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

Abstract

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⊇D₄⊇C₄ or O_h⊇D₄⊇D₂ 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.