Relaxation rates, intramolecular

In the following discussion, the effect of environment on the intramolecular relaxation rates 3, ke, and 4 in Cr complexes is reviewed. In addition, the variation in intermolecular transfer efficiency with environment is also discussed. 

If measurements of 4>p and/or Tp are to be used to evaluate intramolecular relaxation rates, the effect of intermolecular processes on these quantities must be assessed. In addition, the eflBciency of excitation energy transfer is of intrinsic interest, especially in connection with solid state photochemical and photophysical processes. If excitation energy is transferred to an identical center, i,e, the same species in precisely the same environment, then all of the relaxation rates k2-ks are unaffected, and no change in measureable quantities (except polarization) is expected. However, if transfer occurs between non-identical centers, then observable changes will occur. Two situations can be distinguished (36) (a) single step donor-acceptor transfer and (b) migration transfer. 

Intramolecular relaxation rates have also been determined from the linewidths of CH stretch overtones.The linewidths are about 100 cm which corresponds to a lifetime for the initially prepared states of approximately 5 x 10 s. What is not known is whether this lifetime results from dephasing or true intramolecular vibrational energy relaxation. In allyl isocyanide,for which... 

Similar considerations have been exploited for the systematic analysis of room-temperature and molecular-beam IR spectra in temis of intramolecular vibrational relaxation rates [33, 34, 92, 94] (see also chapter A3.13 V... 

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

Davis, M. J. Bottlenecks to intramolecular energy transfer and the calculation of relaxation rates, J. Chem. Phys., 83 (1985), 1016-1031... 

At ambient temperature, H, and 0 relaxation is in the extreme narrow range and dispersion curves are perfectly flat (see Fig. 9 bottom) precluding any correlation time determination. Furthermore as inter- and intramolecular contributions to proton relaxation cannot be easily separated and as the deuterium and 0 quadrupole coupling constants are not known with sufficient accuracy, there is a real problem for determining a meaningful correlation time. This problem was solved only in the early 1980s by resorting to the cross-relaxation rate which is purely intramolecular... 

The spin-dynamics method was applied to the intramolecular PRE in the case of aqueous and methyl protons in the Ni(II)(acac)2(H20)2 complex (acac = 2,4-pentanedione) (131,132). The two kinds of protons are characterized by a different angle between the principal axis of the static ZFS and the dipole-dipole axis. The ratio, p, of the proton relaxation rates in the axial (the DD principal axis coinciding with the ZFS principal axis) and the equatorial (the DD principal axis perpendicular to the ZFS principal axis) positions takes on the value of unity in the Zeeman limit and up to four in the ZFS limit. A similar spin-dynamics analysis of the NMRD data for a Mn(II) complex has also been reported (133). 

It is clear that the function U ( qint ) tmy be approximated by an expression of the form of eqn. (6). Whether a potential of Ais form, involving no explicit description of the solvent, is appropriate depends on the relative relaxation rates of the solvent motions and the macromolecular intramolecular coordinates. For the slow, conformationally most significant, glycosidic and exocyclic bond rotations of the carbohydrate it is apparent Aat averaging of solvent motions can occur easily on the time scale of these torsions. It is more ficult, however, to know how much important conformational detail is submerged by the averaging process. 

The neat chloroform proton Tj data are in substantial agreement with those of Bender and Zeidler.— Unlike chloroform relaxation, which Is almost exclusively by intramolecular dipole-dipole relaxation, relaxation has Intermolecular as well as intramolecular contributions. By means of dilution with CDCI3 one can obtain separately the intramolecular and the various intermolecular contributions.— Additional intermolecular terms must be included in the presence of polymer. Expressed in terms of relaxation rates. 

Effects of solvent mixtures can be seen in biochemical systems. Ligand binding to myoglobin in aqueous solution involves two kinetic components, one extramolecular and one intramolecular, which have been interpreted in terms of two sequential kinetic barriers. In mixed solvents and subzero temperatures, the outer barrier increases and the inner barrier splits into several components, giving rise to fast intramolecular recombination. Measurements of the corresponding solvent structural relaxation rates by frequency resolved calorimetry allows the discrimination between solvent composition and viscosity-related effects. The inner barrier and its coupling to structural relaxation appear to be independent of viscosity but change with solvent composition (Kleinert et al., 1998). 

The structural information derived from relaxation enhancement studies depends somewhat on the model chosen to describe the interaction of solvent protons with the protein molecules. For example even if the experiments indicated that the dispersion of Tfpr were essentially determined by the correlation time for rotational tumbling of the protein the tumbling of the hydration waters would not necessarily have to be restricted to that of the entire hydrated protein. Evidence was found that fast intramolecular tumbling about an axis fixed with respect to the surface of the hydrated species reduced the proton and O17 nuclear relaxation rates even in extremely stable aquocomplexes of Al3+ and other metal ions (Connick and Wiithrich (21)). The occurrence of similar... 

The internal viscosity of the macromolecule is a consequence of the intramolecular relaxation processes occurring on the deformation of the macromolecule at a finite rate. The very introduction of the internal viscosity is possible only insofar as the deformation times are large, compared with the relaxation times of the intramolecular processes. If the deformation frequencies are of the same order of magnitude as the reciprocal of the relaxation time, these relaxation processes must be taken explicitly into account and the internal viscosity force have to be written, instead of (2.26) as... 

This result is purely statistical. Replacing the distribution function by particular expressions, depending on the temperature, is the last operation When a dynamical process occurs the equilibrium distribution function (maxwellian) should be modified, and the greater the reaction rate compared to the relaxation rates of both the velocities and the intramolecular states, the greater the modification Thus it is only for low reaction rates that equilibrium distribution functions can be inserted in the formulas above, and that the reaction rate depends on the temperature, but neither on the time nor on the concentrations. 

C NMR resulting in short Ti, the Si relaxation times tend to be long. This results from a combination of two factors a lower magnetogyric ratio for Siand a longer Si-H bond length(148 A for a C-H bond), which when incorporated in equation (24) results in a tenfold lowering of the Si DD relaxation rate, / i(DD) compared with In equation (24), which describes intramolecular DD relaxation for spin-j nuclei ... 

Figure 14 Measured relative molar shifts (a) 8 = the dielectric relaxation time, and (b) 8 = the intramolecular proton magnetic relaxation rate, of aqueous alkali-metal halide solutions these are plotted on the vertical axis against negative ion radii on the horizontal axis and against positive ion radii on the third axis...

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