Molecular mimicry of the bond length-bond strength variations in oxide crystals

Abstract

Minimum energy theoretical bond lengths R t obtained with robust split-basis molecular orbital calculations for 27 hydroxyacid molecules containing first- and second-row cations X n+ reproduce XO bond lengths in crystals. Plots of ln(R t ) vs. ln(s), where s is the Pauling bond strength, define two different but essentially parallel trends (for first- and second-row cations, respectively) as observed for crystals. A new bond strength parameter p=s/r is defined where r=1 for first- and r=2 for second-row main-group cations. When a ln(R t ) vs. ln(p) plot is prepared with these theoretical bond lengths, a single trend is obtained. A regression analysis of this data set shows that more than 99 percent of the variation of ln(R t can be explained in terms of a linear dependence on ln(p), yielding R=1.39 p −0.22 as an estimator of the bond lengths. A comparison of 153 mean XO bond lengths compiled by Shannon (1976) for main-group closed-shell X-cations from all 6 rows of the periodic table with those estimated with this formula for r=1, 2, ..., 6, respectively, shows that these bond lengths are estimated within 0.05 A on average with nearly 85 percent estimated within 0.10 A of the observed value. More than 97 percent of the variation of these observed bond lengths can be ranked in terms of a linear dependence on the estimated bond lengths. The success of these calculations is further evidence that the forces that govern bond length variations in oxide crystals behave as if they are short-ranged.