Strategies for advanced applications of permutation-inversion groups to the microwave spectra of molecules with large amplitude motions

This article presents permutation-inversion group-theoretical strategies and recipes aimed at helping a high-resolution molecular spectroscopist use the existing pedagogical literature to carry out their own treatment of the basic symmetry questions in rotating molecules with large-amplitude vibrational motions. Topics addressed include: determination of the feasible permutation-inversion group and its symmetry species and character table; a general equation defining coordinates that can describe translation, overall rotation, large-amplitude vibrations and small-amplitude vibrations for a large class of floppy molecules; and the determination of symmetry species for basis functions and selection rules for operators written in these coordinates. The article is intended to be more advanced than existing pedagogical works, but it still leaves many important topics untreated.