Molecular Vibrations of the PO43− Ion, Site Symmetry <i>D</i>2<i>d</i>, in YPO4

Abstract

Molecular vibrations of the PO43− ion at a site having D2d symmetry are treated theoretically. Symmetry coordinates and G-matrix elements are derived. Analytical F-matrix elements corresponding to a generalized valence force field are given. Two of the four observed infrared absorptions are assigned to the B2 and two to the E species and corresponding F matrices calculated. The distribution of potential energy among the internal symmetry coordinates for each infrared-active normal mode is derived. The results indicate a marked increase in the force constant for bending along the S4 axis for the B2 species which is interpreted as evidence for the formation of P–O–Y bonds.