Fourier transform reorientation

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... 

Subtractively normalized interfacial Fourier transform infrared spectroscopy has been used to follow the reorientations of isoquinoline molecules adsorbed at a mercury electrode. Field induced infrared absorption is a major contribution to the intensities of the vibrational band structure of aromatic organic molecules adsorbed on mercury. Adsorbed isoquinoline was observed to go through an abrupt reorientation at potentials more negative than about -0.73 V vs SCE (the actual transition potential being dependent on the bulk solution concentration) to the vertical 6,7 position. 

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

Once the diffusive reorientation contribution has been subtracted from the deconvolved time-domain response, a final Fourier transform yields the intermolecular spectrum (often referred to as the reduced spectral density). 

Fig. 42. The form of the DQ-DQ correlation experiment.68 DQ coherence is excited and reconverted using a /-encoding pulse sequence such as BABA. In the experiment, conducted under rapid MAS, t is set equal to t2 and the reorientation of a homonuclear dipolar tensor is monitored through the DQ rotor-encoded spinning sidebands that emerge from Fourier transforming in the t — t — t2 time domain.

Fluorescence depolarization measurements of aromatic residues and other probes in proteins can provide information on the amplitudes and time scales of motions in the picosecond-to-nanosecond range. As for NMR relaxation, the parameters of interest are related to time correlation functions whose decay is determined by reorientation of certain vectors associated with the probe (i.e., vectors between nuclei for NMR relaxation and transition moment vectors for fluorescence depolarization). Because the contributions of the various types of motions to the NMR relaxation rates depend on the Fourier transform of the appropriate correlation functions, it is difficult to obtain a unique result from the measurements. As described above, most experimental estimates of the time scales and magnitudes of the motions generally depend on the particular choice of model used for their interpretation. Fluorescence depolarization, although more limited in the sense that only a few protein residues (i.e., tryptophans and tyrosines) can be studied with present techniques, has the distinct advantage that the measured quantity is directly related to the decay of the correlation function. 

C, the presence of water molecules causes a decrease of T values due to their reorientation. The change however, is not large, suggesting that all water molecules in these films are bound to silk fibroin molecules with rapid rotation of the methyl groups of the Ala residues. This conclusion was also supported from the temperature dependence of the solid-echo Fourier transform spectra of silk fibroin films without immersion in methanol (Fig. 26). These spectra consist of mobile and immobile components. The fraction of the mobile component was determined as 10% in the peak area the content of the mobile component is almost the same as the water content determined by the Karl-Fischer method." In contrast, the mobile component can scarcely be observed in film prepared from silk fibroin in D2O instead of H2O (data not shown). Therefore, the mobile component is attributable to the water. This peak is still observed at —20 and —40°C, indicating bound water. 

Electron spectroscopy for chemical analysis (ESCA) [9] and Fourier transform infrared (FTIR) spectroscopy [10] with attenuated total reflectance (ATR) can also be used for routine surface studies. FTIR spectroscopy is known to have the sensitivity to determine the average orientation and reorientation of interfacial chains. But it does not directly provide information on the motion itself. The mobility of a solute in the neighborhood of an alkyl chain can be measured by fluorescence spectroscopy [11]. 

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. 

An example of typical ESR spectra, measured in the first derivative mode, is shown in Fig. 12. Just like NMR, ESR can be used to detect phase transitions and to study the orientation and dynamics of liquid crystals. The spectra shown in Fig. 12, for example, are from a study comparing the dynamics of the spin label at the end of the polymer chain and the freely dissolved spin probe in a liquid-crystalline polyether by continuous wave ESR (Fig. 12) and 2D Fourier transform ESR experiments [137]. The end label showed smaller ordering and larger reorientational rates than the dissolved spin probe. Furthermore, it was demonstrated that the advanced 2D FT ESR experiments (see below) on the end-labeled polymer chain could not be explained by the conventional Brownian model of reorientation, although this model could explain the ID spectra. This led to the development of a new motional model of a slowly relaxing local structure, which enabled differentiation between the local internal modes experienced by the end label and the collective reorganization of the polymer molecules around the label. The latter was shown to be slower by two orders of magnitude. 

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