Knowledge Bank

In order to compute the rotation-vibration energy of $XY4$ molecules in a degenerate vibrational state, it is necessary to solve for the roots of heavy secular equations in which the elements of the secular determinant depend upon unknown molecular parameters. The case of a twofold degenerate vibrational state $v2=1$ will be treated including a discussion on the order of magnitude of the various off diagonal elements appearing in the secular matrix. It will be shown that it is worthwhile considering at the same time two different descriptions of the problem by choosing as z axis either a threefold axis or a fourfold axis of the molecule.