The Influence of the Completeness of the Data Set on the Charge Density Obtained with the Maximum-Entropy Method. A Re-examination of the Electron-Density Distribution in Si

The charge densities derived with the maximum-entropy method (MEM) may be influenced to some extent by the completeness of the data set. In order to examine the effects of the incompleteness, structure-factor data of Si measured by the Pendellösung method [Saka & Kato (1986). Acta Cryst. A42, 469–478] were re-analysed by the MEM. This data set is incomplete: it contains all space-group-allowed reflections with sinθ/λ = 0.86 Å⁻¹, and in addition 844 and 880 with sinθ/λ = 1.04 Å⁻¹. Results of a MEM analysis of the complete subset of data are compared with those from the full but incomplete set published previously [Sakata & Sato (1990). Acta Cryst. A46, 263–270]. The smaller but complete set was found to give a smooth charge-density distribution that is consistent with previous theoretical work. It is found that the sharp peak maximum at the bond midpoint reported previously is exaggerated owing to the highest-order reflection 880. The completeness of the data set appears to be one of the key factors for obtaining reliable charge densities with MEM. The incompleteness of the data set may cause non-physical fine features of the MEM density distribution.