Pulse imperfections

Phase cycling is widely employed in multipulse NMR experiments. It is also required in quadrature detection. Phase cycling is used to prevent the introduction of constant voltage generated by the electronics into the signal of the sample, to suppress artifact peaks, to correct pulse imperfections, and to select particular responses in 2D or multiple-quantum spectra. 

The phase alteration of the 180° pulse and coaddition of the resulting FIDs serves to cancel the pulse imperfections, thereby producing accurate spin-echoes (Fig. 2.2). 

Unavoidably, the efficiency of the different low-pass J filters in removing direct correlations induces attenuation of the signals associated with long-range couplings. For some molecules, the choice of the most suitable low-pass J filter may be first determined by the attenuation of those signals. Neglecting relaxation, pulse imperfections and offset effects, the... 

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

Fourier transformed to yield a ID isotropic spectrum. Alternatively, the isotropic echoes can be extracted and arranged in ID or 2D arrays, leading to ID DOR-like or 2D isotropic-anisotropic correlation spectra. The STARTMAS method is, however, quite sensitive to pulse imperfections and misadjustments, and unfortunately does not apply to spin I > 3/2 because the k ratio is negative in that case [202],... 

Generally the sensitivity of the isotope filtered/edited version of an NMR experiment will be comparable to that of the corresponding standard experiment. However, some reduction in signal intensity will occur caused by the additional pulses (due to pulse imperfections and Bi inhomogeneity) and delays (due to relaxation) of the filter elements. These losses can become significant in the case of large molecular weight complexes. 

Fig. 4. The CPMG pulse sequence. An echo is formed halfway between two consecutive K pulses. The echo amplitude (or the Fourier transform of the half-echo) provides an evaluation of T2 less affected by translational diffusion than in the simple Hahn sequence. The phase change of k pulses with respect to the initial Jt/2 pulse cancels the effect of (re) pulse imperfections.

Accurate measurements of the frequency-resolved transverse spin relaxation T2) of Rb NMR on single crystals of D-RADP-x (x = 0.20, 0.25, 0.30, 0.35) have been performed in a Bq field of 7 Tesla as a function of temperature. The probe head was placed in a He gas-flow cryostat with a temperature stability of 0.1 K. To obtain the spin echo of the Rb - 1/2 -o-+ 1/2 central transition we have used the standard (90 - fi - 180y -ti echo - (2) pulse sequence with an appropriate phase-cycling scheme to ehminate quadrature detection errors and unwanted coherences due to pulse imperfections. To avoid sparking in the He gas, the RF-field Bi had to be reduced to a level where the 7T/2-pulse length T90 equalled 3.5 ps at room temperature. 

The simplest and most popular experimental method is the well known one-dimensional (ID) NOE difference procedure [3], which is very easily implemented in any spectrometer and which can be routinely set up even by novice spectrometer operators. However, this difference method is based on subtraction of the unperturbed spectrum from the NOE-containing one, both separately recorded, and therefore the required difference information contributes only a small part of the recorded signal. Furthermore, the difference spectrum is very sensitive to subtraction errors, as well as pulse imperfections or missettings, or other spectrometer instabilities, all of which often result in prominent phase distortions or other subtraction artifacts which prevent the accurate measurement of the desired NOE values. Therefore the reliable measurement (or even detection) of enhancements below 1 % is not generally available using this difference method. 

Because of the favorable cross-peak multiplet fine-structure, the HSQC experiment offers superior spectral resolution over the HMQC (heteronuclear multiple quantum coherence) experiment [13, 14], On the other hand, the HMQC experiment works with fewer pulses and is thus less prone to pulse imperfections. The real advantage of the HSQC experiment is for measurements of samples at natural isotopic abundance and without the use of pulsed field gradients, since the HSQC experiment lends itself to purging with a spin-lock pulse. Spin-lock purging in the HMQC experiment... 

