A CNDO/2 Molecular Orbital Study of Shared Tetrahedral Edge Conformations in Olivine-Type Compounds

Abstract

Semi-empirical molecular orbital calculations have been used to study the shortening of tetrahedral shared edges in olivine-type compounds. The shared edge conformation in forsterite was modelled by a cluster of SiO₃(OH)Mg₃(OH)₁₀⁷- composition, consisting of a silicate tetrahedron sharing edges with three magnesium-containing octahedra. Predicted tetrahedron edge lengths agree well with observed values. Calculations on similar clusters representing shared edge conformations in sinhalite, chrysoberyl, and γ-Na₂BeF₄ also predict shortening of shared edges with d(X2-X3) < d(X3-X3), (X = O,F), as observed. Calculations on Mg₂SiS₄ fail to predict shortened shared edges. Detailed analysis of the individual molecular orbital energy terms indicates that the minimum energy configuration is determined by a complex sum of one- and two-centre energies. Distortions due to dimensional misfit of polyhedra in olivine structure space group P bnm appear to have relatively little importance in shortening the shared edges of the tetrahedron.