Gaussian-shaped pulses

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

Gaussian pulses are frequently applied as soft pulses in modern ID, 2D, and 3D NMR experiments. The power in such pulses is adjusted in milliwatts. Hard" pulses, on the other hand, are short-duration pulses (duration in microseconds), with their power adjusted in the 1-100 W range. Figures 1.15 and 1.16 illustrate schematically the excitation profiles of hard and soft pulses, respectively. Readers wishing to know more about the use of shaped pulses for frequency-selective excitation in modern NMR experiments are referred to an excellent review on the subject (Kessler et ai, 1991). 

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

Similarly to non-selective experiments, the first operation needed to perform experiments involving selective pulses is the transformation of longitudinal order (Zeeman polarization 1 ) into transverse magnetization or ly). This can be achieved by a selective excitation pulse. The first successful shaped pulse described in the literature is the Gaussian 90° pulse [1]. This analytical function has been chosen because its Fourier transform is also a Gaussian. In a first order approximation, the Fourier transform of a time-domain envelope can be considered to describe the frequency response of the shaped pulse. This amounts to say that the response of the spin system to a radio-frequency (rf) pulse is linear. An exact description of the... 

The principle of multiple selective excitation has been incorporated into a few ID and 2D experiments, the schemes of which are shown below (fig. 1). Depending on the experiment, either a DANTE pulse train (ID TOCSY [2]), frequency selective 180° pulses (ID NOE [3], ID INADEQUATE [4], ID C/H COSY [5] and 2D TOCSY-COSY [6]) or frequency selective 90° pulses (2D HMBC [11]) are applied to selectively perturb and uniquely label selected spins. Besides the DANTE pulse , composed itself of a series of non-selective rectangular pulses, Gaussian-shaped 180° and... 

The double-selective TOCSY-ROESY and TOCSY-NOESY techniques are particularly useful. They allow one to measure NOE and ROE correlations in spectra with high degree of overlap as often found in carbohydrates. In addition to the DANTE, DANTE-Z [66], and Gaussian pulses as described earlier for selective excitation, self-refocusing shaped pulses such as BURP (EBURP and UBURP) [67] have also been used for this purpose [64]. 

The CC pulse train experiments in Refs [63-65] utilize shaped pulses that use a transform-limited (TL) Gaussian pulse its phase is modulated in the frequency domain with a sine function, p ( ) = a sin( -I- c), while keeping the amplitude profile intact. The parameters a, b, and c are further varied to control molecular populations. In Reference [35], the effect of different values of these parameters on the IC dynamics of pyrazine and / -carotene is investigated and the significant role of overlapping resonances is exposed. 

Various models are used in the literature to account for the kinetics of the excitons involved in optical processes. In the simplest cases, the signal evolution n(t) can be reproduced by considering either a single exponential or multiexponential time dependences. This model is well suited for solutions or solids in which monomolecular mechanisms happen alone. Since in most transient experiments the temporal response is a convolution of a Gaussian-shaped pulse and of the intrinsic kinetics, the rate of change with time of the excited-state population decaying exponentially is given by... 

Recently, it has been shown that a Gaussian-shaped pulse can be used for selective excitation under the condition of MAS.34 This strategy has... 

It is rather tedious to move the spectral window every time we want to select a peak with a shaped pulse, but it is necessary as the center of the Gaussian excitation profile is at... 

We use common sense to find the correct power level We know we want lower power, and for Bruker that means a larger number. So we add this to 3 dB to get a power setting of 58.4 dB. As this power level corresponds to the maximum power of the Gaussian shaped pulse, we can set this power level for our shaped pulse and get a 180° rotation. This would be the starting point for the pulse calibration. 

In a pulse reactor, the effect of axial dispersion on the peak width can be minimized by introducing a dispersion column ahead of the catalyst bed to broaden the Gaussian-shaped pulses. 

Such excitations have been called shaped pulses, and a considerable effort has been expended in an attempt to optimize their shapes. A simple Gaussian shape is a considerable improvement over a rectangular pulse, but is not entirely effective in achieving an optimal peak shape. The use of more elaborate mathematical functions improves the shape of the signal, although with increasing loss of intensity. The BURP Band selective. Uniform Response, Pure phase) family utilizes an exponentially dependent sinusoidal series of Gaussians with considerable success in a variety of situations (EBURP for REBURP for 180 ). 

Figure 9.12. Absolute value frequency domain excitation profiles for (a) a rectangular pulse and (b) a Gaussian shaped pulse.

Much effort has been put into getting round both of these problems. The key feature of all of the approaches is to shape the envelope of the RF pulses i.e. not just switch it on and off abruptly, but with a smooth variation. Such pulses are called shaped pulses. The simplest of these are basically bellshaped (like a gaussian function, for example). These suppress the wiggles at large offsets and give just a smooth decay they do not, however, improve the phase properties. To attack this part of the problem requires an altogether more sophisticated approach. 

Figure 6. (A) The intensity of the CARS signal versus delay time of photon three (psec). The pulse shapes are gaussian with time constant a = 0.5 psec, and T/vr - 0- 15 psec. The frequency difference, Aa> = a>8 + - w2 — w, = 0. The decay of the CARS signal is determined by the... 

The following Check its will use the Bloch simulator module of NMR-SIM to study and analyse a number of different shaped pulses. Time Evolution, the Excitation Profile and the Rf field profile simulation are illustrated using a 90° Gaussian pulse while an adiabatic CHIRP pulse is used for the Waveform analysis. 

In Check it 5.3.1.4 the x- and y-profiles of the transverse magnetization for a 270° Gaussian pulse [5.91], a 90° half-GAUSSiAN pulse [5.92] and a 90° Gaussian Pulse Cascade G4 [5.93] are compared. Finally the H spectra of dibromopropionic acid with selective excitation of the proton at 2.85 ppm is simulated for all three shaped pulses. 

A second point to consider is the use of GAUSSIAN shaped pulses as a 180° inversion pulse. Check it 5.3.1.5 compares a 180° half-GAUSSiAN pulse with a 180° Gaussian pulse to determine whether the half-GAUSSlAN pulse is superior in this context. 

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