An algebraic model to describe inelastic collisions between an atom and a diatomic molecule within the semiclassical approximation framework is presented. For the interaction in the diatomic system a Morse potential is considered, while an exponential function is taken for the atom-diatom interaction. The original atom-diatom Hamiltonian is transformed into a time-dependent Hamiltonian for the diatomic system. In the interaction picture framework the interaction potential is approximated by a linear expansion in terms of the generators of the SU(2) group, the dynamical algebra for the Morse potential bound states. A minimization procedure to determine the time-dependent coefficients is proposed. The transition intensities are given in terms of matrix elements of the product of exponentials of the Morse potential dynamical group generators. A comparison of the algebraically obtained transition probabilities with the exact semiclassical results is presented.