1977/10/15 by Jean-Paul Champion, Jean‐Paul Champion
Chemistry · #Molecular Spectroscopy and Structure #Molecular spectroscopy and chirality #Spectroscopy and Laser Applications
paper · doi:10.1139/p77-221
crossref issued 1977/10/15 · crossref published 1977/10/15 · crossref published-print 1977/10/15 · openalex publication_date 1977/10/15 · crossref created 2011/04/23 · crossref deposited 2025/07/02 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
Using an unsymmetrized coupling scheme in the group T d , we determine all the vibration–rotation operators of the Hamiltonian of XY 4 molecules, including all possible interactions, up to any order of approximation. We define a basis of Hamiltonian matrices of which the matrix elements are functions of coupling coefficients of the group chain [Formula: see text] only. Thus, we develop a general formalism available for any vibrational sublevels of whatever symmetry. The parameters relative to the different vibrational sublevels are known linear combinations of the coefficients of the Hamiltonian expansion. From these, we deduce simple relations between the parameters associated with the ground state, the fundamentals, and the harmonic and combination bands.We apply this formalism to the study of the Coriolis interaction between ν 2 and ν 4 of CH 4 . With only 21 parameters for the two bands, we obtain a standard deviation of 34 mK for 251 Raman transitions of ν 2 and 20 mK for 243 ir transitions of ν 4 .