Abstract
A semi-empirical molecular orbital study was performed on the atomic charges in β-Mg2SiO4 to clarify the crystal chemical properties of this mantle-constituting material. A large cluster of atoms was cut out from the crystal structure for each of the independent atoms, with the atom put in the center of the cluster. Hydrogen atoms were attached to the outer oxygens to preserve the charge neutrality in the cluster. The atomic charge on the central atom was determined by the CNDO/2 method, using the minimal basis set of Slater-type orbitals for all the atoms. The SCF calculation for the Si cluster failed in convergence. The charges on the three Mg and the four O atoms were successfully determined and compared with the electrostatic site energies which were obtained from the formal point charges of these atoms.
As a result, three Mg atoms (Mg1, Mg2, and Mg3), which have nearly the same electrostatic site energies, converged to almost the same values of atomic charges of 0.68, 0.68 and 0.69e, respectively. The O1 oxygen, which is “undersaturated” in the sense of Pauling’s valence balance rule and has a very high electrostatic site energy, produced a small charge of −0.56e. On the contrary, the “oversaturated” O2 oxygen, which has a very low electrostatic site energy, exhibited a large charge of −0.66e. The O3 and O4 oxygens, which have intermediate electrostatic site energies, yielded intermediate values of −0.59 and −0.61e, respectively. These results indicate that the atomic charge depends qualitatively on the electrostatic site energy in order to gain a larger electrostatic stability and to compensate the disadvantage in breaking Pauling’s rule. The relationship found between the atomic charge and the electrostatic site energy will open the way to modify the charge values in interatomic pairwise potentials widely used in silicate minerals.
