Analytical presentation of symmetrized vibrational functions of high symmetry molecules for applications in molecular spectroscopy and chemical physics: Accurate prediction of the vibrational spectrum of GeH[formula omitted] up to 8000 cm−1 as a relevant application example

Abstract

We report here the analytical description of vibrational wave functions being most important for applications in quantum mechanics, molecular and chemical physics as applied to the high symmetry XY4 (Td) molecules. A general method is discussed and, for the first time, all vibrational functions of such molecule type are presented in an analytical and symmetrized form for all polyads up to the polyad number N=4. To illustrate the relevant application of the derived results, an accurate prediction of all vibrational band centers up to 8000 cm−1 is made for five stable isotopologues MGeH4(M=76,74,73,72,70) of the germane molecule.