Efficiency at high spinning frequencies of heteronuclear decoupling methods designed to quench rotary resonance

The performance of two recently developed heteronuclear decoupling schemes designed to quench rotary resonance, phase-inverted supercycled sequence for attenuation of rotary resonance (PISSARRO) and high-phase two-pulse phase modulation (high-phase TPPM), are probed at high spinning frequencies. High-phase TPPM may be useful at the n1⁄41 rotary resonance condition while PISSARRO permits efficient decoupling over a broad commonly used range of rf amplitudes, even at very high spinning frequencies. New insights into the response of spin systems to both decoupling schemes have been gained. High-phase TPPM is sensitive to the offsets of remote protons, their chemical shift anisotropies, and the relative orientations of the heteronuclear dipolar and proton chemical shift tensors. Since PISSARRO is virtually immune against such effects, the method is especially suited for very high magnetic fields. & 2011 Elsevier Inc. All rights reserved.


Introduction
Heteronuclear decoupling is of prime importance to obtain highresolution NMR spectra of organic and biological solids containing dilute spins such as carbon-13. In polycrystalline or amorphous powders studied with fast magic-angle spinning (MAS), where flipflop exchange between abundant protons slows down, the performance of continuous-wave (CW) decoupling is poor [1]. This drawback was overcome in the mid-1990s by substituting CW radiofrequency (rf) irradiation by phase-alternated irradiation [1], later called XiX [2], which offers a dramatic improvement in decoupling efficiency. This was followed by the popular two-pulse phasemodulated (TPPM) technique [3] and its variants [4][5][6][7], as well as a number of more sophisticated decoupling schemes [8][9][10].
Recent progress in MAS probe technology has opened the way to high spinning frequencies, which lead to efficient suppression of spinning sidebands at high magnetic fields and allow one to avoid line broadening in carbon-13 enriched systems due to rotational resonance (R 3 ) that occurs when an integer multiple of the spinning frequency n rot is roughly matched to the difference Dn iso between two isotropic chemical shifts (nn rot ¼Dn iso ) [11].
Fast spinning can only be achieved with rotors of a small diameter that allow one to record spectra with as little as $1 mg sample with good filling factors. However, in typical solids with strongly coupled spin networks, spinning frequencies n rot 430 kHz bring new challenges for heteronuclear decoupling because it becomes difficult to avoid rotary resonance recoupling (R 3 ). This phenomenon has the most deleterious effects when the rf amplitude is a multiple of the spinning frequency (n 1 ¼nn rot ) [12]. R 3 effects lead to a dramatic breakdown of the decoupling efficiency of standard decoupling schemes over a wide range of rf amplitudes [7,[13][14][15][16]. Until recently, it was difficult to avoid R 3 effects at very fast spinning speeds without resorting to unreasonably high rf decoupling amplitudes.
To overcome this problem, a heteronuclear decoupling scheme dubbed phase-inverted supercycled sequence for attenuation of rotary resonance (PISSARRO) was developed [14]. This method turned out to be efficient over a wide range of rf amplitudes at n rot ¼ 30 kHz and medium static fields (e.g., 400 MHz for protons at 9.4 T). Under these conditions, PISSARRO decoupling proved to be more effective in quenching rotary resonance effects in the vicinity of n ¼2 than established methods such as XiX [1,2], TPPM [3] or SPINAL-64 [17]. At high rf amplitudes, far from any R 3 conditions, PISSARRO has the same decoupling efficiency as XiX and TPPM [14]. Moreover, it has been shown that at high spinning frequencies (n rot ¼60 kHz) and high static fields (900 MHz for protons at 21T), PISSARRO decoupling remains remarkably efficient at commonly used rf amplitudes (n 1 $ 80-100 kHz) [15,18]. Indeed, at these conditions, we have practically perfect quenching of rotary resonance at the n ¼2 condition under PISSARRO decoupling while such a performance remains unattainable for standard decoupling techniques, which require much higher rf amplitudes to reach the same efficiency [15,18]. This permits a reduction of the rf power dissipation in heat-sensitive samples such as hydrated proteins. Very recently, Paul et al. [19] introduced high-phase TPPM. This method is derived from the TPPM [3]  High-phase TPPM PISSARRO  TPPM. At the same time, the flip angle b of the pulses must be proportional to the rf amplitude (as opposed to b$p in conventional TPPM) [18]. Paul et al. [19,20] demonstrated that high-phase TPPM has a better performance than PISSARRO when n 1 ¼n rot (n ¼1) for n rot ¼20 and 30 kHz.
In this work, we compare the decoupling performance of PISSARRO and high-phase TPPM at high magnetic field (B 0 ¼18.8 T, 800 MHz for 1 H) for a wide range of rf amplitudes 15rn 1 r160 kHz at two spinning frequencies n rot ¼32 and 64 kHz.
We also discuss why the spin systems respond in different ways to   high-phase TPPM and to PISSARRO irradiation. The different responses can be understood with the help of numerical simulations.

