A molecular orbital study of bond length and angle variations in framework structures

Molecular orbital calculations on a variety of silicate and aluminosilicate molecules have been used to explore the bonding forces that govern tetrahedral bond length variations, r(TO), in framework silicates and aluminosilicates. Not only do the calculations provide insight into the variety of structural types and the substitution limits of one tetrahedral atom for another, but they also provide an understanding of the interrelationships among r(TO) and linkage factors, bond strength sum, coordination number, and angles within and between tetrahedra. A study of these interrelationships for a theoretical data set shows that r(SiO) and r(AlO) are linearly correlated with (1) p_o, the bond strength sum to a bridging oxygen, (2) f_s(O), the fractional s-character of a bridging oxygen, and (3) f_s(T), the fractional s-character of the T atom. In a multiple linear regression analysis of the data, 92% of the variation of r(SiO) and 99% of the variation of r(AlO) can be explained in terms of a linear dependence on p_o, f_s(O), and f_s(T). Analogous regression analyses completed for observed r(Al, SiO) bond length data from a number of silica polymorphs and ordered aluminosilicates account for more than 75% of the bond length variation. The lower percentage of bond length variation explained is ascribed in part to the random and systematic errors in the experimental data which have a negligible effect on the theoretical data. The modeling of more than 75% of the variation of r(Al, SiO) in the framework silicates using the same model used for silicate and aluminosilicate molecules strengthens the viewpoint that the bonding forces that govern the shapes of such molecules are quite similar to the forces that govern the shapes of chemically similar groups in solids. The different regression coefficients calculated for f_s(T) indicate that SiO and AlO bond length variations in framework structures should not be treated as a single population in estimating the average Al, Si content of a tetrahedral site.