We present a theoretical and numerical description of the spin dynamics associated with TRAPDOR-HMQC (T-HMQC) experiment for a ¹H (I) – ³⁵Cl (S) spin system under fast magic angle spinning (MAS). Towards this an exact effective Hamiltonian describing the system is numerically evaluated with matrix logarithm approach. The different magnitudes of the heteronuclear and pure S terms in the effective Hamiltonian allow us to suggest a truncation approximation, which is shown to be in excellent agreement with the exact time evolution. Limitations of this approximation, especially at the rotary resonance condition, are discussed. The truncated effective Hamiltonian is further employed to monitor the buildup of various coherences during TRAPDOR irradiation. We observe and explain a functional resemblance between the magnitude of different terms in the truncated effective Hamiltonian and the amplitudes of various coherences during TRAPDOR irradiation, as function of crystallite orientation. Subsequently, the dependence of the sign (phase) of the T-HMQC signal on the coherence type generated is investigated numerically and analytically. We examine the continuous creation and evolution of various coherences at arbitrary times, i.e., at and between avoided level crossings. Behavior between consecutive crossings is described analytically and reveals ‘quadrature’ evolution of pairs of coherences and coherence interconversions. The adiabatic, sudden, and intermediate regimes for T-HMQC experiments are discussed within the approach established by A. J. Vega. Equations as well as numerical simulations suggest the existence of a driving coherence which builds up between consecutive crossings and then gets distributed at crossings among other coherences. In the intermediate regime, redistribution of the driving coherence to other coherences is almost uniform such that coherences involving S-spin double-quantum terms may be efficiently produced.

我们提出了与 TRAPDOR-HMQC (T-HMQC) 实验相关的自旋动力学的理论和数值描述，用于快速魔角旋转 (MAS) 下的¹ H ( I ) – ³⁵ Cl ( S ) 自旋系统。为此，使用矩阵对数方法对描述系统的精确有效哈密顿量进行了数值评估。异核和纯 S的不同量级有效哈密顿量中的项允许我们提出截断近似，这被证明与精确时间演化非常一致。讨论了这种近似的局限性，尤其是在旋转共振条件下。截断的有效哈密顿量进一步用于监测 TRAPDOR 辐照期间各种相干性的建立。我们观察并解释了截断有效哈密顿量中不同项的大小与 TRAPDOR 辐照期间各种相干振幅之间的功能相似性，作为微晶取向的函数。随后，对 T-HMQC 信号的符号（相位）对生成的相干类型的依赖性进行了数值和分析研究。我们在任意时间检查各种相干性的不断创造和演变，即，在避免的平交道口处和之间。分析地描述了连续交叉之间的行为，并揭示了相干对和相干互变。T-HMQC 实验的绝热、突然和中间状态在 AJ Vega 建立的方法中进行了讨论。方程式和数值模拟表明存在驱动连贯性，这种连贯性在连续的交叉点之间建立，然后在交叉点处分布在其他连贯性之间。在中间状态下，驱动相干性重新分配给其他相干性几乎是均匀的，因此可以有效地产生涉及S自旋双量子项的相干性。