The bond angle dependence of the asymmetry parameter of the oxygen-17 electric field gradient tensor

From primarily geometric starting points, simple formulae for the bond angle dependence of the 17O quadrupolar asymmetry parameter eta were derived. Expressions for the bond angle dependence of the components of the electric field gradient (EFG) were first derived by Vega. Poplett used these expressions to discuss the 17O NQR results obtained for the water molecule. The formulae presented in this paper were derived essentially from other starting points and contain only the bond angle of a A- 17O-A oxygen bridge and all details concerning the electron distribution within the bonds will cancel out. Since no assumptions concerning the p-orbital occupancies had to be invoked, these geometric eta formulae are valid for most bridging oxygens. A necessary prerequisite of the eta formulae was that the electron distribution around the oxygen atom under study should exhibit C2v or D2 symmetry. The formulae were applied to explain the data of water molecules in the gaseous state, of various ice polymorphs and of crystal water. As supposed, the theory worked best for the free water molecule because of its perfect C2v symmetry. The differences between experiment and theory for water in solid compounds were mostly smaller than 6%. In the case of silicates and zeolites it was demonstrated that the eta formulae correctly described the experimental trends of the 17O NMR measurements of these substances. It could be demonstrated that reliable A-O-A-bond angles could be obtained from an eta measurement independent of the bond partner A. Comparing calculated eta values with ab initio calculations of this parameter, the largest difference was observed in the case of a Si-O-Si bond angle near 90 degrees. The eta formulae gave slightly lower eta values than ab initio calculations but the general trends were correctly reflected.