The homogeneous line shape of the infrared spectrum of a single molecule physisorbed on ionic substrates is determined on the basis of a renormalization technique of the total system Hamiltonian. The absorption profile can be written in terms of a limited cumulant series expansion of the dynamical couplings between the optical system formed by the vibration-orientation modes of the molecule, and the bath modes characterized by molecular translations and substrate phonons. The various causes of homogeneous broadening of the lines are studied, implying phase and population relaxations through intramolecular transfers, In this latter case, two situations are considered depending on whether the internal vibration modes of the admolecule are localized or resonant (quasi-resonant) with the substrate phonon modes. These situations are usual for small polyatomic molecules adsorbed on substrates with extended optical phonon bands. An application to the calculation of the Q*, P* and RX branch widths for CO, CO2 and NH3 molecules adsorbed on NaCl(001) and/or MgO(001) is extensively discussed. We show that, at low temperature T less than or similar to 20 K, the homogeneous width is quite negligible and inhomogeneity must be invoked to interpret the measured width. By contrast, for increasing T values (T greater than or similar to 50 K), homogeneous broadening increases and contributes significantly (about to 50%) to the measured width for CO and CO2 molecules adsorbed on clean substrates.