Développement complet de l'hamiltonien de vibration–rotation adapté à l'étude des interactions dans les molécules toupies sphériques. Application aux bandes ν2 et ν4 de 12CH4

Abstract

Using an unsymmetrized coupling scheme in the group Td, we determine all the vibration–rotation operators of the Hamiltonian of XY4 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 ν2 and ν4 of CH4. With only 21 parameters for the two bands, we obtain a standard deviation of 34 mK for 251 Raman transitions of ν2 and 20 mK for 243 ir transitions of ν4.