The shift in the harmonic vibrational frequency of the ArH stretch of FArH on formation of the linear FArH...Rg complexes (Rg=He, Ne, Ar, Kr), and of the FH stretch on formation of the linear FH...Rg complexes, has been determined by ab initio computations. These shifts are in agreement with predictions from a model based on perturbation theory and involving the first and second derivatives of the interaction energy with respect to displacement of the ArH (FH) bond length from its equilibrium value in the monomer. In the FH...Rg dimers, small blue shifts were obtained for the He and Ne complexes and red shifts for those with Ar and Kr. In the FArH...Rg dimers, blue shifts were obtained for all four complexes. These vibrational characteristics are rationalized by considering the balance between the interaction energy derivatives obtained from the perturbative model. The bond length changes on complexation are also well predicted by the model. Our computations were restricted to the linear geometry since the objective was to investigate the validity of the perturbation model and to illuminate the causes of the red and blue shifts.