Phonons in disordered molecular solids: Raman spectra of heavily doped mixed crystals of benzene and perdeuterobenzene

Raman spectra of mixed crystals of benezene-h6 and benzene-d6 have been studied throughout the whole concentration range (0%–100%). They are discussed in the virtual crystal limit, suitable for small trap depths. It is shown that within this limit: (1) All the phonons are delocalized in mixed crystals; (2) k-designation is still valid, and (3) no appreciable broadening is expected in mixed crystals. In particular, because the trap depths are the same for all three rotations in benzene mixed crystals, it is further inferred that: (1) There is a one-to-one correspondence between the mixed crystal absorption and the pure crystal absortion; (2) spectral line positions depend on the concentration linearly; and (3) the normal coordinates in the mass (or moment of inertia)-weighted coordinates remain unchanged from benzene-h6 to mixed crystals to benzene-d6. All these conclusions are supported by the experimental data. More general cases, where trap depths are different for different degrees of freedom, are also discussed. Implications of the phonon delocalization in isotopic mixed crystals to the interpretation of phonon sidebands of electronic spectra of isotopic mixed crystals are also pointed out.