Remarks Concerning the Definition of Operators

A remark should be made concerning the definition of operators G for semirigid, quasirigid and nonrigid molecules. These operators are associated with coordinate transformations 

The actual definition of the operators PG for SRMs differs from that for QRMs and NRMs. This originates from the fact that these operators are defined by their action in function spaces which are different for SRMs on one hand and QRMs and NRMs on the other hand. For SRMs the basis is Xk( ), on which PG induces a rotation or a permutation20  

For QRMs and NRMs, the operators PG are defined by their action on the dynamical variables xk (infinitesimal displacements) 

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