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

Abstract: Firstly, a sequential symmetry adaptation procedure is derived for semidirect product groups. Then, this sequential symmetry adaptation procedure is used in the development of new method named Monomer Basis Representation (MBR) for calculating the vibration-rotation-tunneling (VRT) spectra of molecular clusters. The method is based on generation of optimized bases for each monomer in the cluster as a linear combination of some primitive basis functions and then using the sequential symmetry adaptation procedure for generating a small symmetry adapted basis for the solution of the full problem. It is seen that given an optimized basis for each monomer the application of the sequential symmetry adaptation procedure leads to a generalized eigenvalue problem instead of a standard eigenvalue problem if the procedure is used as it is. In this paper, MBR method will be developed as a solution of that problem such that it leads to generation of an orthogonal optimized basis for the cluster being studied regardless of the nature of the primitive bases that are used in the generation of optimized bases of the monomers.