Compared to other multidimensional experiments the exchange experiments are fairly simple and, thus, easy to optimize. Experiments are robust with regard to the pulse imperfections and miscalibration. All artifacts except coherence transfer can be removed with standard phase cycling of RF pulses and receiver. The coherence transfer can be removed by appropriate pulse sequences, preferably with T-ROESY. 

Thus, from a parabolic fit to the REDOR evolution data, the second moment can be evaluated. As mentioned in Section 1, this analysis has to be restricted to the initial part of the evolution curves AS/Sq <0.3, as exemplified in Figure 2. However, the first order approximation entails a systematic imderestimation of M2, as shovm by Bertmer and Eckert. Numerous variations of the original REDOR pulse sequence have been established to adapt the technique to specific needs. To accoimt for pulse imperfections and other experimental errors, Chan and Eckert introduced compensated REDOR. In this approach, an /-channel 7r-pulse in the centre of the pulse sequence cancels the reintroduction of the 7-S dipolar couplings hence the echo amplitudes are solely attenuated by the... 

DEPT is usually performed with broadband H decoupling. It is relatively insensitive to the precise matching of delays with coupling constants, and so is much easier to use than the closely related INEPT or the JMOD (APT) (see section 3.3.2.3) sequence. DEPT, on the other hand, is more sensitive to pulse imperfections than INEPT or JMOD. 

A number of different multiple pulse sequences (8-, 24- and 52-pulse sequences) have also been introduced in order to obtain better resolution or line narrowing, i.e. to affect the first- and second-order terms in the average Hamiltonian. Since pulse imperfections are the major source of resolution limitations, these composite pulse sequences are designed with corresponding symmetry properties which allows the canceling of specific rf pulse imperfections. 

A rigorous quantum mechanical treatment shows that the process is more complex, particularly when pulse imperfections are taken into account. The basic four-pulse cycle just given (called WAHUHA after its inventors)85 has been supplanted in practice by cycles that use 8-24 pulses (e.g., MREV-8, MREV-16, BLEW-24). The cycle is repeated many times during the period T2, and observation of the magnetization is made after each cycle during one of the t periods. These multiple pulse cycles are difficult to apply but are quite effective in narrowing lines. 

Inhomogeneity of the B, rf field causes nuclei in different parts of the sample to experience values of Bt that are not what is desired. In addition, as we have seen, nuclei that are off resonance experience a Beff that has a magnitude and direction not coincident with the applied B,. Thus the effective pulses may be different from the nominal 90° and 180° pulses that are desired. The result of such pulse imperfections can be particularly troublesome if there is a cumulative effect in successive applications of pulses in a sequence. We describe two ways in which imperfections can be overcome in different situations. 

If CYCLOPS is used to eliminate artifacts in quadrature detection, this eight-step cycle must then be nested within CYCLOPS to give a 32-step cycle overall. In this simple treatment we have not taken into account the effect of pulse imperfections, which generate additional coherence pathways from coherences that were found to vanish in the preceding analyses, so that further phase cycling is often necessary. 

Ideally an uncoupled 13C shows only longitudinal magnetization, hence gives no signal. In practice, pulse imperfections give rise to a component Mry, which is cancelled by the phase cycle shown for INADEQUATE. For convenience, the coherence pathway can be divided into evolutions due to chemical shifts and coupling, as follows ... 

Figure 3.5. Schematic representation of pulse imperfections with Tr the rise time and Tp the...

Figure 2.30. The operation of the CPMG sequence in the presence of pulse imperfections. The 180° pulse is assumed to be too short by a° meaning vectors will fall above (dark grey) or below (light grey) the x-y plane following a single 180° pulse and so reduce the intensity of odd echoes. By repeating the sequence the errors are cancelled by the imperfect second 180° pulse so even echoes can be used to accurately map T2 relaxation.

The NOE enhancement will also depend on the degree of target inversion, which may well be less than complete owing to pulse imperfections and other experimental shortcomings. 

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