Knowledge Bank

The theory of local modes provides a good model for highly excited stretching vibrational states in molecules [1]. Morse oscillators are associated with all equivalent bands: but it is difficult to take into account molecular symmetry so that no general theory is available. Non degenerate and triply degenerate anharmonic oscillators have been introduced [2] through group chains: these can be generalized to n dimensional anharmonic oscillators with the chain: $U(n+1)\supset U(n)\supset O(n)$ We propose to associate such an oscillator with each set of n equivalent bonds. As a first approximation O(n) is almost a symmetry group and we may define symmetric coordinates. Next the O(n) symmetry is broken but group algebra allows to build an Hamiltonian in which the dominant operator responsible for the spiltting appears and is diagonal.