Partial dynamical symmetry in molecules

It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule with it bonds and having a point group P as its symmetry group may have the S-n superset of P partial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, the XY(6) molecule has the S-6 superset of O-h partial dynamical symmetry. The model of Iachello and Oss for n coupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique revels of the XY(6) molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in the S-6 superset of O-h symmetry adapted basis with greatly reduced dimension. (C) 1997 Academic Press.