Knowledge Bank

The spherical tensor $formalism1$ is applied to rotation-vibration interactions in the first overtones of the infrared active fundamentals of tetrahedral $XY4$ molecules. Theory predicts five P, Q and R branches of comparable intensity provided that the separation of the E and $F2$ vibrational components of the $l=2$ vibrational state is small compared with the splittings which arise from the $2B\zeta (P.l)\to \to$ term. $2\nu 4\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ of $CH4$ falls into this category. If, however, the separation between the E and $F2$ vibrational components is very large, theory predicts an overtone spectrum with a single strong P, Q and R branch structure. In that case transitions to the levels associated with the E vibrational substate are extremely weak, and the P, Q, and R lines associated with the $F2$ vibrational substate are similar to those of the fundamentals. $2\nu 3$ of both $CH4\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ and $CD4\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ fall into this second category, although the splitting of lines belonging to the same J value is much larger in $CD4$. Several molecular constatnts for $CH4$, and $CD4$ have been determined from a detailed quantitative analysis of these bands.

1960