Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: the importance of level crossings.
Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: the importance of level crossings.
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DOI：
10.1063/1.4747449
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发表时间：
2012-08
期刊：
影响因子：
--
通讯作者：
K. Thurber;R. Tycko
中科院分区：
文献类型：
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作者：
K. Thurber;R. Tycko
本文对魔角自旋（MAS）条件下核磁共振中交叉效应引起的动态核极化（DNP）进行了理论计算。使用一个三自旋模型（两个电子和一个核），交叉效应DNP与MAS的电子自旋与一个大的g-各向异性可以被看作是一系列的自旋跃迁在避免交叉的能级，具有不同程度的绝热性。如果电子自旋-晶格弛豫时间T（1 e）相对于MAS旋转周期较大，则交叉效应可以作为两个单独的事件发生：（i）当一个电子自旋共振（ESR）频率与微波频率交叉时，一个电子自旋被施加的微波部分饱和，以及（ii）当两个ESR频率的差与核频率交叉时，所有三个自旋翻转，如果两个电子自旋具有不同的极化，则其将极化转移到核自旋。此外，两个ESR频率变得相等的绝热电平交叉用于维持ESR线上的非均匀饱和。我们提出的分析结果的基础上的Landau-Zener理论的绝热转变，以及数值量子力学计算的时间依赖的三自旋系统的演变。这些计算提供了深入了解交叉效应DNP对各种实验参数的依赖性，包括MAS频率，微波场强度，自旋弛豫速率，超精细和电子-电子偶极耦合强度，以及双自由基掺杂剂的性质。
We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.