Isometric Transformations Associated with Quasirigid Molecules

1 Isometric Transformations Associated with Quasirigid Molecules 

In this section we will show that our group theoretical treatment for nonrigid molecules, approximated by a SRM is strictly analogous to the familiar symmetry treatment of quasirigid molecules (QRM)5S-S7 A QRM may be characterized by the nuclear configurations 

This equation again shows that the re-structure NCe is a fixed point NC for all isometric transformations (4.7) and is the analogue of Eq. (2.53) for SRMs. However, for difference concerning the definition of operators PG for SRMs and QRMs see Sect. 4.3. 

This transformation formula formed the starting point for the study of the symmetry of nonrigid molecules by Hougen6 and later more generally by Longue t-Higgins7, cf. Sect. 4.4.1. 

From the fact that r Ncf 3% is the isometric group of the NC (4.1) it follows by the same reasoning as for SRMs that e is the symmetry group of the rotation-vibration hamiltonian. Though the representation (4.11) is commonly used in vibrational spectroscopy55-S7 it only seldom has been characterized as a group of isometric transformations57.  

---

In this section we first present a set of general transformation formulae for tensor operators associated with SRMs. These then serve as a mathematical tool for the formulation of Wigner-Eckart theorems and selection rules for irreducible tensor operators associated with multipole transitions of SRMs. The concept of isometric groups will allow a formulation of selection rules in strict analogy to the group theoretical treatment of quasirigid molecules first presented by Wigner5. ... 

---