Electronic Consequences of Vibrational Deficiency in Polyatomic Molecules

Vibrationally deficient molecules have been defined as those molecules whose symmetry species for the normal vibrational modes of a molecule fail to span all of the irreducible representations of the corresponding point group. A comprehensive group‐theoretical study of all of the finite point groups and of the infinite point groups $C_{\mathrm{\infty \nu }}$ and $D_{\mathrm{\infty h}}$ has been undertaken in order to determine the extent of vibrational deficiency for various molecular geometries. An important electronic consequence of vibrational deficiency is the identification of special examples of electronic transitions which are forbidden even when considering perturbation by a single antisymmetric normal vibrational mode. Thus, in the second part of this group‐theoretical study, electric‐dipole selection rules have been determined in order to ascertain possible examples of these forbidden transitions in vibrationally deficient molecules. First‐order forbidden vibronic transitions are found to be physically possible in certain polyatomic molecules in $D_{\text{3h}}$ , $D_{\text{4h}}{T}_d$ , $O_h$ , $C_{\mathrm{\infty \nu }}$ , and $D_{\mathrm{\infty h}}$ point groups. An analysis of electronic transitions of vibrationally deficient molecules in the above point groups was made in order to establish and to predict examples of this specially forbidden transition which will be manifest as an anomalously weak absorption. A second electronic consequence of vibrational deficiency is predicted in small polyatomic molecules where missing antisymmetric vibrations may have a critical influence on the pathway of intramolecular radiationless processes. The probability of a radiationless transition in an isolated polyatomic molecule may be considered to depend upon a vibrational factor and an electronic factor. This present work indicates that in vibrationally deficient molecules, the electronic factor may have a significant influence on the nonradiative transitions. The fluorescence of SO₂ from the second excited singlet state to the ground state is considered as a possible example of the influence of the electronic factor on radiationless processes in vibrationally deficient molecules.