Semiclassical assignment of the vibrational spectrum of N2O

The vibrational spectrum of N2O as given by an effective spectroscopic Hamiltonian based on the existence of a superpolyad number is analyzed and assigned in terms of classical motions. The effective Hamiltonian includes a large number of resonances of which only one is dominant for low and intermediate superpolyad numbers. In this energy range, the corresponding classical system is quasi-integrable and can be described in terms of a system with only one nontrivial degree of freedom. This integrable system can be analyzed by considering the so-called quantizing trajectories on a polyad sphere. This method is no longer applicable when the superpolyad number is further increased and classical chaos comes into play. We then turn to a powerful universal method based on the graphical representation of semiclassical wave functions on a naturally appearing toroidal configuration space. These wave functions are obtained using the already known transformation matrix used in fitting the effective Hamiltonian. Experience with the interpretation of the resulting figures allows one to draw conclusions on the classical internal motions and therefore on the assignment of the quantum states without any further calculation. As such, the method is of particular interest to nontheorists and to nonspecialists in the fields of nonlinear dynamics and quantum calculation. For higher superpolyad numbers, the chaos remains mainly concentrated about the direct neighborhood of a separatrix of the former integrable system so that a great part of the vibrational spectrum can still be assigned in terms of the EBK quantum numbers of quantized tori.