Knowledge Bank

It is generally thought that the vibrational spectra relative to the transition $\Delta w=2$ for $XH2$ systems are intermediate between those typical of normal modes, which are observed for $\Delta v=1$, and those typical of local modes, which are observed for $\Delta >3$ (1), the parameters in the potential being the determining factor 1n higher or lower local mode character of the $\Delta v-2$ spectra. However the semiclassical method of the phase space spheres representing vibrational polyads introduced by xiao and Kellman (2) poses some questions about this simple picture. The absorption spectra at low resolution for molecules containing one or several equivalent $CH2$ groups show two distinct types of behaviors at $\Delta v=2$, the first one with two band and the second with a characteristic couplet and a third band, with marked differences in intensities. the sum of power spectra of classical trajectories (3) for various total energies in a system of two coupled Morse oscillators, predicts in a quite qualitative way the existence of two bands at $\Delta v=1$, of three bands at $\Delta v=2$ and of one band at $\Delta v\ge 3$. However, in order to be more quantitative, it is found that semiclassical quantization conditions besides, the right parameters in the model Hamiltonian are important in making the vibrational assignement.