Understanding high-resolution spectra of nonrigid molecules using group theory.

Permutation-inversion group theory has developed to become an important tool in the high-resolution spectroscopy of nonrigid molecules. This large class of molecules is very intriguing to study. Small molecules such as ammonia or Na(3) are known to be nonrigid. With increasing size, however, several large-amplitude motions are possible in a molecule, and can even interact with each other. The high-resolution spectra of nonrigid molecules are known to be quite complicated and very rich in information. Details about the molecule and its internal dynamics can be extracted, such as the molecular structure, the character of the chemical bonds, and the barrier heights to internal rotation and their dependence on the chemical bonds. However, due to the nonrigidity of the molecule and the complexity of such spectra, their analysis is usually quite challenging. Theoretical methods are needed for their prediction and analysis. This Review concentrates on permutation-inversion group theory and its usefulness for the analysis of high-resolution spectra of nonrigid molecules, which is examined in more detail using different examples. In a separate section, a special aspect of molecular symmetry is discussed: the breakdown of symmetry principles. Special emphasis is placed on the breakdown of space inversion symmetry (parity violation) in chiral molecules and its possible implications in high-resolution spectroscopy.