Ernst Matthias, Geen Helen, Meier Beat H
Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland.
Solid State Nucl Magn Reson. 2006 Feb;29(1-3):2-21. doi: 10.1016/j.ssnmr.2005.08.004. Epub 2005 Oct 10.
This paper centers on a theoretical study of amplitude-modulated heteronuclear decoupling in solid-state NMR under magic-angle spinning (MAS). A spin system with a single isolated rare spin coupled to a large number of abundant spins is used in the analysis. The phase-alternating decoupling scheme (XiX decoupling) is analyzed using bimodal Floquet theory and the operator-based perturbation method developed by van Vleck. An effective Hamiltonian correct to second order is calculated for the spin system under XiX decoupling. The results of these calculations indicate that under XiX decoupling the main contribution to the residual line width comes from a cross-term between the heteronuclear and the homonuclear dipolar couplings. This is in contrast to continuous-wave decoupling, where the residual line width is dominated by the cross-term between the heteronuclear dipolar coupling and the chemical-shielding tensor of the irradiated spin. For high-power decoupling the method results in very good decoupling provided that certain unfavorable recoupling conditions, imposed by specific ratios of the amplitude modulation frequency and the MAS frequency, are avoided. For low-power decoupling, the method leads to acceptable decoupling when the pulse length corresponds to an integer multiple of a 2pi rotation and the rf-field amplitude is less than a quarter of the MAS frequency. The performance of the XiX scheme is analyzed over a range of values of the rf power, and numerical results that agree well with the most recent experimental observations are presented.
本文围绕魔角旋转（MAS）下固态核磁共振中调幅异核去耦的理论研究展开。分析中使用了一个具有单个孤立稀有自旋与大量丰富自旋耦合的自旋系统。利用双峰弗洛凯理论和范弗莱克开发的基于算符的微扰方法对相位交替去耦方案（XiX去耦）进行了分析。计算了XiX去耦下自旋系统精确到二阶的有效哈密顿量。这些计算结果表明，在XiX去耦下，对剩余线宽的主要贡献来自异核和同核偶极耦合之间的交叉项。这与连续波去耦不同，在连续波去耦中，剩余线宽由异核偶极耦合与被辐照自旋的化学屏蔽张量之间的交叉项主导。对于高功率去耦，只要避免由调幅频率和MAS频率的特定比值所施加的某些不利的再耦合条件，该方法就能实现非常好的去耦。对于低功率去耦，当脉冲长度对应于2π旋转的整数倍且射频场幅度小于MAS频率的四分之一时，该方法能实现可接受的去耦。在一系列射频功率值范围内分析了XiX方案的性能，并给出了与最新实验观测结果吻合良好的数值结果。
