Tetrahedral bond length variations in sulfates

Observed S—O bond lengths for sulfate tetrahedral oxyanions isolated from crystalline solids correlate with the tetrahedral angles impressed upon these ions by their environments. An algorithm is presented which can account for more than 90 percent of the S—O bond length variations from a consideration only of the average of the three angles common to each bond. Extended Hückel molecular orbital theory serves to rationalize these correlations by relating changes in bond overlap population (i.e., bond strength) to angular distortions of sulfate ions observed in a large number of natural and synthetic compounds.