We study the many-quanta problem of an intramolecular vibrational excitation interacting with optical phonons, that may represent the nonlinearity from intrinsic electron-lattice interactions. In the adiabatic limit we calculate numerically the ground-state energy and the corresponding wave functions for N vibrational quanta. In the one-dimensional case we find strong redshifts in the overtone spectra and an increasing spatial localization as the number of quanta increases. Through model parameter fitting we achieve very good quantitative agreement with experimental resonant Raman scattering measurements in the quasi-one-dimensional charge transfer solid PtCl. Accurate analytical expressions for the redshifts are also obtained.