  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.
