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The-Lie algebraic approach based on the dynamical groupto describe a set of  n  local oscillators is analysed from the point of view of its connection with configuration space. First, the matrix elements of a general Hamiltonian involving Casimir operators of the two dynamical algebrasandare revised and subsequently the equivalent Hamiltonian in configuration space is established. This relationship permits us to evaluate the order of the interactions traditionally taken into account in thevibron model with the additional advantage of providing the connection with force constants. Starting from configuration space our analysis is applied to the description of vibrational excitations of the molecule of methylene chloride including both stretching and bending degrees of freedom.

Connection between the SU(2) Lie algebraic approach and configuration space: application to methylene chloride