Symmetry-Based Vibrational Analysis of Polyatomic Ionic Species in Polymer Electrolytes:  Application to the Compounds Poly(ethylene oxide)₃LiCF₃SO₃ and Poly(ethylene oxide)NaCF₃SO₃

A symmetry-based vibrational analysis of the compounds (PEO) 3 LiCF 3 SO 3 and (PEO)NaCF 3 SO 3 is described which preserves the distinct identity of the CF 3 SO 3 - intramolecular vibrational modes in the one-dimensional and three-dimensional space groups appropriate to each compound. The infrared and Raman spectra in the δ s (CF 3 ) spectral region of the two compounds are discussed in terms of this formalism, although a similar analysis of the ν s (SO 3 ) region is limited to the (PEO) 3 LiCF 3 SO 3 compound. A one-dimensional space group is sufficient to describe the δ s (CF 3 ) spectral region in both compounds and the ν s (SO 3 ) region in (PEO) 3 LiCF 3 SO 3 .