Decoupling adiabatic

Phase incremented double adiabatic decoupling for compensation... 

Fig. 14. Arrays of H spectra from a sample of 13C ( 64%) labelled CH3I with a WURST-20 adiabatic decoupling (a), a frequency-shifted WURST-20 decoupling (b), and a Double-WURST-20 decoupling (c). For the WURST-20,/imax= 1.39 kHz and /inns = 0.88/imax = 1.22 kHz and for the Double-WURST-20,/imax = 2.78 kHz and/irms = 0.62/imax = 1.72 kHz. Reprinted from Ref. 45 with permission from Elsevier.

As with any other homonuclear decoupling, the transverse magnetization of the 13C , for example in the evolution time, is perturbed by the decoupling pulse, resulting in an additional precession virtually around the z axis. Since the adiabatic decoupling is applied during the entire evolution time of the 13C , a non-linear frequency shift rather than a phase shift appears in the spectrum. This is termed the Bloch-Siegert (frequency) shift in the NMR literature in honour of their discovery of the phenomenon. 

The BSFS by a single adiabatic decoupling can be obtained as follows. For a period of an adiabatic decoupling T, the phase accumulated by the... 

Fig. 15. Adiabatic decoupling of 13CO from 13C with a compensating pulse applied on the other side of the peaks. The compensating and decoupling pulses have the same shape but opposite frequency sweep. Due to the Bloch-Siegert effects, both the left and the right peaks are pushed towards the center while the centre peak is balanced and remains in its position. Reprinted from Ref. 47 with permission from Elsevier.

The spectrum at the bottom of Fig. 16 is obtained with the double adiabatic decoupling pulse, one located at —23.2 kHz and the other at 23.2 kHz. The BSFS is compensated and sidebands are eliminated by the compensating pulse. In addition, the amplitude of the peak is higher than that in the middle, showing a better decoupling effect. Similar results were obtained for 13C off-resonance <5 ranging from —3 to 3 kHz, where < /A/<0.13 can be treated as close to on-resonance. 

As shown in Fig. 17, the BSFS, by a double adiabatic decoupling, is not only significantly reduced compared with that by a single adiabatic decoupling but it also becomes linear as a function of the offset as predicted by Eq. (102). This linear BSFS is corrected by the application of a dilated evolution time =[l+(/lnnS/A/)2]h. 

While all that material presented in this section looks very elementary, the structure presented thus far is the dynamical system theory basis of the reaction path TS theory. If, in a complicated landscape with many dimensions, we reduce dynamics to following a winding path, the above images are enough for aU our purposes. They are also a very good basis in the first approximation of 2-DOF and even n-DOF, if we adiabatically decouple the reaction coordinate and all the other coordinates, which are called bath coordinates. 

Choice of Pulse Sequence. Many variants of these basic pulse sequences exist. HMQC sequences are often preferred in studies of low-y metal nuclei, while HSQC sequences are preferred by authors interested in N. The present authors experience is in line with these prejudices . We have found versions incorporating adiabatic decoupling of third nuclei (eg., H, N HSQC with adiabatic decoupling of P) particularly useful (Figure 19). 

Analytical expression for amplitudes and phases of adiabatic decoupling sidebands... 

Removal of sidebands from the adiabatic decoupling in the indirect dimension... 

If one aims to explore the PES this approach is rather illuminating. For dynamics calculations, however, one faces the challenge that due to the curvilinear nature of the coordinates, the kinetic energy operator takes a rather complicated form. This necessitates further approximations such as the adiabatic decoupling between the reaction coordinates and the orthogonal oscillator modes. It is probably because of this difficulty that the approach has not been fully explored for the use in HT reaction dynamics for many years. It has been only recently that interest has been revived and a number of studies focused on this approach [23-26]. 

Abrams et al. introduced a novel method for efficiently sampling in X by heating the X degrees of freedom to increase motion, but adiabatically decoupling them from the rest of the system by greatly increasing the mass to avoid perturbing the... 

---