Recoupling Experiments

A new pulse sequence has been described for the recoupling of heteronuclear dipolar interactions under MAS. The method is similar to the PISEMA experiment, but employs a well-defined amplitude modulation of one of the two RF fields. The technique was used for measurements of dipolar couplings in 

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Average or effective Hamiltonian theory, as introduced to NMR spectroscopy by Waugh and coworkers [55] in the late 1960s, has in all respects been the most important design tool for development of dipolar recoupling experiments (and many other important experiments). In a very simple and transparent manner, this method facilitates delineation of the impact of advanced rf irradiation schemes on the internal nuclear spin Hamiltonians. This impact is evaluated in an ordered fashion, enabling direct focus on the most important terms and, in the refinement process, the less dominant albeit still important terms in a prioritized manner. 

The REDOR experiment has formed the basis for a large number of ideal pulse type recoupling experiments, and later finite pulse variants, for heteronuclear dipolar recoupling. These include experiments such as frequency selective REDOR (FS-REDOR) [80], TEDOR (Transferred Echo DOuble Resonance) [25], and 3D variants of TEDOR [81, 82], which have found important applications, e.g., for measurement of intemuclear 13C-15N distances in biological solids. We should also mention that rotor-encoded variants of TEDOR, such as REPT, HDOR [83], and REREDOR [84], have been proposed for 1H13C dipolar recoupling under high-speed MAS conditions. 

We note that DRAMA has also formed the basis for refined variants such as the chemical-shift-compensated MELODRAMA [85], windowless DRAWS [29], and the DRAMA-XY4 [86] experiments, finding important applications for example for measurement of 13C-13C distances involving carbonyl spins. We should also note the existence of many other important pulsed homonuclear recoupling experiments such as the widely used Radio Frequency Driven Dipolar Recoupling (RFDR) [24] and Back-to-Back (BaBa) [87] experiments. 

Recently a new type of proton assisted recoupling experiments has been developed for coherence transfer where rf irradiation is taking place on all involved rf channels. This embraces the homonuclear proton assisted recoupling (PAR) [45, 140, 141] and the later resonant second-order transfer (RESORT) [142] experiments, as well as the heteronuclear proton assisted insensitive nuclei (PAIN) cross polarization [44] experiments. In PAR and PAIN, spin-lock CW irradiation is applied on both passive ( H) and active spins (13C, 15N) without matching rotary resonance conditions. In RESORT a phase alternation irradiation scheme for the passive spins is used. 

While all methods described above have been derived by analytical means, we will in this section describe the design of recoupling experiments by numerical means in an optimal control setting. The idea behind the use of alternative design strategies... 

We note that optimal control is a universal tool for experiment design and has also, in solid-state NMR spectroscopy, found additional applications in the design of homonu-clear dipolar recoupling [41], broadband rf pulses and quantum gates [71], building blocks of symmetry-based recoupling experiments [129], quadrupolar multiple-quantum MAS experiments [165], and improved pulses for quadrupolar nuclei [166]. Numerous references to further applications with regard to liquid-state NMR can be found in [72]. 

The CP can also be used for polarization transfer to MQ coherences of half-integer quadrupolar nuclei [222, 223, 228-231]. This type of transfer is mainly used in the context of MQMAS [228,229,231], although the spin-locking of MQ coherences is also featured in experiments involving homonuclear dipolar recoupling experiments [232]. 

To fulfill these needs, we recently undertook the task of developing and implementing optimal control design procedures into the SIMPSON software and described the first applications of this method to solid-state NMR spectroscopy by designing new dipolar recoupling experiments. Optimal control theory is an ideal vehicle for optimizing... 

With reference to the description of dipolar recoupling in the previous sections and our first presentation of these data in Ref. 70, we here demonstrate the applicability of optimal control theory for the design of dipolar recoupling experiments for transfer of coherence from N to which could involve typical and spin... 

Mathematica routines for symmetry-based dipolar recoupling experiments at Southhampton University, UK http //www.mhl.soton.ac.uk/. 

A theoretical treatment of the DREAM adiabatic homonuclear recoupling experiment has been given using Floquet theory. An effective Hamiltonian has been derived analytically and the time evolution of the density operator in the adiabatic limit has been described. Shape cycles have been proposed and characterized experimentally. Application to spin-pair filtering as a mixing period in a 2D correlation experiment has been explored and the experimental results have been compared to theoretical predictions and exact numerical simulations. 

Fig. 2. Pulse sequence of the rotary resonance recoupling experiment (R ) where the amplitude of u>2 matches an integer multiple of Wr. Here we have assumed a spin system with additional presence of H spins in the sample, hence the pulse sequence includes (ramped) cross polarization H— S and H decoupling during acquisition. This assumption will be made throughout as this represents the most typical circumstance. However, replacing CP by direct single-pulse Si excitation and omitting the H decoupling, the R pulse sequence and all sequences discussed in the following are also applicable to (Si, S2) spin systems in the absence of H spins.

The FDR (frequency-selective dipolar recoupling) experiment utilizes a pulse sequence (Fig. 11a) similar to the REDOR sequence. The major difference is that 7t/2 pulses are applied at the Larmor frequency of the nonobserved spin S2 instead of tt pulses as applied in REDOR. In the FDR experiment, dipolar dephasing of the Si spin depends on the chemical shielding of the S2 spin, as will be shown. Using AHT, Bennett et have calculated the evolution of the magnetization of the Si spin under the influence of the pulse sequence depicted in Fig. 11a as... 

For the following section, dealing with dipolar recoupling experiments on homonuclear spin systems, we will use an isolated pair of 1 /2 spins ( i, 2), for general purposes of illustration. The Hamiltonian of such a spin pair is derived from Eq. (1) as... 

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