Application of the maximum entropy method to electron density determination

The principle of maximum entropy is adopted to derive a procedure for obtaining the electron density distribution in crystals from incomplete X-ray diffraction data. This method was applied to cementite and the result proved to be better than the conventional Fourier inversion in resolution as well as in the absence of ripples. The potential advantages of this method are: (1) the amount of subjective judgment imposed on unavailable data is significantly limited, and (2) the result of this method is consistent with the known information and maximally noncommittal with regard to the unknowns. It is shown that the method is especially well suited to the problem of the determination of a high-resolution electron density map from insufficient experimental data.