Computational study of the vibrational spectra of alpha- and beta-Keggin polyoxometalates.

The structures and vibrational frequencies of the alpha- and beta-isomers of the phosphomolybdate Keggin anion [PMo(12)O(40)](3-) have been calculated by using density functional theory. Good agreement between the calculated unscaled vibrational frequencies and those determined experimentally and between the calculated and observed IR traces has been obtained allowing the IR and Raman spectra to be assigned. For the alpha-isomer, the agreement with experiment using the current level of theory is superior to that obtained previously. For the beta-isomer, for which no non-empirical study has previously been reported, the agreement with experiment is slightly poorer but still allows the spectrum to be assigned unambiguously. To calculate the structure and vibrational spectra of these large molydate cluster ions requires large basis sets and a good treatment of electron correlation and relativistic effects. For the 53-atom [PMo(12)O(40)](3-) ions, the computational demands are very high, requiring several months computational time. The calculated IR spectral traces for the two isomers are quite similar due to the relative flexibility of the molybdates, where the slight weakening of the bonding of the rotated trimetallic unit to the rest of the cluster in the beta-isomer is compensated by contraction of the bonds within the unit, and the structure of the [MO(6)] and [PO(4)] units in the two isomers is nearly identical. The vibrations characteristic of the bridging Mo-O-Mo bonds involve both the "2-2" junctions between rotated [M(3)O(13)] units and the "1-2" junctions between rotated and unrotated units. The separation of "ligand" and "interligand" vibrations is not clear. The vibrational analyses confirm the high symmetry, namely T(d) and C(3v) for the alpha- and beta-isomers, respectively, assumed by previous workers in this field. The characteristic group frequencies for the Type I polyoxometalates containing both edge- and corner-sharing I octahedra have been identified.