Redfield pulse

A wide range of other methods for solvent suppression has been developed which may collectively be classed as tailored excitation. These rely on the application of appropriate combinations of pulses to excite protons lying outside a narrow band of frequencies while leaving those within that band (i.e. the solvent) undisturbed. Examples of these are the Redfield pulse [38], the jump-return technique [39] and binomial sequences [40]. 

The theory of nuclear spin relaxation (see monographs by Slichter [4], Abragam [5] and McConnell [6] for comprehensive presentations) is usually formulated in terms of the evolution of the density operator, cr, for the spin system under consideration from some kind of a non-equilibrium state, created normally by one or more radio-frequency pulses, to thermal equilibrium, described by Using the Bloch-Wangsness-Redfield (BWR) theory, usually appropriate for the liquid state, we can write [7, 8] ... 

It is possible to shape an excitation profile with weak pulses in such a way as to have zero excitation at a certain frequency. This was first due to Redfield [9],... 

Fig. 9.1. (A) Gaussian (a) and sine (b) excitation profiles. (B) Composite (G3) Gaussian pulse. (C) Train of soft pulses modified after the DANTE sequence to achieve selective off-resonance excitation. (D) Redfield 21412 sequence. (E) Binomial 11, 121, 1331, 14641 sequences. (F) JR (a) and compensated JR (or 1111) (b) sequences. (G) Watergate sequence. (H) Weft (Superweft) sequence. (I) Modeft sequence. (J) MLEV16 sequence. (K) NOESY sequence with trim pulse. (L) MLEV17 sequence with trim pulses. (M) Clean-TOCSY sequence.

As we saw in Section 3.4, quadrature phase detection discriminates between frequencies higher and lower than the pulse frequency, but it does not prevent foldover from frequencies higher than the Nyquist frequency. For a desired spectral width FT, there are two common methods for carrying out quadrature phase detection, as was indicated in Section 3.4. One method uses two detectors and samples each detector at FT points per second, thus acquiring 2 FT data in the form of FT complex numbers. The other (commonly called the Redfield method ) requires only a single detector and samples at 2 FT points per second while incrementing the phase of the receiver by 90° after each measurement. (In two-dimensional NMR studies, a variant of this method is usually called the rime-proportional phase incrementation, or TPPI, method.) Because these methods result in quite different treatment of folded resonances, we now consider these approaches in more detail. 

Additional features arise from spontaneous transfers of coherence particularly, but not exclusively, when the population relaxations are very fast. The coherence equations, which are effectively the Redfield relations without interchanges of population with coherence, must be solved during each time interval and probabilities worked out for the appearance of coherences other than those that are driven by the excitation pulses. This procedure is particularly important for vibrational systems, where there are often a significant number of transitions having nearly the same frequency. For example, the coherence pj,. oscillates... 

A. G. Redfield and R. K. Gupta, Pulsed-Fourier-Transform Nuclear Magnetic Resonance Spectrometer, J. S. Waugh, ed. (Academic Press, New York, 1971), pp. 81-115. 

One of the first fields where the quantum nature of the underlying system carmot be ignored, simply because there is no classical limit, is that of NMR. This is also a field where decay is directly observed in spin relaxation back to equilibrium. By giving a radio frequency pulse to an equilibrium system of spins, these are brought out of equilibrium, and, after the pulse, decay back to the equilibrium state. This free induction decay was first modeled phenomenologically by the Bloch equations, which pointed to the existence of two relaxation times, commonly called Tj and T2, but at a later stage Redfield used the density operator formalism to... 

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