discussed based on the bias-corrected MEM densities.