Overall molecular reorientation

Small-step rotational diffusion is the model universally used for characterizing the overall molecular reorientation. If the molecule is of spherical symmetry (or approximately this is generally the case for molecules of important size), a single rotational diffusion coefficient is needed and the molecular tumbling is said isotropic. According to this model, correlation functions obey a diffusion type equation and we can write... 

Dielectric relaxation measurements on some amines (aniline, N,N-di-methylaniline, benzidine. ..) display two relaxation times a longer one (of the order of 20—30.10-12 sec) attributed to overall molecular reorientation, and a shorter one (of the order of 1.10-12 sec) which may be interpreted as arising from an intramolecular process and has been attributed to nitrogen inversion 19-aa>, although this attribution is not unequivocal (rotation about the N—C bond may also contribute to the observed relaxation). 

However, there is compelling evidence that rjsiAw i)) < rjs(o) for n-hexadecane. The shear viscosity will have at least three contributions (1) a translational structural relaxation, (2) overall molecular reorientation, and (3) intramolecular conformational relaxation. Thus ysM can be represented as ... 

Solid-state NMR spectroscopy is well suited for studies of intramolecular dynamics because side chain motions can be analyzed Independent of overall molecular reorientation in crystalline samples. It is an alternative spectroscopic strategy to solution NMR because partial motional averaging of the anisotropic spin interactions occurs. Dipolar, chemical shift, and quadrupolar interactions can be used to describe the dynamics of aromatic rings of proteins and peptides. 

Overall molecular reorientations and internal motions take place in the 10 10 s time window and information about them can be accessed using relaxation rate measurements. By far the best approach is to use NMR experiments where deuterium Zeeman and quadrupolar spin-lattice relaxation times are measured on selectively deuteriated mesogens or on deuteriated probes dissolved in the mesophase. Frequency, orientation and temperature dependence of the spectral densities obtained in these relaxation studies give indications about the various motional modes and are extremely useful for testing orientational diffusion and chain dynamics models. Different deuterium relaxation experiments can be employed to extend the observable dynamic range the quadrupolar echo sequence gives spin-spin relaxation times sensitive to motions in the range s, while extremely slow motions... 

Most of the relaxation data which have been obtained on peptides has been for This nucleus has the advantage that relaxation, in the absence of paramagnetic species, is dominated by intramolecular dipole-dipole interaction with directly bonded protons. For rigid molecules, data can be interpreted in terms of rates of overall molecular reorientation. In systems where intramolecular motion is possible, one must separate contributions from overall molecular motion and internal motion to the observed relaxation rate. 

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 non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

Formally, S2 represents a decrease in the autocorrelation function caused by the motion S2=0 corresponds to completely unrestricted motion of a bond (N-H in this case), while S2=0 is expected if the bond reorientations are frozen. It was shown recently that the order parameter may be related to the statistical mechanical properties of a protein molecule [33-35] hence, changes in the NMR-derived order parameters can indicate localized contributions to overall molecular entropy. 

Up to this point only overall motion of the molecule has been considered, but often there is internal motion, in addition to overall molecular tumbling, which needs to be considered to obtain a correct expression for the spectral density function. Here we apply the model-free approach to treat internal motion where the unique information is specified by a generalized order parameter S, which is a measure of the spatial restriction of internal motion, and the effective correlation time re, which is a measure of the rate of internal motion [7, 8], The model-free approach only holds if internal motion is an order of magnitude (<0.3 ns) faster than overall reorientation and can therefore be separated from overall molecular tumbling. The spectral density has the following simple expression in the model-free formalism ... 

The molecular reorientational correlation time tends to dominate the overall correlation time of low molecular weight Gd(III) chelates, particularly in the high field region, and therefore represents a key parameter in governing their relaxivity. The effect of the increase in x on the shape and amplitude of the NMRD profiles was understood in detail early on and, as a consequence, the attempts at optimizing the relaxivity were primarily focused on slowing down the rotation by increasing the size of the... 

Plotting the logarithm of the dipole-dipole relaxation time Tj (DD) versus the reciprocal temperature therefore gives an activation energy AE for molecular reorientation, which is of the order of 8.4 kJ/ mol for most of the molecules hitherto studied. In the case of 4,4 -dimethylbiphenyl a value of 16.8 kJ/ mol was found from the temperature dependence of Ti for C-2 and C-3 (Fig. 3.21) [169], For 7) of the methyl carbon atom the Arrhenius plot is curved at lower temperatures, since the internal rotation of this group is then probably faster than the overall motion of the molecule. 

