Vibrational Excitons. II. Degenerate Vibrations

Abstract

The energy of the first vibrational excited state of a molecular crystal is derived in terms of exciton theory, for the special case of an exciton state derived from a doubly degenerate molecular excited state. We also treat the case where the degeneracy is lost due to the anisotropic environment of the molecule in the crystal. From the several allowed values of such energies, the correlation field splittings in such bands are derived in terms of three-dimensional ``chain sums.'' The origin of such splittings in certain cubic crystals is traced to the intermolecular exchange of the sense of vibrational angular momentum. An expression is also derived for ``site splittings,'' observable in solid solutions of molecules in their isotopically substituted modifications. A new interpretation of such splittings is offered. Finally, the effects of isotopic substitution in such crystals are discussed and several rules of isotopic invariance are derived. An appendix is included which treats as an example the vibrational fundamentals of crystal benzene derived from the e1u molecular modes.