Luminescence in the vacuum UV/visible region has been recently recorded for atomic cadmium isolated in the rare gas solids Ne, Ar, Kr, and Xe, and because of the availability of diatomic Cd . RG and RG . RG pair potentials, theoretical calculations are now performed and compared to the recorded luminescence spectra. Calculations were first done for the gas-phase excited-state cluster species Cd(P-1(1)). RG(n), where n is the number of rare gas atoms in the cluster. The Cd . RG(4), Cd . RG(5), and Cd . RG(6) clusters showed energy minima for the Cd p(z) orbital situated at the center of the planar rare gas clusters. With the rare gas distances in the planar clusters fixed at the rare gas dimer bond lengths, the cluster showing the greatest stabilization was the Cd RG(5) species. The cluster calculations were then extended into the solid state for Cd occupying a single substitutional site of the solid rare gas lattice. Two vibronic modes lead to a preferential interaction between the guest and four rare gas atoms, thereby reducing the excited-state energy and leading to distinct minima. The modes are (a) the "body" mode (Q(2)), which involves the motion of the Cd atom toward an octahedral interstitial site and (b) the "waist" mode (Q(3)), which involves the in-phase contraction of four rare gas atoms in a single plane toward the Cd atom. Calculations based on single substitutional site occupancy of Cd in the rare gases indicate excited state stabilization for the waist mode for all hosts except neon. The body mode exhibits stabilization in Kr and Xe only. The pair of singlet emission bands observed in the Cd/Kr system is identified as originating from the stabilization of both vibronic modes in the excited state. The lack of stabilization for either mode in Ne, even though singlet emission exists in Cd/Ne, is indicative that a multivacancy site occupancy is likely here.