Local molecular orientation relationship

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

In order to extract information on the molecular orientation distribution, the relationship between the macroscopic surface susceptibilities and the molecular hyperpolarizabilities, needs to be considered. It is usual to consider the intrinsic non-linear response of each of the molecules as independent of the other molecules so that the interfacial response is an average over the orientational distribution and scales with the molecular density (squared). Even the modification of this response due to local field... 

The most intuitively acceptable explanation for the breakdown of the theory relating IR dichroism and the uniaxial molecular orientation is that some of the molecular structural parameters, such as i and Aq, are indeed affected by dynamic orientation processes. In other words, molecules undergoing dynamic reorientation processes do not always rotate as rigid and independent entities. Changes in local molecular environments and molecular conformations induced by the macroscopic perturbations imposed on the system significantly affect the submolecular spatial relationship between the individual electric dipole transition moments arising from the vibrations of the molecular constituents and the principal orientation axis of the molecule. 

Cascading. In most cases, the distinction between second- and third-order nonlinearities is evident from the different phenomena each produce. That distinction blurs, however, when one considers the cascading of second-order effects to produce third-order nonlinear phenomena (51). In a cascaded process, the nonlinear optical field generated as a second-order response at one place combines anew with the incident field in a subsequent second-order process. Figure 2 shows a schematic of this effect at the molecular level where second-order effects in noncentrosymmetric molecules combine to yield a third-order response that may be difficult to separate from a pure third-order process. This form of cascading is complicated by the near-field relationships that appear in the interaction between molecules, but analysis of cascaded phenomena is of interest, because it provides a way to explore local fields and the correlations between orientations of dipoles in a centros5nnmetric material (52). 

The molecular basis for depolarized light scattering by model molecules that resemble polymers was described by Patterson and Carroll(l,2), who discuss intensities and linewidths for depolarized light scattering modes and their relationship to orientation fluctuations. Depolarized light scattering is in part sensihve to local chain mohons and in part sensihve to whole-chain mohons, as shown by the behavior of the VH spectrum. 

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