Point-group symmetrized boson representation. Algebraic solution for symmetry-adapted bases of O-h

A point group symmetrized boson representation (SBR) is introduced that is particularly convenient for describing molecular vibrations. In this paper the SBR is elucidated using the example of the molecule SF6 with O-h symmetry. The advantages of the SBR are that its basis vectors have a clear physical picture, their number is very small (equal to one-eighth of the dimension of the reducible representation for O-h), and the irreducible bases for any concrete cases can be obtained trivially from those for the general case without any projection. All the irreducible bases for the group chains O-h superset of D-4 superset of C-4 or O-h superset of D-4 superset of D-2 are tabulated once and for all. As an application, the Hamiltonian in the algebraic model of Iachello and Oss for stretching vibrations of the molecule SF6 is diagonalized in the symmetry adapted bases. (C) 1996 American Institute of Physics.