Force constants and transition intensities in the U (ν + 1) model for molecular vibrational excitations

A connection between the unitary group approach U (ν + 1) and the traditional description in configuration space of vibrational excitations is proposed. Local operators bˆi†(bˆi) satisfying the su (2) commutation relations are used to establish approximate algebraic expansions of the local coordinates and momenta. The use of the proposed relations allows to obtain an algebraic representation of traditional Hamiltonians in terms of the U (ν + 1) model. This approach provides in natural form the connection between the spectroscopic parameters and force constants. Using the linear expansion of the coordinates in terms of the bˆi†(bˆi) operators, an approach to study local dipole transition intensities based on traditional descriptions is proposed. A closed general analytical expression for the local dipole operators is obtained. The analysis of the stretching vibrational excitations of arsine is taken as an example for the determination of both force constants and the description of dipole transition intensities.