Partial Dynamical Symmetry in Molecules

Abstract It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule with n bonds and having a point group P as its symmetry group may have the S n ⊃ 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 ⊃ 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 levels 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 ⊃ O h symmetry adapted basis with greatly reduced dimension.