Knowledge Bank

The symmetry description of rovibronic energy levels of tunneling malonaldehyde can be made using a permutation-inversion group, $G4$, of order 4. The elements (1) of this group are: $E^$, the identity; $E^\ast$, the inversion of all the coordinated of the atoms through the molecular center of mass; $P^$, the permutation of the positions and spins of equivalent nuclei; and $\hat{P}^{}=\hat{P}=\hat{E}^{}=\hat{E}^{*} $P. The isomorphic mapping of the elements of $G4$ and those of the point group $C2v$ (the group of a rigid symmetric structure) may be conveniently used to determine the reduction of the character of the various degrees of rotations, vibrational and electronic freedom of the molecule. The net result is to justify, on group theoretical grounds, the use of ""effective"" $C2v$ symmetry arguments. The tunneling coordinate of malonaldehyde is one special normal vibrational coordinate of large amplitude (2). The correlation of the high and low barrier limits in the tunneling coordinate is presented. The selection rules for rovibronic transitions of the tunneling molecule are presented and the results for the electronic spectrum are presented in the following paper.