Tilted rotating frame

If the condition 7S1 2> 6v is not fulfilled, then the experiment is called the off-resonance spin-lock or T p experiment in a tilted rotating frame . The experiments of this type, employing off-resonance conditions to a variable extent, have actually been proposed as a tool for varying the frequencies at which the spectral densities are being sampled [49]. The advantage of this approach is that it provides a means of estimating the rotational correlation time for macromolecules in solution. 

Evaluation of the density matrix is facilitated by transformation of the spin Hamiltonian into the rotating frame, the z -axis of which is tilted at the magic angle tilted rotating frame),... 

When the chemical shift difference is very small, it is difficult to perform the RR experiment, because of the overlap of the resonance lines of the dipolar coupled nuclei, leading to difficulty in the analysis of the RR data. In this case, a rotating resonance experiment in the tilted rotating frame [30] can be used because a much higher spinning speed can be adopted for the case of a smaller chemical shift difference in the system. 

The most efficient way to speed up spin diffusion is the so-called r.f.-driven spin-diffusion experiment [15, 19] where the chemical-shift differences are removed by r.f. irradiation. For small chemical-shift differences, r.f.-driven spin diffusion can be implemented by applying a continuous-wave r.f. field to the S-spins which can theoretically be described by a transformation into a tilted rotating frame (see Appendix B). To zeroth-order average Hamiltonian theory the chemical-shift differences are removed (fl, — fty = 0 for all spins i and j) and the dipolar-coupling frequencies are scaled by a factor s = -1/2. The scaled-down (or ideally vanishing) chemical-shift difference allows one to keep the zero-quantum line narrow by decoupling the protons. This results in fast spin-diffusion rates. Furthermore, the rate constants are now determined by the S-spin coupling network, and the proton spins need not be considered for the data analysis. 

Rotational resonance in the tilted rotating frame R2TR Application of an RF field allows selective recoupling when the chemical shift difference is small (Takegoshi K, Nomura K and Terao T (1995) Rotational resonance in the tilted rotating frame. Chemical Physics Letters 232 424—428). 

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

Taking the effective field into consideration is, particularly, important for pulses of weak amplitude co. Such pulses are selective pulses, because the rotation angle depends on the offset S2q of the NMR frequency from the rf frequency, which serves as a reference for the rotating frame. The angle 6 by which the effective field is tilted from the z-direction (Fig. 2.2.7) is given by... 

Fig. 3.10 In the rotating frame the effective field Beff is the vector sum of the reduced field AB and the B1 field. The tilt angle, 0, is defined as the angle between AB and Beff.

Each group of chemically distinct spins in a molecule may precess at slightly different frequencies due to chemical shift. Figure 2.6a shows a perspective of the rotating frame as viewed from above. Two chemically distinct sets of spins (A and B) allow the net magnetization vector M to be split into two components and Mg. When tilted from... 

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