Molecular reorientational dynamics

Probe site dynamics on a time scale dictated by properties of the nucleus in question typically nanoseconds (exchange dynamics, molecular reorientational correlation times) is available. 

The dielectric medium is normally taken to have a constant value of e, but may for some purposes also be taken to depend for example on the distance from M. For dynamical phenomena it can also be allowed to be frequency dependent i.e. the response of the solvent is different for a fast reaction, such as an electronic transition, and a slow reaction, such as a molecular reorientation. 

Fig. 6 Dynamic molecular motions can gate DNA-mediated charge transport. Two time constants (5 and 75 ps) are observed for hole transfer from photoexcited ethidium, tethered and intercalated near the end of a 14-base pair DNA duplex, to a base analog, 7-deazaguanine, in DNA. The 5 ps time constant, which is independent of distance between 10-17 A, is due to direct hole transfer, while the 75 ps time constant corresponds to reorientation of the ethidium before hole transfer. Adapted from [96]... 

As seen from the above theoretical developments, accessing geometrical (and stereochemical) information implies at least an estimation of the dynamical part of the various relaxation parameters. The latter is represented by spectral densities which rest on the calculation of the Fourier transform of auto- or cross-correlation functions. These calculations require necessarily a model for describing molecular reorientation... 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

The dynamic simulation of crystals at equilibrium is quite feasible [64] and gives information on molecular detail like the anisotropy of librations, or the frequency of molecular reorientations. Second-order phase transitions are also within scope. 

The highly detailed results obtained for the neat ionic liquid [BMIM][PFg] clearly demonstrate the potential of this method for determination of molecular reorientational dynamics in ionic Hquids. Further studies should combine the results for the reorientational dynamics with viscosity data in order to compare experimental correlation times with correlation times calculated from hydrodynamic models (cf [14]). It should thus be possible to draw conclusions about the intermolecular structure and interactions in ionic liquids and about the molecular basis of specific properties of ionic liquids. 

Antony, J. H., Mertens, D., Dolle, A., Wasserscheid, R, and Carper, W. R., Molecular reorientational dynamics of the neat ionic liquid l-butyl-3-methyl-imidazolium hexafluorophosphate by measurement of C nuclear magnetic relaxation data., Chem. Phys. Chem., 4, 588-594, 2003. 

The population and reorientational dynamics are not indicated in the figure, but may be also derived from the pump-probe measurements. The population lifetime Ti in the first excited level can be inferred from the excited state absorption monitoring (lie v = I v = 2 transition. The molecular reorientation becomes experimentally accessible, introducing polarization resolution in the probing step. For known structural and population dynamics the temporal evolution of the width of the observed spectral hole also provides information on the dephasing time T2 of the vibrational transition (63). 

Lastly, we consider the diffusive contribution to the signal. Since this portion of the signal arises from molecular reorientation, it should be completely depolarized unless these diffusive reorientational dynamics also have a significant DID component. The orientational decay will be made up of exponential components, the number of which depends on the molecular symmetry and the relationship between the principal axes of the diffusion and polarizability tensors of the molecules (8). If these tensors share no axes, the orientational decay will be composed of a sum of five exponentials. If the tensors share one axis, the decay will be composed of three exponentials. If the tensors share all three axes, the decay will be composed of two exponentials. If the molecule is further a symmetric top, then reorientation about the axis of symmetry cannot be observed, and the decay will be composed of a single exponential. In principle, considerably more information is available when the principal axes of the diffusion and polarizability tensors are not shared however, in practice it is virtually impossible to find a unique fit to the sum of five exponentials, some of which may have very small amplitudes. In the remainder of this chapter we will therefore concentrate on symmetric-top liquids. 

Rothschild WG, Rosasco GJ, Livingston RC. Dynamics of molecular reorientational motion and vibrational relaxation in liquids. Chloroform. J Chem Phys 1975 62 1253-1268. 

II. Selected Methods to Study Molecular Reorientation Dynamics... 

II. SELECTED METHODS TO STUDY MOLECULAR REORIENTATION DYNAMICS... 

The dynamic window of a given NMR technique is in many cases rather narrow, but combining several techniques allows one to almost completely cover the glass transition time scale. Figure 6 shows time windows of the major NMR techniques, as applied to the study of molecular reorientation dynamics, in the most often utilized case of the 2H nucleus. Two important reference frequencies exist The Larmor frequency determines the sensitivity of spin-lattice relaxation experiments, while the coupling constant 8q determines the time window of line-shape experiments. 2H NMR, as well as 31P and 13C NMR, in most cases determines single-particle reorientational dynamics. This is an important difference from DS and LS, which access collective molecular properties. 

The NMR frequencies at two times separated by the time tm, and thus the corresponding orientations [cf. Eq. (15)] are correlated via cosine functions. The correlation function CSin(fm tp), where the cosine functions are replaced by sine functions, may also be accessible modifying pulse lengths and pulse phases in an appropriate way. This is possible for both CSA and Q interactions. Rotational jumps of the molecules during the mixing time tm lead to 0)>(0) / tm), and hence to a decay of CCOSjSin(fm tp). Therefore, these correlation functions provide access to the details of the molecular reorientation dynamics. 

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