Pulse Gaussian

The conceptually simplest approach towards controlling systems by laser field is by teaching the field [188. 191. 192 and 193]. Typically, tire field is experimentally prepared as, for example, a sum of Gaussian pulses with variable height and positions. Each experiment gives an outcome which can be quantified. Consider, for example, an A + BC reaction where the possible products are AB + C and AC + B if the AB + C product is preferred one would seek to optimize the branching ratio... 

The potential energy curves (Fig. 1), the non-adiabatic coupling, transition dipole moments and other system parameters are same as those used in our previous work (18,19,23,27). The excited states 1 B(0 ) and 2 B( rio) are non-adiabatically coupled and their potential energy curves cross at R = 6.08 a.u. The ground 0 X( Eo) state is optically coupled to both the and the 2 R( nJ) states with the transition dipole moment /ioi = 0.25/xo2-The results to be presented are for the cw field e(t) = A Yll=o cos (w - u pfi)t described earlier. However, for IBr, we have shown (18) that similar selectivity and yield may be obtained using Gaussian pulses too. 

Pulse shapes other than rectangular can be used to obtain the same result. Triangular or Gaussian pulses could be used, for example. The Umit must be taken as the pulse duration becomes infinitesimally short while the amount of injected tracer remains finite. Any of these limits will correspond to a delta function input. 

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). 

A 90° Gaussian pulse is employed as an excitation pulse. In the case of a simple AX spin system, the delay t between the first, soft 90° excitation pulse and the final, hard 90° detection pulse is adjusted to correspond to the coupling constant JJ x (Fig- 7.2). If the excitation frequency corresponds to the chemical shift frequency of nucleus A, then the doublet of nucleus A will disappear and the total transfer of magnetization to nucleus X will produce an antiphase doublet (Fig. 7.3). The antiphase structure of the multiplets can be removed by employing a refocused ID COSY experiment (Hore, 1983). 

Figure 7.2 Pulse sequences for 1D COSY and 1D relayed COSY. A soft 90° Gaussian pulse serves as an excitation pulse for these experiments. (Reprinted from Mag. Reson. Chem. 29, H. Kessler et al., 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

The pulse sequence for the ID TOCSY experiment is shown in Fig. 7.6. The original experiment used a Gaussian pulse, but a half-Gaussian... 

The SELINCOR experiment is a selective ID inverse heteronuclear shift-correlation experiment i.e., ID H,C-COSYinverse experiment) (Berger, 1989). The last C pulse of the HMQC experiment is in this case substituted by a selective 90° Gaussian pulse. Thus the soft pulse is used for coherence transfer and not for excitation at the beginning of the sequence, as is usual for other pulse sequences. The BIRD pulse and the A-i delay are optimized to suppress protons bound to nuclei As is adjusted to correspond to the direct H,C couplings. The soft pulse at the end of the pulse sequence (Fig. 7.8) serves to transfer the heteronuclear double-quantum coherence into the antiphase magnetization of the protons attached to the selectively excited C nuclei. 

The pulse sequence involving excitation by a half-Gaussian pulse is shown in Fig. 7.15 (Kessler et al., 1989a). Its use was demonstrated by semiselective excitation of the NH spectral region of a hexapeptide. 

When the full width at half maximum (fwhm) of a Gaussian pulse is 20 fs, its frequency width is 740 cm as the fwhm. Frequency components Ql and fis are present in the pulse and are used to generate the vibrational coherence, where Ql — iis is equal to the vibration frequency ox... 

Figure 8.1 (a) Block diagram of the femtosecond near-infrared laser microscope system, (b) Spectrum ofthe light pulse from the Cr F laser, (c) Interferometric autocorrelation trace of SHG signal with envelope curve calculated assuming a chirp-free Gaussian pulse with 35 fs fwhm. 

An improved RAPT sequence utilizing frequency-switched Gaussian pulses (FSG-RAPT) was later proposed [68], This method also allows for the measurement of Cq values. The dependence of the FSG-RAPT enhancement on offset frequency for nuclei with different CgS has been exploited to design pulse schemes for the selective selection of nuclei with large quadrupole couplings [69-71]. 

The Gaussian pulse is truncated at 2.5% in order to keep its duration finite without introducing distortions in the profile its half-height full width is 43.5% of its total duration. The flip angle is calibrated to 270° in order to use the self-refocussing properties of this pulse [15]. 

For a system with scalar coupling(s), antiphase terms such as 2Iylf arise in the course of the pulse, as shown in fig. 2, which illustrates the creation and subsequent disappearance of this term during a 270° Gaussian pulse. 

This phenomenon is due to the self-refocussing effect [15], which leaves only a small amount of antiphase term at the end of the pulse and is necessary in extended spin systems. All pulses described in this contribution, except the rectangular, the 90° Gaussian, and the 180° Gaussian pulses, feature some degree of self-refocussing effect. 

For selective inversion or refocussing, a universal pulse is a good choice. In cases where singlets are to be inverted and where relaxation or exchange during pulses is critical, one may need to use a 180° Gaussian pulse which is the shortest selective inversion pulse available [24]. 

Fig. 8. ID ROESY-TOCSY. (a) H spectrum of the oligosaccharide 3 (5 mg/0.5 ml D2O). (b) ID ROESY spectrum of 3 acquired using the pulse sequence of fig. 7(a) with selective excitation of the H-lb proton. Duration of the 270° Gaussian pulse and the spin-lock pulse ( yBi/ K = 2.8 kHz) was 49.2 ms and 0.5 s, respectively. The spin-lock pulse was applied 333.3 Hz downfield from the H-lb resonance. The time used for the frequency change was 3 ms. (c) ID ROESY-TOCSY spectrum acquired using the pulse sequence of fig. 7(c) and the selective ROESY transfer from H-lb followed by a selective TOCSY transfer from H-4c. Parameters for the ROESY part were the same as in (b). A 49.2 ms Gaussian pulse was used at the beginning of the 29.07 ms TOCSY spin lock. 256 scans were accumulated. A partial structure of 3 is given in the inset. Solid and dotted lines represent TOCSY and ROESY...

---