Experimental
Spectra of a polycrystalline sample of uniformly 13 C-labeled L-histidine in a partially deprotonated form [21,22] were recorded on a Bruker AVANCE-II spectrometer operating at B 0 ¼18.8 T and n rot ¼32 or 64 kHz. The PISSARRO pulse sequence [14] consists in a train of forty pulses 5 organized in four blocks, each block containing five pulse pairs with opposite phases. The recommended pulse length t for each spinning frequency n rot is t¼0.3t rot for decoupling near the n¼1 condition, t¼0.2t rot for decoupling near the n¼2 condition and t¼0.9t rot or 1.1t rot for high rf amplitudes (e.g., n 1 H b2n rot ) [14].
These pulse durations can be used blindly, although an experimental optimization in the vicinity of the recommended lengths may provide minor improvement in decoupling efficiency. For low rf amplitudes, the pulse length t should be optimized so that the nutation angle b¼2pn 1 t is in the vicinity of a multiple of 2p [15].
In analogy to high-amplitude PISSARRO, half and full rotor periods should be avoided. For high-phase TPPM, the pulse duration was experimentally optimized in the range 4ot o6 ms. Numerical simulations were carried out with SPINEVOLUTION [23], considering the 5-spin systems C a H a H b1 H b2 H N and H a C b H b1 H b2 H N of L-serine using internuclear distances derived from the crystallographic structure. These spin systems are similar to C a H a C b H b1 H b2 or C a H a H b1 H b2 H N1 H N2 H N þ of L-histidine and other common amino acids. For high-phase TPPM, the pulse duration was numerically optimized in the range 2oto8 ms.

Decoupling with high rf amplitudes
The performance of high-phase TPPM and PISSARRO at n rot ¼32 and 64 kHz is compared in Figs. 1   describing the orientation of the H a CSA tensor with respect to the principal axis system of the dipolar C a H a tensor. All other parameters are as in Fig. 5.
of rf decoupling amplitudes was tested and expressed in terms of the ratio n 1 /n rot . In agreement with earlier observations [19,20], highphase TPPM is more efficient than PISSARRO near n¼1 for both n rot ¼32 and 64 kHz. For both spinning frequencies, the best decoupling performance was observed with rf amplitudes n 1 4100 kHz. At n rot ¼32 kHz and n 1 ¼160 kHz, PISSARRO yields gain in peak height of 10% or 14% for the C b H 2 or C ar H groups, respectively. At n rot ¼64 kHz, the best decoupling is observed for both methods at n 1 ¼2n rot (n¼2).
High-phase TPPM yields C b H 2 and C ar H signals with peak heights that are 78% and 59% of those obtained with PISSSARRO.

Low-amplitude decoupling
It has been shown recently that at very high spinning frequencies, it is possible to use low-power versions of CW, XiX, TPPM and PISSARRO decoupling [7,15,16,[24][25][26]. At n rot ¼60 kHz in a magnetic field B 0 ¼21 T, PISSARRO with a very low rf amplitude n 1 ¼15 kHz yielded virtually the same decoupling performance for both CH 3 and CH signals in alanine as with the highest accessible rf amplitudes [15]. On the other hand, the peak height of CH 2 in a-glycine [27] observed with n 1 ¼15 kHz was 20% lower than could be obtained with n 1 ¼150 kHz [15]. As shown in Fig. 3, in the case of the C b H 2 signal of L-histidine recorded at n rot ¼64 kHz, high-phase TPPM and PISSARRO provide the same performance with low-amplitude decoupling of 15 kHz while at n 1 ¼10 kHz PISSARRO performs significantly better than highphase TPPM (data not shown). In analogy to a-glycine, at B 0 ¼18.8 T and n 1 ¼15 kHz, both suffer from a 20% loss of peak height compared with high-power PISSARRO decoupling at n ¼2.

