Frequency-rotation domain

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Fig. 2 (a) DRAMA pulse sequence (using % = t/2 = rr/4 in the text) and a representative calculated dipolar recoupled frequency domain spectrum (reproduced from [23] with permission), (b) RFDR pulse sequence inserted as mixing block in a 2D 13C-13C chemical shift correlation experiment, along with an experimental spectrum of 13C-labeled alanine (reproduced from [24] with permission), (c) Rotational resonance inversion sequence along with an n = 3 rotational resonance differential dephasing curve for 13C-labeled alanine (reproduced from [21] with permission), (d) Double-quantum HORROR experiment along with a 2D HORROR nutation spectrum of 13C2-2,3-L-alanine (reproduced from [26] with permission)... 

I. Gryczynski, J. R. Lakowicz, and R. F. Steiner, Frequency-domain measurements of the rotational dynamics of the tyrosine groups of calmodulin, Biophys. Chem. 30, 49-59 (1988). 

The elucidation of the intramolecular dynamics of tryptophan residues became possible due to anisotropy studies with nanosecond time resolution. Two approaches have been taken direct observation of the anisotropy kinetics on the nanosecond time scale using time-resolved(28) or frequency-domain fluorometry, and studies of steady-state anisotropy for xFvarying within wide ranges (lifetime-resolved anisotropy). The latter approach involves the application of collisional quenchers, oxygen(29,71) or acrylamide.(30) The shortening of xF by the quencher decreases the mean time available for rotations of aromatic groups prior to emission. 

Even in a molecule the size of benzene the resolution achieved in this way is sufficient to investigate the dynamic behavior of individual rotational states. For this it is necessary to eliminate the Doppler broadening of the rovibronic transitions. Two methods have been applied (i) the elimination of Doppler broadening in a Doppler-free two-photon-transition and (ii) the reduction of Doppler broadening in a molecular beam. Measurements of the dynamic behavior have been performed in the frequency [3] and time domain [4]. We will briefly summarize the results from high-resolution measurements and discuss the conclusions on the intramolecular decay mechanism. Then it will be discussed how the intramolecular dynamics is influenced by the attachment of an Ar or Kr atom to the benzene molecule, leading to a weakly bound van der Waals complex. 

As any time domain function F (r), a square wave rf pulse of width tp can be approximated by a Fourier series of sines and cosines with frequencies w/2 tp (n — 1, 2, 3, 4, 5,...) [14, 7]. An rf pulse of width t thus simulates a multifrequency transmitter of frequency range A = 1/4 (p (eq. (2.14)). Accordingly, an rf pulse of 250 ps simultaneously rotates the M0 vectors of all Larmor frequencies within a range of at least A = 1 kHz. It simulates at least 1000 simultaneously stimulating transmitters, the resolution in the Fourier transform depending on the number of FID data points (eq. (2.16)), not the stimulation time t-. 

It is an essential feature of the sequence (Fig. 2.53) that only the x components of the doublet vectors 1 and 2 will be rotated by the 90° pulse in (f). The magnitudes of these components depend on the phase angle cp, which is related to the proton shift <5H. To conclude, the extent of polarization transfer (Fig. 2.53 (f-g)) is a function of proton chemical shift. After the first Fourier transformation in the t2 domain, carbon-13 signals with modulated amplitudes will be obtained when ty is varied. Chemical shifts of the attached protons are the modulation frequencies. Therefore, a second Fourier transformation in the lL domain provides maximum signals located at the chemical shifts b H and <5C of the coupling proton and carbon-13 nuclei. 

The calculated impedance I/Q is represented in Fig. 5-3. The curves in solid line correspond to the behaviour previously calculated for the rotating disk electrode (see Section 3.1) and in reference [57], for the isolated microelectrode. The different curves in dots and dashes were obtained for the microelectrode in the wake of the large electrode. The first two curves (solid line) show only a monotonic decrease with increasing frequency. The controlled microelectrode curves display, at variance, nonmonotonic evolutions with two characteristic frequency domains ... 

As will be shown later, the NMR relaxation parameters are frequency-dependent quantities. Therefore, we are interested in ways to measure these frequencies associated with the nature of the rotational motion. The Fourier transform of the TCF, which evolves in the time domain, yields a spectrum of motional frequencies in which the value of the function, J((o), at each frequency is known as the spectral density423... 

Equation 11 represents an important relationship because it describes the frequency-dependence of any relaxation process involving rotational correlation. Also, it provides a means of characterizing the frequency distribution and the intensity of the fluctuations in Hloc in the frequency domain, and hence their effectiveness in causing relaxation. 

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