Derivation of Force Field Parameters, and Force Field and Quantum Mechanical Studies of Layered α- and γ-Zirconium Phosphates

A set of force field (FF) parameters was derived for bonds and atoms of the uncommon structural units (Zr−O; O−Zr−O; Zr−O−P; etc.) in layered α- and γ-zirconium phosphates (α- and γ-ZrP). To accomplish this parametrization we relied on the technique of energy derivatives obtained from ab initio quantum mechanics on a model compound as outlined by Dinur and Hagler. To check the reliability of the derived FF parameters the crystal structures of α- and γ-ZrP were calculated using the Open Force Field routine of Cerius 2 . The computed results were compared with the experimental X-ray crystal structures and also with the energy results obtained from the CRYSTAL95 program that performs quantum mechanical calculations on periodic systems. The discrepancies between the FF optimized structures and the experimental structures for α- and γ-ZrP were quite acceptable. The unit cells attained differences smaller than 6% (β angle of the γ-ZrP cell), while for the valence coordinate the maximum root-mean-square deviation values were 0.03 Å for the bond distances (P−O in γ-ZrP), and 5.82° for the bond angles (Zr−O−P in α-ZrP). The CRYSTAL95 calculated energies (per zirconium phosphate unit) using as input the experimental X-ray structure, and the FF optimized geometry, showed small differences. The Δ E values (1.26 and 3.26 kcal mol - 1, for α- and γ-ZrP, respectively, in favor of the X-ray geometry) does not rule out the population of both experimental and FF structures. Furthermore, their calculated electronic characteristics were analogous. Finally, comparisons made using vibrational spectroscopy data as benchmarks showed that calculated vibrational bands were in acceptable agreement with experiments.