Partitioning of the various modes of reorientation—even for the simplest member of this class, a disaccharide molecule—is not an easy task. For instance, separation of rotatory diffusion from internal oscillations around the glycosidic bonds is not feasible because no ring carbon atom in the disaccharide moiety relaxes exclusively via the overall molecular motion. This problem becomes more serious if the internal motion of exocyclic substituents, such as a hydroxymethyl group, is considered in the process of dynamic modeling. 

Force field validation. In addition to ensuring that the force field reproduces results of QC calculations we have compared predictions of MD simulations using this force field with the available experimental data. Gas phase MD simulations using the quantum-chemistry based force field accurately reproduced the gas phase structure of DMNA as determined from electron diffraction studies. Liquid phase MD simulations of DMNA predicted the densities and solubility parameter as well as the activation energy and correlation times associated with molecular reorientation that are in good agreement with experimental data [34], As we will show in Section 4, comparison to structural and thermal data for the three pure crystalline polymorphs of HMX support the overall validity of our formulation and parameterization. 

Although in some cases a consistent analysis of LS or DS spectra was carried out by applying the asymptotic laws of MCT, there are strong indications that these features are not completely appropriate to quantitatively describe, for example, DS as well as LS spectra. As discussed above, this is by now well known for PC and glycerol, at least. In order to tackle the problem of different experimental probes in a more realistic fashion, several MCT approaches have been published [265,380,400]. In a two-correlator schematic model, in which the dynamics of some probe (e.g., molecular reorientation in a dielectric experiment) is coupled to the overall structural relaxation in a simple manner, a simultaneous description of LS, DS, and NS spectra was possible even below Tc. Some of the results are... 

The relaxation times have been interpreted on the basis of a large-step isotropic reorientation model. The results show that in methylamine the internal reorientations of the methyl group are fast compared to the overall molecular rotations, whereas in dimethylamine they are of comparable magnitude and in trimethylamine the overall molecular motions are the faster. (171)... 

From the experimental data we were able to determine both the intramolecular and intermolecular relaxation rates as a function of pressure and temperature. The availability of shear viscosities and self-diffusion coefficients of EHB, which were measured earlier in our laboratory, provided the opportunity to test the dependence of the experimental cross-relaxation rates on viscosity and/or diffusion of EHB. The reorientational correlation time Tc describing overall molecular motion is coupled to the rj/T term through the Debye equation, which in a modified form is ... 

Second, the positions and llneshapes of resonances arising from potentially mobile parts of the peptide (e,g, side chains) have revealed dynamical aspects of the solid-state structures of peptides. The analysis of molecular motions is simplified In the solid state by the absence of overall molecular tumbling, which modulates spin interactions and leads to complex frequency -dependent spectral responses. In particular, signals arising from aromatic ring side chains are well separated from other resonances, and may be interpreted in terms of reorientation models of these side chains. Such ring dynamics are of great importance in protein structures, and studies with model peptides can help elucidate fundamental aspects of these processes. 

Temperature-dependent interfacial structural changes at temperatures of 100 K and UHV conditions that were observed via HREELS vibrational analysis were interpreted as molecular reorientation on the surface the difference in emission signals at 300 and 100 K was also attributed to ion rearrangement at the interface, and not to ionic liquid decomposition [19]. The overall results from elastic emission and electron energy loss signals confirmed again that both cation and anions are found on the top layers irrespective of temperature, but HREELS data alone could not provide specific details on the exact reorientation [19]. 

For chains larger than propane (for which no torsional motion about (CH2)-(CH2) bonds exists) it is quite conceivable that the increasing hinderance to molecular reorientation which broadens d mode comes from torsional motions of the molecular skeleton, i.e., its overall torsional flexibility. In other words, when a flexible molecule tries to tumble it necessarily drives the motions of the torsional angles. We expect these contributions to increase with increasing... 

To the extent that molecular reorientation may be considered as approximatively isotropic the overall rotation is characterized by a single correlation time For small - or medium - size mole-... 

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