On the estimation of atomic charges by the X-ray method for some oxides and silicates

Based on accurate X-ray diffraction intensity data collected from spherically shaped single crystals, net atomic charges and electron density distributions have been studied for MnO, Mn₂SiO₄, Mg₂Si₂O₆, LiAlSi₂O₆ and CaMgSi₂O₆. Examination of various procedures for determining atomic charges in a given structure has led to the conclusion that the following approach appears to be most reliable. (1) For cations: the number of electrons in the sphere of radius ER, effective distribution radius, which is defined according to the characteristics of radial distribution functions or difference-Fourier maps, is calculated. (2) For oxygen atoms: with the cation charges fixed at the values obtained from the above procedure and the total charge of the crystal constrained to be neutral, oxygen charges are estimated from least-squares refinements using atomic scattering factors. The final charges of atoms examined are less ionic than the corresponding formal ones: those of Li, O, Mg, Al, Si, Ca and Mn are respectively + 0.7 (1), -1.1 to -1.5, + 1.4 (1) to + 1.8, + 2.4(1), + 2.2 (1) to + 2.6, + 1.4 (2) and + 1.2 (1) to + 1.6 e. Residual electron densities between Si and O have been clearly observed in difference-Fourier maps after charge refinements for crystals of LiAlSi₂O₆, CaMgSi₂O₆ and Mg₂Si₂O₆.