The Infrared Spectra and the Molecular Structure of Pyramidal Molecules

Abstract

It is necessary to have explicit expressions for the rotational term values for the vibration states ν₂ and ν₄ in order to make use of the analysis of the data on the low frequency bands in the spectra of pyramidal XH₃ molecules. These frequencies are coupled by a Coriolis interaction which gives rise to a submatrix, for each value of J, in the complete energy matrix which has 3(2J+1) rows and columns. These submatrices further break up into smaller ones which have at most three rows and columns. Explicit relations for the term values ν₂ and ν₄ require that these be diagonalized independently. It has been possible to expand the determinants of these submatrices in special cases where, for example, the quantum number K=J and where K=0 so that explicit relations for these states may readily be had. Using the frequency positions of lines involving transitions to these states permits the evaluation of the Coriolis factor ζ₄^(z). The structure of the molecules may also be fixed if then B^(xx) and ζ₃^(z) can be determined, use being made of the zeta‐sum for XH₃ molecules, i.e., ${\zeta }_3^{\mathrm{(z)}}{\mathrm{+\zeta }}_4^{\mathrm{(z)}}{\text{=−1+B}}^{\mathrm{(xx)}}{\text{/2B}}^{\mathrm{(zz)}}$ .