Quantum and semiclassical description of a triply degenerate anharmonic oscillator

Quantum and semiclassical energies are compared as a function of anharmonicity using the Hecht Hamiltonian for the triply degenerate anharmonic oscillator for octahedral and tetrahedral molecules. Semiclassical energies are found by turning on the potential adiabatically and the corresponding classical trajectories are described in terms of an adiabatic vibrational energy (VE) surface. Accurate semiclassical energies are obtained for chaotic trajectories near the separatrix of the VE surface. The quantum wave functions corresponding to the semiclassical trajectories after the onset of chaos are used to disprove a recently proposed quantum analog to classical quasiperiodic motion