Spacings distribution for highly excited vibrational states: Role of dynamical symmetry

Statistical analysis of energy level spacings is reported for models of O₃, H₂O, CO₂ and HCN. The levels and their dynamical symmetries are determined by the algebraic approach. Specifically we use Hamiltonians with partial symmetry breaking which therefore have an incomplete set of constants of the motion. Wigner-like nearest-neighbour distributions are found for such non-chaotic systems. In particular, counting of states of the same dynamical symmetry type leads to a Wigner-like distribution. The results suggest that experimental level spacing distributions can serve as a signature for the presence of dynamical (i.e. not necessarily geometrical) symmetries in molecular systems.