Angular Correlations between Molecules

Cotton-Mouton studies are discussed extensively by Beams. Measurements of the Cotton-Mouton constant in the gas phase permit determinations of the diamagnetic anisotropy of molecules when performed in condensed phase, they yield the angular correlations between molecules. ... 

For systems of such molecules in the absence of angular correlations between molecules it may be shown (85-88) that the induced part of the Kerr-effect has a step—on and step—off response function given The dipolar part of the step-off function is also given <2(t) the step-on function is much more involved (85-88). 

Figure 24. Coincidence-imaging spectroscopy of dissociative multiphoton ionization processes in NO2 with 100-fs laser pulses at 375.3 nm, using angle-angle correlations. The polar plots show, at time delays of Ofs, 350 fs, 500 fs, 1 ps, and 10 ps, the angular correlation between the ejected electron and NO photofragment when the latter is ejected parallel to the laser field polarization vector. The intensity distributions change from a forward-backward asymmetric distribution at early times to a symmetric angular distribution at later times, yielding detailed information about the molecule as it dissociates. Taken with permission from Ref. [137]...

The vector of the electromagnetic field defines a well specified direction in the laboratory frame relative to which all other vectors relevant in photodissociation can be measured. This includes the transition dipole moment, fi, the recoil velocity of the fragments, v, and the angular momentum vector of the products, j. Vector correlations in photodissociation contain a wealth of information about the symmetry of the excited electronic state as well as the dynamics of the fragmentation. Section 11.4 gives a short introduction. Finally, we elucidate in Section 11.5 the correlation between the rotational excitation of the products if the parent molecule breaks up into two diatomic fragments. 

If one corrects for the effects of attractive forces, the corrected values are much smaller than the observed values the correction overestimates the importance of attractive forces on the value of the diffusion coefficient. Although attractive forces have an effect on the diffusion coefficient at low density, they are not nearly as Important as they are in determining the value of the angular momentum correlation time. Diffusion is primarily determined by the repulsive forces between molecules, even at the lowest densities. 

Simultaneous Rotation and Fluctuation. The scalar product p(0)-(r(t) has the value /n(0) /x(/) cos 6(0 so the dipole auto-correlation function is (fdP) MO cos 6(/)>, where 6(t) is the angular displacement of the dipole axis and MO), MO the relevant magnitudes. The correlation function will separate into free rotation. If the variation of dipole moment and molecular size is relatively small, the correlation between that and the rotation may be negligible. In that case, if is independently known, may be obtained from an experimentally determined -... 

Other Contributions to the Kerr Constant. In the case of naturally anisotropic molecules, the deviation tensor df in the expansion (195) does not vanish, causing a cross-effect as well as higher-order fluctuational effects to appear, in addition to the previous angular correlation effect (I77a). The cross-effect appears owing to co-operation between molecular angular correlations-the first term of equation (195) and the translational fluctuations described by the second term of (195). We shall consider this effect in the next subsection. 

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