We establish a reliable quantum-mechanical approach to evaluate the vibrational properties of donor-acceptor molecular crystals. The anthracene-PMDA (PMDA = pyromellitic dianhydride) crystal, where anthracene acts as the electron donor and PMDA as the electron acceptor, is taken as a representative system for which experimental non-resonance Raman spectra are also reported. We first investigate the impact that the amount of nonlocal Hartree-Fock exchange (HFE) included in a hybrid density functional has on the geometry, normal vibrational modes, electronic coupling, and electron-vibrational (phonon) couplings. The comparison between experimental and theoreticalRaman spectra indicates that the results based on the αPBE functional with 25%-35% HFE are in better agreement with the experimental results compared to those obtained with the pure PBE functional. Then, taking αPBE with 25% HFE, we assign the vibrational modes and examine their contributions to the relaxation energy related to the nonlocal electron-vibration interactions. The results show that the largest contribution (about 90%) is due to electron interactions with low-frequency vibrational modes. The relaxation energy in anthracene-PMDA is found to be about five times smaller than the electronic coupling.