Relationship between bond stretching frequencies and internal bonding for [16O4]- and [18O4]phosphates in aqueous solution

A normal-mode analysis is used to show that the fundamental stretching frequency, defined as v(2) = (v(s)(2) + n(a)v(a)(2))/(n(a) + 1) where v(s) and v(a) are the symmetric and asymmetric modes, respectively: and n(a) the degeneracy of the asymmetric modes, depends almost entirely on the force constant and reduced mass of a P - O (or P-OH) bond in phosphoric acid or its anions to a good approximation. On the other hand, v(s) or v(a), separately, depend not only on these parameters but also on molecular geometry. Thus, P - O (or P-OH) bond order is more closely related to the fundamental frequency than to the symmetric or asymmetric stretching frequencies. Similar conclusions apply to V - O (or V-OH) bonds in vanadate molecules. The frequencies for the four different P - O bonds and three different P-OH bonds in [O-18(4)] phosphoric acid and its three anions were measured by Raman and FT-IR spectroscopy. The measured values, plus those for [O-16(4)] phosphates, were correlated with P - O Valence bond order, by using a modification of the Hardcastle-Wachs procedure (Hardcastle, F. D.; Wachs, I. J. Phys. Chern. 1991, 95, 5031). The bond order/stretching frequency correlations thus produced are expected to hold accurately over a wide range, for both [O-16] and [O-18] phosphates. Thus, P - O bond order and bond length in phosphates can be determined from vibrational spectra by using the derived bond order/stretching frequency correlation and the bond length/bond order correlation of Brown and Wu (Acta Crystallogr. 1976, B32, 1957). The accuracy;s very high. The error in these relationships is estimated to be within +/-0.04 vu and +/-0.004 Angstrom for bond orders and bond lengths, respectively, as judged by examining the affects of neglecting small terms in normal-mode analysis and by comparisons of derived bond lengths of P - O bonds from frequency data to the results from small-molecule crystallographic data.