Knowledge Bank

The Raman spectrum of the $\nu 2$ vibration-rotation band of $\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}CH4$ has been recorded with a half-intensity linewidth of about $0.10cm-1$. The resolution obtained much better than the resolution of the infrared spectra of this band. Most of the fine structure is split. The analysis of this doubly degenerate band is presented. 126 transitions are assigned up to J = 10. The energy levels of the excited state $\nu 2$ = 1, computed up to the fourth-order of approximation, present an interesting structure: It is shown that the vibration-rotation interactions (described in the group Td) have a spherical symmetry in first approximation (group 0(3)). Consequently, the use of spherical tensors seems to be particularly adapted to the theoretical treatment of the doubly degenerate vibrations as well as to the triply degenerate ones. The results obtained in that way are discussed.