Knowledge Bank

In this communication, the character table for the triple equivalent methyl rotation is determined from the Non-Rigid-Molecule-Group theory (NRG), in which the dynamical symmetry operations are defined as physical operations. This Group of order 648 is shown to be a product of two subgroups, the $G324$ corresponding to planar trimethylamine and the pyramidal inversion subgroup. For this purpose, the structure of the NRG of planar trimethylamine is first deduced, i.e., the number of classes, irreducible representions as well as their dimensions. Finally, guidelines are given to deduce systematically the symmetry eigenvectors developed on the basis of quadrupole products of trigonomeetric functions.