Knowledge Bank

Using the general development of AMAT and NIELSEN’s transformed Hamiltonian, expressed in a convenient form of tensorial operators by MORET-BAILLY for the tetrahedral $XY4$ molecules, it becomes possible to extend to large values of J the analysis of the three-fold degenerate fundamental bands $\nu 3$ and $\nu 4$ of these molecules. Starting with the formula of MORET-BAILLY we construct. Hamiltonian matrices, the elements of which depend linearly on 19 parameters. The usual procedure is to evaluate these parameters by least squares adjustment of theoretical results in agreement with spectral data. The contribution to energy of some seven parameters may be expected to be appreciable mainly for large values of the rotational quantum number J. For these values, the bases used in MORET BAILLY’s representation become inadequate, the corresponding selection rules become less and less accurate and other lines, improperly called ``forbidden’’ lines, appear the influence of non-diagonal matrix elements, due to the increasing value of J, is so important that finally the eigen-states are a complex mixture of MORET-BAILLY’s bases and the same effect is also observed in the line intensities. In other words, most of the transitions allowed by group-theory are possible. This theory has been applied to the bands $\nu 3$, $\nu 4$ of $CH4$ and $\nu 4$ of $CD4$. Our computed results are in good agreement with the experimental data and explain entirely the fine details of the I.R. spectra of these bands.