1676 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
it follows that, opposite to the conclusions above, for an orientationally disordered crystal the IR spectrum reflects the DOS while the Raman spectrum is given by the k 0 frequencies with mode dependent depolarization ratios. The case in which both g- and u-type properties contribute to the resonance has been discussed in ref 2 on a rudimentary level. Obviously, the resulting spectrum must be somewhere between the two limiting cases. From this fact I conjecture that by including g- and u-type molecular properties in the calculation of intermolecular resonance interactions one can explain the frequency dependence of the depolarization ratio without the assumption of ref 1 that the crystal is partially ordered.
Laboratorium f u r Physikalische Chemie ETH-Zentrum CH-8092 Zurich, Switzerland
G . Zumofen
Received: May 24, 1988; In Final Form: October 12, 1988
Reply to Comment on “Raman Line Shapes of the v, Stretching Mode in Orlentationally Disordered N,O Crystals” Sir: In his comment of our paper’ dealing with Raman line shapes of the v , stretching mode in orientationally disordered N,O crystals, Zumofen pointed out an important and challenging problem. It is conjectured that by including higher order terms of g and u symmetries in the resonance intermolecular interactions one can explain the frequency dependence of the depolarization ratio without assuming a partially ordered crystal. Crystals made up of molecules with no inversion center like CO or N 2 0 display a particular head-tail orientational disorder of lsing type for the dipole moments. The effects of this disorder, both diagonal and off-diagonal, on the vibrational line shapes was previously investigated by Zumofen on a-CO crystak2 Consideration of the various terms in the molecular interactions make the problem difficult to handle. Nevertheless, it is known that
Comments for internal modes the induced dipole-induced dipole is the predominant one and reproduces quite well the LO-TO splittings as well as the density of vibron states. The inclusion of the diagonal disorder due to the fluctuations in the site energies leads to a broadening of the transition frequencies and does not strongly modify the energetics of the disordered crystal. We agree with the fact that this diagonal disorder cannot give rise to a frequency-dependent depolarization ratio. The main problem discussed in the comment concerns the effect on the IR and Raman line shapes of the higher order terms in the resonance intermolecular interactions. Assuming that solid N 2 0 is totally disordered at any temperature (Le., with a crystal the limitation of the resonance intermolecular space group interactions to the dipole-dipole part does not allow reproduction of the low-energy side of the v , Raman band. As suggested by Zumofen, the inclusion in the crystal Hamiltonian of higher order contributions, especially the quadrupolar terms of a g symmetry, is judicious. However, this contribution has to be relatively large to produce the drastic effect observed on the Raman line shapes and also have an important counterpart in the corresponding IR spectrum. An estimation of this effect is unfortunately not available from molecular data. But, a detailed analysis of the Raman band shapes with polarized light of the stretching vibration of a - C O crystal would be very useful to check out the effects of partial ordering and quadrupolar interactions. Actually it is known that a-CO crystals are not totally disordered (residual entropy of 3.3 J K-l mol-]) and the transition quadrupolar moments are known from ab initio calculation^.^ In conclusion the existence of a partial ordering in N 2 0 is the simplest way to account for our experimental observations. It is clear, however, that a more refined analysis of experimental data would include higher order resonance interactions as well as Fermi resonance interactions between the stretching mode v1 and the overtone 2u2 of the bending mode.
c)
Dcpartement de Recherches Physiques UniversitP P. et M . Curie Tour 22, 4 , Place Jussieu 75252 Paris Cedex 05, France
J.-P. Lemaistre* R. Ouillon P. Ranson
Receiued: July I I 1988; In Final Form: October 4, 1988 ( I ) Lemaistre, J.-P.; Ouillon, R.; Ranson, P. J . Phys. Chem. 1988, 92, 1070. (2) Zumofen, G. J . Chem. Phys. 1978, 68, 3747.
(3) Nesbet, R. K . J . Chem. Phys. 1964, 40, 3619.
