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Firstly, a sequential symmetry adaptation procedure is derived for semidirectproduct groups. Then, this sequential symmetry adaptation procedure is used inthe development of new method named Monomer Basis Representation (MBR) forcalculating the vibration-rotation-tunneling (VRT) spectra of molecularclusters. The method is based on generation of optimized bases for each monomerin the cluster as a linear combination of some primitive basis functions andthen using the sequential symmetry adaptation procedure for generating a smallsymmetry adapted basis for the solution of the full problem. It is seen thatgiven an optimized basis for each monomer the application of the sequentialsymmetry adaptation procedure leads to a generalized eigenvalue problem insteadof a standard eigenvalue problem if the procedure is used as it is. In thispaper, MBR method will be developed as a solution of that problem such that itleads to generation of an orthogonal optimized basis for the cluster beingstudied regardless of the nature of the primitive bases that are used in thegeneration of optimized bases of the monomers.

Monomer Basis Representation Method For Calculating The Spectra Of Molecular Clusters I. The Method And Qualitative Models