Effect of second-order cross-terms between C-H dipole-dipole and 1 H CSA interactions
As mentioned above, CW decoupling copes poorly with the fact that spin diffusion slows down at high spinning frequencies [1]. For on-resonance decoupling, the resulting spectral broadening is largely due to cross-terms between the heteronuclear dipolar and proton CSA interactions [28,29]. To investigate the role of these terms under PISSARRRO and high-phase TPPM, we have simulated the carbon-13 line-shape of an isolated C-H two-spin system at n rot ¼64 kHz for two rf amplitudes n 1 ¼128 kHz (i.e., at the n¼2 condition) and n 1 ¼210 kHz. We assume that both tensors are collinear, since this assumption leads to the largest second-order splitting [28]. Indeed, as shown in Fig. 4, we observe a broadened doublet for high-phase TPPM, which is reminiscent of the secondorder splitting observed with CW decoupling [28,29]. This stands in contrast to the narrow carbon-13 line simulated for the same spin system with PISSARRO decoupling.
To probe further to what extent the dipolar/CSA cross-terms influence the efficiency of high-phase TPPM and PISSARRO decoupling at the n¼2 condition, we carried out numerical simulations for the C a H a H b1 H b2 H N and H a C b H b1 H b2 H N spin systems of L-serine. All intramolecular homo-and heteronuclear dipolar interactions were taken into account. Fig. 5 shows the carbon-13 line-shape of the C b H 2 group, simulated for different Euler angles describing the orientation of the H b1 -and H b2 -CSA tensors in the principal axis systems of the dipolar C b H b1 and C b H b2 tensors [30] for three different values of the anisotropies of the proton chemical shifts. With PISSARRO decoupling, the amplitudes are nearly independent of the Euler angles, but significant variations in peak heights appear with high-phase TPPM as a function of these Euler angles. This is due to orientation-dependent second-order broadening that occurs with high-phase TPPM. Notably, larger proton chemical shift anisotropies lead to a decrease in the peak heights with high-phase TPPM, while only marginal effects occur with PISSARRO decoupling. Fig. 6 shows simulations of the carbon-13 peak height of the C a H group as a function of the Euler angles describing the orientation of the H a -CSA tensor in the principal axis system of the dipolar C a H tensor [31,32]. Here again one observes substantial changes in peak heights for high-phase TPPM, in striking contrast with PISSARRO decoupling.
For completeness, Fig. 7 shows numerical simulations of the carbon-13 peak height of the C a H group at the n¼2 condition as a function of spinning frequency 40on rot o70 kHz at static magnetic fields corresponding to 1 H resonance frequencies between 400 and 1000 MHz for the system C a H a H b1 H b2 H N1 H N2 H N þ of L-histidine. Despite the limited number of protons, these simulations show that the efficiency of high-phase TPPM suffers from (i) the offsets of the remote protons, (ii) the chemical shift anisotropies of the protons, and (iii) the relative orientations of the CSA and dipolar tensors. By contrast, PISSARRO decoupling is practically immune to these parameters. A thorough discussion of the mechanism of quenching of rotary resonance recoupling effects by PISSARRO is presented elsewhere [18].

Conclusions
The decoupling efficiency of two recently proposed heteronuclear decoupling schemes designed to quench rotary resonance, PISSARRO and high-phase TPPM, was tested over a wide range of rf decoupling amplitudes. At very high spinning frequencies, high-phase TPPM may be useful at the n ¼1 rotary resonance condition while PISSARRO remains efficient over a broad commonly used range of rf decoupling amplitudes. Extensive numerical simulations reveal that high-phase TPPM is sensitive to the offsets of remote protons, their chemical shift anisotropies and the relative orientations of the tensors, all of which may be important at high static fields. Since PISSARRO is virtually immune to these effects, the method is especially suitable at very high magnetic fields.