Reorientational correlation functions spectroscopy

A useful and common way of describing the reorientation dynamics of molecules in the condensed phase is to use single molecule reorientation correlation functions. These will be described later when we discuss solute molecular reorientational dynamics. Indirect experimental probes of the reorientation dynamics of molecules in neat bulk liquids include techniques such as IR, Raman, and NMR spectroscopy. More direct probes involve a variety of time-resolved methods such as dielectric relaxation, time-resolved absorption and emission spectroscopy, and the optical Kerr effect. The basic idea of time-resolved spectroscopic techniques is that a short polarized laser pulse removes a subset of molecular orientations from the equifibrium orientational distribution. The relaxation of the perturbed distribution is monitored by the absorption of a second time-delayed pulse or by the time-dependent change in the fluorescence depolarization. 

One of the most direct methods of examining reorientational motion of molecules is by far infrared absorption spectroscopy or dielectric absorption. In the absence of vibrational relaxation, the relaxation times obtained by IR and dielectric methods are equivalent. In both these techniques we obtain the correlation function, [Pg.209]

The above equations provide two alternative routes for calculating kinetic coefficients from simulations of a system at equilibrium. Averages in the above equations are ensemble averages, hence the results are ensemble-sensitive. The time correlation functions contain more information than just the kinetic coefficients. The Fourier transforms of time correlation functions can be related to experimental spectra. Nuclear magnetic resonance (NMR) measures the time correlation functions of magnetization, which is related to the reorientation of particular bonds in the polymer molecule inelastic neutron scattering experiments measure the time correlation functions of the atom positions infrared and Raman scattering spectroscopies measure the time correlation function of dipole moments and polarizabilities of the molecules. 

Most experimental techniques do not probe reorientational motions directly but measure the time-dependence of properties which themselves are sensitive to orientation. Thus in far infrared and Raman spectroscopy one measures dipole or polarizability fluctuations with respect to particular normal modes of vibration. Although the interpretation can be complicated, in cases where the fluctuations arise predominantly from rotational motions of localized groups correlation functions of the first and second Legendre polynomials, C t) and 2(1) respectively, can be retrieved from the data. 

In bulk isotropic media, experiments such as IR and NMR spectroscopy and fluorescence anisotropy decay can give information about these correlation functions or their moments.At an interface with a cylindrical symmetry, SHG and SFG spectroscopies give information about out-of-plane and in-plane reorientation, and they involve more complicated time correlation functions.Nonetheless, the simple C/(t) are still useful for a direct comparison between bulk and surface reorientation. 

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