Anisotropy molecular vibrations

GNP, (CN3Hg)2[Fe(CN)5NO], may be considered as a calibration standard for NIS applications since nitroprusside complexes have been studied in detail over the past decades by a variety of experimental and theoretical methods. In addition, single crystals of GNP are well suited for the investigation of the anisotropy of molecular vibrations because the two nonequivalent NP anions, [Fe(CN)5NO] , in the unit cell of GNP have an almost antiparallel orientation. 

Consequently, the Raman scattered light emanating from even a random sample is polarised to a greater or lesser extent. For randomly oriented systems, the polarisation properties are determined by the two tensor invariants of the polarisation tensor, i.e., the trace and the anisotropy. The depolarisation ratio is always less than or equal to 3/4. For a specific scattering geometry, this polarisation is dependent upon the symmetry of the molecular vibration giving rise to the line. 

The optical anisotropy, as characterized by the difference between the absorption of IR light polarized in the directions parallel and perpendicular to the reference axis (i.e., the direction of applied strain), is known as the IR linear dichroism of the system. For a uniaxially oriented polymer system [10, 28-30], the dichroic difference, A/4(v) = y4 (v) - Ax v), is proportional to the average orientation, i.e., the second moment of the orientation distribution function, of transition dipoles (or electric-dipole transition moments) associated with the molecular vibration occurring at frequency v. If the average orientation of the transition dipoles absorbing light at frequency is in the direction parallel to the applied strain, the dichroic difference AA takes a positive value on the other hand, the IR dichroism becomes negative if the transition dipoles are perpendicularly oriented. 

Cox [11] has discussed the relaxation mechanisms in this type of system in detail with experimental results and simulations to clearly demonstrate the various aspects. The most likely candidate that would account for the relaxation due to molecular dynamics is shown to be the fluctuation of the hyperfine interaction or the so called Fermi contact term. The hyperfine constant is in fact a thermal average over the different vibrational modes of the molecule. Therefore the molecular vibrations or librations will modulate the hyperfine constant. Hyperfine interaction is in general anisotropic, except in the gas or liquid state when the fast molecular tumbling averages out the anisotropy leaving the isotropic part. One can think of two separate mechanisms of relaxation depending on the modulation of either the isotropic part or the anisotropic part. 

As outlined above, the interaction of oxygen atoms with the atoms and molecules considered here will be represented by an effective two-body anisotropic interaction and the anisotropy, at the distances sampled by these experiments, is mainly attributed to the atomic open shell structure. For P2 and CH4 this amounts to assuming that the system behaves adiabatically with respect to molecular vibration while molecular rotations are averaged (a reason for using E>2 instead of H2 is to make this last assumption more plausible). 

If polymer chains are preferentially oriented, the absorbance associated with a certain molecular vibration becomes anisotropic. This anisotropy is studied with a linearly polarized incoming light the simplest representation is by dichroic ratio... 

Figure 5 presents an example of the excitation probability S (v) and the VDOS D (v) for the iron atom in the molecule Fe(TPP)(l-MeIm)(CO), as determined from measurements on a polycrystalline sample. Sharp features in both representations of the experimental data clearly identify vibrational frequencies above 100 cm, although low-frequency vibrational features are more apparent in the VDOS representation. The VDOS also provides the most convenient estimate of the mode composition factor ej, since the area of each feature directly yields the sum of values for all contributing vibrations. This avoids the need to remove the additional factors in equation (5) that contribute to the area of a feature in S (v), with the subtleties associated with determining an appropriate value for the recoilless fraction Z. However, calculation of D (v) from S (v) involves implicit assumptions that may not be valid in some situations, for example, when more than one molecular species contributes to the experimental signal or when vibrational anisotropy is significant. 

Table III.6. Molecular Zeeman parameters for ethylene oxide. For the rotational constants and the geometry of the nuclear frame, see Fig. III.8. Quoted uncertainties of g-values and susceptibility anisotropies are standard deviations from the least squares fit described in the text. They do not account for errors introduced through the neglect of vibrations. Uncertainties of derived quantities follow from standard error propagation...

The basic effects of nondegenerate vibrational motions on the rotational constants, molecular g-values, and susceptibility anisotropies may be demonstrated by the model of a diatomic molecule with its center of mass fixed in space and with the nuclear motion restricted to a plane perpendicular to the exterior magnetic field. 

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