Low-power decoupling at high spinning frequencies in high static ﬁelds Journal of Magnetic Resonance

We demonstrate that heteronuclear decoupling using a P hase- I nverted S upercycled S equence for A tten- uation of R otary R es O nance (PISSARRO) is very efﬁcient at high spinning frequencies ( m rot = 60 kHz) and high magnetic ﬁelds (900 MHz for protons at 21 T) even with moderate radio-frequency decoupling amplitudes ( m 1 I = 15 kHz), despite the wide range of isotropic chemical shifts of the protons and the increased effect of their chemical shift anisotropy.


Introduction
Recently, a novel heteronuclear decoupling scheme dubbed PISSARRO (Phase-Inverted Supercycled Sequence for Attenuation of Rotary ResOnance) [1] was demonstrated to be efficient over a wide range of amplitudes m 1 I of the radio-frequency (rf) field applied to the protons I. Initial trials were conducted at moderate spinning frequencies (30 kHz) and medium static fields (400 MHz for protons at 9.4 T). Under these conditions, PISSARRO decoupling proved to be more effective in quenching rotary resonance effects than established methods such as XiX [2,3], TPPM [4] or SPINAL-64 [5]. In particular, these conventional decoupling methods suffer from destructive interference due to rotary resonance effects, i.e., when m 1 I % nm rot with n = 1, 2, 3. . .. The interference of spinning and decoupling leads to undesirable line-broadening over wide ranges of rf amplitudes m 1 I , which is particularly annoying at high spinning frequencies m rot > 30 kHz. For CW decoupling with m rot = 40 kHz, rotary resonance effects broaden the lines of CH and CH 2 groups unless m 1 I > 200 kHz [6] while for m rot = 70 kHz, such interference effects only disappear if m 1 I > 300 kHz [7]. Thus it would seem that conventional decoupling methods would necessitate the use of ever increasing rf amplitudes with increasing spinning frequencies. Fortunately, it has been shown recently that it is also possible to use decoupling methods such as CW, XiX, and TPPM with much lower rf amplitudes m 1 I << m rot , provided that m rot > 40 kHz [6,8,9]

Experimental
The PISSARRO sequence is composed of N pulse pairs (s p ) x (s p ) Àx followed by N pairs (s p ) y (s p ) Ày that together form a block. We shall use N = 5 throughout this work. The choice of N = 5 yields optimal performance for 20 < m rot < 60 kHz. Four such blocks are combined to form a supercycle [1]. There is only a single adjustable parameter, i.e., the pulse width s p , or, equivalently, the ratio s p /s rot , where the rotor period is s rot = 1/m rot .
Polycrystalline powders of uniformly 13 C, 15 N labelled L-alanine and 13 C a labelled L-glycine were used without further purification. All experiments were performed on a 900 MHz Bruker Avance II spectrometer with a double resonance CP/MAS probe using rotors with 1.3 mm outer diameter spinning at m rot = 60 kHz. Ramped cross polarization (CP) [10] and a simple excitation by a 90°pulse were used to record spectra of L-glycine and L-alanine, respectively. Numerical simulations of PISSARRO and CW decoupling were carried out with SPINEVOLUTION [11]. For L-alanine, a cluster comprising one 13 C a nucleus and six intramolecular protons with distances derived from the crystallographic structure as well as two additional protons from the neighborhood was considered in the simulations. The latter two protons were assumed to be on resonance, and the rotation of the methyl protons was assumed to be very fast.

Quenching interference due to rotary resonance
The performance of CW and PISSARRO decoupling at m rot = 60 kHz MAS is compared in Fig. 1 for CH and CH 2 groups. In the regime m 1 I >> m rot , CW decoupling suffers from recoupling effects due to rotary resonance m 1 I % nm rot (n = 1 and 2) [12] over a wide range of rf amplitudes. With PISSARRO, these interference effects almost completely disappear for CH and CH 3 groups (the latter are not shown in Fig. 1), even with moderate rf amplitudes m 1 I % 100 kHz. Compared to earlier observations at m rot = 30 kHz [1], the efficiency of PISSARRO with m rot = 60 kHz is particularly satisfying for CH 2 groups. The recommended ratios are s p /s rot = 0.305 for m 1 I % m rot , s p /s rot = 0.197 for m 1 I % 2m rot , and s p /s rot = 0.9 or 1.1 for higher rf amplitudes m 1 I >> 2m rot . Half and full rotor periods should be avoided, i.e., s p /s rot -k/2 with integer k. These recommendations can be followed blindly, although an empirical optimization in the vicinity of the recommended ratios s p /s rot may provide a minor improvement in decoupling efficiency. In practice, the optimal ratio s p /s rot is nearly the same at m rot = 60 and 30 kHz, which obviously makes it easy to set up PISSARRO decoupling.
As in earlier work [1], we noted for CH groups a significant 50% drop of the performance of XiX decoupling near the n = 1 rotary resonance condition, and a 30% drop near n = 2, in spite of careful optimization over a wide range of the pulse widths s p . For very high rf amplitudes, XiX and PISSARRO offer the same decoupling performance. PISSARRO reaches the best efficiency at lower rf amplitudes [1]. This is particularly important for CH 2 groups with strong dipolar proton-proton couplings, where low-amplitude decoupling might not be sufficient in certain applications (vide infra).

