Knowledge Bank

Using a tensorial formation in the Td group, we have determined all the vibration-rotation operators of the dipole moment of $XY4$ molecules, up to any order of approximation [1]. This general formalism is available for any transition between vibrational sublevels of whatever symmetry. It can be used for the analysis of isolated bands and for the analysis of interacting bands as well. The theory will be applied to the analysis of rovibrational line strengths of the two bands $\nu 2$ and $\nu 4$ of $\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}CH4$ alone and as a polyad, on the basis of a second order expansion of the dipole moment. Five operators are needed to analyse the strengths of the isolated $\nu 4$ band. It will be shown that the empirical Hermann-Wallis polynomial is not adapted to this problem, especially in the case of the forbidden” lines. The I.R. forbidden” $\nu 2$ band has been analysed as an isolated band with two operators. As pointed out by many authors, the best model for these two interacting bands is the diad scheme. On this basis, we have also analysed the line strengths with the adapted second order expansion of the dipole moment. The physical meaning of the obtained parameters, which depends on the used scheme, will be also discussed. [1] M. LOETE, Can. J. Phys., in press.