Semiclassical quantization of strongly chaotic vibrations in an M₇-like cluster

We report semiclassical energy spectra of vibrational state of a cluster composed of seven identical atoms like Ar₇ in terms of our previously developed semiclassical wave function, which we call the action-decomposed function. The classical dynamics of this vibrational state is strongly chaotic and undergoes a large amplitude motion due to structural isomerization, which demands a long run of trajectory calculation. Permutation of identical particles should also be taken into account as a quantum effect, since a single molecular shape can be shared by many permutational isomers. Furthermore, chaos causes a spurious divergence in the amplitude factor of a correlation function in the initial value representation, which arises from the amplitude factor (prefactor) of a semiclassical wave function, while the final-state representation is suffered from the well-known divergence arising at caustics. Both approaches therefore face tremendous difficulty in a long-time calculation of the correlation functions. We challenge to extract some limited number of spectral lines from such chaotic dynamics. We further apply a correlation function that is free of such a troublesome amplitude factor. Numerical results from all these schemes are reported.