Low-amplitude decoupling
As shown in Figs. 1 and 2, PISSARRO decoupling is also remarkably efficient in the low-amplitude regime. For CH 3 and CH signals, despite a reduction of the rf power by a factor of 100, low-amplitude PISSARRO offered virtually the same decoupling performance as with the highest accessible amplitudes. On the other hand, the peak heights of CH 2 groups observed with m 1 I = 15 kHz are only $20% lower. Such a loss might be acceptable for heat-sensitive biological samples. We found the optimal performance of low-power ing to the optimal rf strength for low-amplitude PISSARRO for all resonances, and the latter to the best rf amplitude for CH resonances with CW decoupling. In all cases the lineshapes are affected by partially resolved 13  When using PISSARRO with low rf fields, the pulse length s p should be optimized so that the nutation angle b = 2pm 1 I s p is in the vicinity of a multiple of 2p (Fig. 3). Furthermore, in analogy to high-amplitude PISSARRO, half and full rotor periods should be avoided, i.e., s p /s rot -k/2 with integer k. However, compared to high-amplitude PISSARRO, the dips near the conditions s p /s rot = k/2 are less pronounced, which makes the sequence more robust with respect to minor misadjustments and instrumental instabilities.
To appreciate in more detail to what extent CW and PISSARRO decoupling are sensitive to resonance offsets and CSA of the irradiated spins, we carried out numerical simulations of low-amplitude decoupling. In all simulations, the spinning frequency was m rot = 60 kHz. In agreement with our experimental observations, the best performance of PISSARRO decoupling was found for m 1 I = 15 kHz. The optimal pulse length s p corresponds to a ratio s rot /s p $ 3.86, which is equivalent to a nutation angle b $ 349°. This is in good agreement with the experimental observation that the optimal nutation angles should be in the vicinity of multiples of 2p For low-amplitude CW decoupling, the best performance was found for m 1 I = 30 kHz, which roughly matches our experimental findings and relates to the so-called HORROR proton-proton recoupling condition m 1 I = nm rot with n = 1/2 [13]. Indeed, the resulting reintroduction of homonuclear couplings leads to a restoration of spin exchange in the proton network and improves the efficiency of CW decoupling in rotating solids [2,7]. Fig. 4a shows the height of the C a peak in L-alanine as a function of the offset of the proton carrier from the isotropic shift of the H a proton, simulated for two different static fields corresponding to 500 and 900 MHz. Fig. 4b shows simulations with and without CSA of the irradiated spin at 900 MHz. In contrast to PISSARRO, CW decoupling suffers from a pronounced offset dependence, even if the rf amplitude is twice as high. This leads to line-broadening and hence to a loss of peak height at high magnetic fields. The presence of amino H N protons and H b methyl protons as well as various residual homo-and heteronuclear dipolar couplings in L-alanine leads to the asymmetry in the responses of Fig. 4. In fact, because of stronger couplings between the C a carbon and its directly at-tached H a proton with the neighboring H N protons than with the methyl protons, the broadening is less pronounced when the carrier frequency is displaced towards the H N resonance. To the best of our knowledge, the implications of the offsets of neighboring protons have not been considered so far in the context of heteronuclear decoupling. A different type of off-resonance decoupling has been reported in calcium formate [14], which contains only a single proton species. In this case, the improved off-resonance decoupling was ascribed to a partial cancellation of higher-order crossterms.   3. Experimental 13 C a H signals of L-alanine obtained with low-amplitude PISSARRO decoupling with m 1 I = 15 kHz as a function of the pulse width s p . Note the presence of dips due to undesired recoupling effects at multiples of half the rotor period, i.e., when s p /s rot = k/2 with integer k.
CW decoupling suffers from second-order recoupling effects due to cross-terms between the heteronuclear dipole-dipole and anisotropic chemical shielding interactions of the irradiated spins [15]. Indeed, as demonstrated in the simulations of Fig. 4b, lowamplitude CW decoupling is significantly affected by the CSA of the irradiated spins, while the efficiency of low-amplitude PISSAR-RO decoupling remains virtually unchanged. This is yet another reason why PISSARRO decoupling should be preferred at very high static fields.

Conclusions
We have shown that the most important feature of PISSARRO decoupling, i.e., its ability to quench interference effects due to rotary resonance, improves at high spinning frequencies. Because of the compensation of resonance offsets and of the chemical shift anisotropy of the irradiated spins, low-amplitude PISSARRO decoupling is particularly efficient at fast spinning in very high static fields.