The absorption spectroscopy of calcium-doped argon clusters is described in terms of an effective diatomic molecule Ca-(Ar-n), in the framework of semiclassical vertical transitions. We show how, upon choosing a suitable reaction coordinate, the effective finite-temperature equilibrium properties can be obtained for the ground and excited surfaces from the potential of mean force (PMF). An extension of the recent multiple range random-walk method is used to calculate the PMF over continuous intervals of distances. The absorption spectra calculated using this single-coordinate description are found to be in good agreement with the spectra obtained from high-statistics Monte Carlo data, in various situations. For CaAr13, we compare the performances of two different choices of the reaction coordinate. For CaAr37, the method is seen to be accurate enough to distinguish between different low-energy structures. Finally, the idea of casting the initial many-body problem into a single degree of freedom problem is tested on the spectroscopy of calcium in bulk solid argon. (C) 2003 American Institute of Physics.