Nuclear modulation effect

More sophisticated pulse sequences have been developed to detect nuclear modulation effects. With a five-pulse sequence it is theoretically possible to obtain modulation amplitudes up to eight times greater than in a tlnee-pulse experunent, while at the same time the umnodulated component of the echo is kept close to zero. A four-pulse ESEEM experiment has been devised to greatly improve the resolution of sum-peak spectra. 

ESE envelope modulation. In the context of the present paper the nuclear modulation effect in ESE is of particular interest110, mi. Rowan et al.1 1) have shown that the amplitude of the two- and three-pulse echoes1081 does not always decay smoothly as a function of the pulse time interval r. Instead, an oscillation in the envelope of the echo associated with the hf frequencies of nuclei near the unpaired electron is observed. In systems with a large number of interacting nuclei the analysis of this modulated envelope by computer simulation has proved to be difficult in the time domain. However, it has been shown by Mims1121 that the Fourier transform of the modulation data of a three-pulse echo into the frequency domain yields a spectrum similar to that of an ENDOR spectrum. Merks and de Beer1131 have demonstrated that the display in the frequency domain has many advantages over the parameter estimation procedure in the time domain. 

Figure 5 shows the change of the ESE intensity monitored at a peak of the six-line spectrum (indicated by arrows in Fig. 4) as a function of t2. These phase relaxation curves do not follow a simple exponential function, but they are empirically expressed by an exponential of the 1.25th power of t2. The jaggedness of the relaxation curves is due to the partially-resolved nuclear modulation effect of protons. The phase relaxation rate for n-alkanes given by the slope of... 

The source of the nuclear modulation effect is an interference effect between allowed and semi-forbidden microwave transitions. 

The nuclear modulation effect was first observed by Rowan, Hahn, and Mims [16], and the theory was later developed by Mims in 1972 [17]. The origin of the nuclear modulation effect can be understood with a semi-quantitative discussion using a two-spin model system consisting of one electron spin (S = Vz) and one nuclear spin (/ = Vi). Assuming an isotropic g-matrix and an anisotropic hyperfme interaction, the spin Hamiltonian in the rotating frame can be written as... 

The nuclear Overhauser effect (NOE) is a consequence of the modulation of the dipole-dipole interactions (through space) between different nuclei and is correlated with the inverse sixth power of the internuclear distance. Experimentally, the NOE is the fractional change in intensity of one resonance when another resonance is irradiated in a double-irradiation experiment. The NOE phenomenon is intimately related to spin relaxation. The NOE varies as a function of the product of the Larmor frequency, co0, and the rotational correlation time, tc. In small molecules, tc is short relative to uo"1. In this extreme motional narrowing situation, the frequency... 

A slightly more complicated case of nuclear Overhauser effect was recently observed in our laboratory in the photoreduction of furil. Furil is considered as a weakly coupled AMX three-proton spin system and the dipolar cross relaxation involves the interplay of all three spins. The experiments were done in a light-modulation mode with a FT spectrometer and a detailed theoretical analysis of the experimental data will allow the evaluation of the various different cross-relaxation rates (138). ... 

Nuclear Overhauser effect (NOE) is another techiuque used to study the dynamics of water near a heterogeneous surface. NOE intensities are modulated by dipole-dipole interactions between protons of protein and water in the hydration layer. This interaction varies as where R is the separation between the two protons. Measurements of magnetization transfer using NOE have been used to obtain the residence time of the hydration water. The residence time of water molecules in the hydration layer immediate to the protein is not easily available by other techniques and is valuable information in quantifying the rigidity of the layer. 

The reason here is that the l N nucleus has a small magnetic moment, which is hard to drive by r.f. fields, the difficulty being compounded in the case of frozen solution samples by line broadening due to the l N nuclear quadrupolar coupling. Echo envelope modulation effects are, on the other hand, quite easy to see for nuclei with small moments. For the simple case of an I = 1/2 nucleus weakly coupled to an S = 1/2 electron, it can be shown that the modulation depth is independent of the nuclear moment and depends only on the ratio between the Zeeman field and the local field at the nucleus due to the electron.15 Breadth of the shfs line is, moreover, not a serious obstacle to detection, provided that at least one modulation cycle can be seen in the echo envelope. 

Nuclear Overhauser effect (NOE) An NMR crossrelaxation effect leading to changes in the intensity of one spin when another spin to which is dipolar coupled is perturbed. Dipolar coupling requires that the distance between the two spins is small. The NOE effect provides evidence for short distances between pairs of spins although it is also modulated by the mobility of the molecule. 

Figure 12. Cross-relaxation between different types of nuclei ( H and Cl) in NMR as the nuclear Zeeman levels cross (adapted with permissi

If in organosilicon compounds, the signal splittings caused by the coupling with the protons are removed by decoupling, then a modulation of the signal intensity occurs that is connected with the dipolar term. If the silicon relaxes by dipolar interaction with the protons only, then the signal intensity is multiplied by a factor of -1.52 from the nuclear Overhauser effect (NOE) ... 

Another recent program is CHEMICS by Sasaki, Funatsu, and co-workers. While it has much of the same capabilities as SESAMI, it has recently included an nuclear Overhauser effect (NOE) module which allows it to utilize NOE data and distance geometry methods to create 3D coordinates. This allows the program to distinguish between diastereomers (when the NOE data is adequate to do so), as well as to provide some information about conformation behavior. 

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