Hard pulses

In the usual preparatioii-evohition-detection paradigm, neither the preparation nor the detection depend on the details of the Hamiltonian, except hi special cases. Starthig from equilibrium, a hard pulse gives a density matrix that is just proportional to F. The detector picks up only the unweighted sum of the spin operators,... 

Precisely controllable rf pulse generation is another essential component of the spectrometer. A short, high power radio frequency pulse, referred to as the B field, is used to simultaneously excite all nuclei at the T,arm or frequencies. The B field should ideally be uniform throughout the sample region and be on the order of 10 ]ls or less for the 90° pulse. The width, in Hertz, of the irradiated spectral window is equal to the reciprocal of the 360° pulse duration. This can be used to determine the limitations of the sweep width (SW) irradiated. For example, with a 90° hard pulse of 5 ]ls, one can observe a 50-kHz window a soft pulse of 50 ms irradiates a 5-Hz window. The primary requirements for rf transmitters are high power, fast switching, sharp pulses, variable power output, and accurate control of the phase. 

Figure 1.15 Time domain representation of a hard rectangular pulse and its frequency domain excitation function. The excitation profile of a hard pulse displays almost the same amplitude over the entire spectral range.

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). 

Hard pulse A pulse which is equally effective over the whole chemical shift range. See Soft pulse. 

Soft pulse Pulse designed to bring about irradiation of only a selected region of a spectrum. See Hard pulse. 

It is well-known that the excitation profile by a periodic pulse also has a pattern of multiple bands in response to the multiple effective RF fields. The DANTE sequence,26 for instance, was one of the most frequently used periodic pulse in the past for selective excitation of a narrow centre band. It is constructed by a long train of hard pulses with a certain delay between two adjacent pulses. The advantage of using the DANTE sequence over the weak, soft RF pulses relies on that it is not necessary to change the RF power level in the pulse sequence. Consequently, phase distortions and certain delays accompanied by the abrupt changes of the RF power level are avoided. 

In general, a periodic pulse is composed of multiple identical shaped pulses and each shaped pulse is in turn composed of a number of back-to-back hard pulses with same or different strengths. The periodic pulse can be described by its x and y components of the RF field, i.e.,/lx(t) and /lv(/) with a period of T and a pulsewidth r. These two components satisfy the periodic conditions o(flx(t+T)=flx(t) and fly(t + T) =/jv(/), respectively. 

Fig. 14.4 Pulse sequences used for the experiments described in this chapter. A [ N HJ-HSQC with water flip back and PFGs. The shaped pulse on the proton channel is a sine-shaped, 1.5 ms soft pulse all other pulses are hard pulses. Gradients are applied as square or sine-shaped pulses. The sign of the last gradient is reversed for anti-echo selection together with the sign of phase 6. B CPMG sequence. C bpPFGLED sequence. The delay T denotes the diffusion delay. Typically, r is set to 1 ms, T to 50-100 ms and Te to 1.2 ms.

This contribution will describe the manipulation of spin multiplets as a whole, and the word selective - or soft - will be used for multiplet-selective pulses, in contrast to band-selective, which refers to a broader bandwidth which may affect several spins, and to transition selective when only one line is affected. The discussion will be based on proton spectra, but all aspects are similar for other nuclei. Soft pulses use lower amplitudes and much longer irradiation times than non-selective hard pulses. Typical durations for soft pulses are of the order of 1 to 500 ms with a peak amplitude... 

Selective pulses are of finite durations and contrarily to infinitely short hard pulses, transverse and longitudinal relaxation occur during the pulses. 

Figure 5 Simulated NMR spectra for a nucleus with spin 5/2 (such as Mg) in a single crystal, in the case of (A) and (B) populations corresponding to thermal equilibrium, with non-selective excitation ( hard pulse) in (A) and CT-selective excitation ( soft pulse) in (B). For (C) and (D) populations achieved after saturation of STs, with non-selective excitation (C) and CT-selective excitation (D). For (E) and (F) Populations achieved after complete inversion of the satellite transitions (in the order first, inversion of STl and ST4 and then inversion of ST2 and ST3), with non-selective excitation (E) and CT-selective excitation (F).The numbers at the right-hand side of the spectra in (B), (D) and (F) indicate the corresponding enhancement factors of the CT resonance.

Fig. 1. Pulse sequence for the X/Y H PFG-HSQC experiment as employed for 19F/13C correlation spectroscopy in Ref. 21. 90° and 180° hard pulses are denoted by solid and open bars, respectively groups of two solid and one open bars denote 90° 0 — 180° +9o — 90° pulse sandwiches that serve as composite 180° pulses. 2 are delays of length 1 /(2 Jx,v), and r is a short delay of the same length as the gradient pulse (typically 1 ms). Phase cycles are as in the standard HSQC experiment, and the ratio of gradient pulse strengths is set to G2/G1 = Yy/Yx- Decoupling is employed using WALTZ-16 ( H) and GARP (Y) pulse trains.

Fig. 8.2. Some of the most common 2D pulse sequences that can be employed using a proper choice of parameters to record 2D spectra of paramagnetic molecules (A) NOESY, (B) ROESY, (C) COSY, (D) ISECR COSY, (E) zero-quantum (double quantum) COSY, (F) TOCSY, (G) HMQC, (H) HSQC. Sequences (A), (B) and (F) are also used to obtain EXSY spectra. SL indicates a soft spin-lock sequence, while MLEV17 indicates a train of spin-locking hard pulses that optimizes the development of J/j coupling. In the reverse heteronuclear experiment (G) the upper and lower levels refer to H and heteronucleus, respectively. The phase cycles are not indicated. For clarity of discussion, all initial pulses can be thought to be applied along the y axis, in such a way that the coherence after the first 90° pulse is always along x. ...

There are more advanced experiments such as DEPT (Chapter 7) that observe 13 C and use the decoupler to supply high power, short duration ( hard ) pulses at the XH frequency. This requires full power from the decoupler, but the parameters dpwr andpll7 are avoided for these pulses. Setting decoupler power to the maximum might lead to disastrous mistakes because the decoupler can only deliver full power for short ( 10 pis) periods of time without burning up the decoupler, the probe, and the sample. Instead, the parameters pp (Varian) and p3 (Bruker) are used for the 90° pulse width for decoupler hard pulses and pplvl (Varian) and pl2 (Bruker) indicate the power level for short-duration high-power decoupler pulses. 

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