Coherence between tunnel-split states of a methyl quantum rotor can be generated and observed in stimulated and spin-locked echo experiments, if hyperfine coupling of a nearby electron spin to the methyl protons breaks C\(_3\) symmetry and is of the same order of magnitude as the tunnel splitting. Here, we consider the case of two methyl groups bound to the same sp\(^{3}\)-hybridized atom, which is important in the context of common nitroxide spin labels. For a simple form of the rotor-rotor coupling Hamiltonian, we provide an approach that allows for density operator computations of this system with 1152 quantum states with moderate computational effort. We find that, in the regime where the ratio between rotor-rotor coupling and rotational barrier is much smaller than unity, three-pulse ESEEM and hyperfine-decoupled ESEEM depend only on the tunnel splitting, but not on this ratio. This finding may simplify the treatment of tunnel-induced electron decoherence in systems where the methyl groups are bound to sp\(^{3}\)-hybridized atoms.

如果附近的电子自旋与甲基质子的超精细耦合破坏了 C \(_3\)对称性并且相同数量级为隧道分裂。在这里，我们考虑两个甲基结合到同一个 sp \(^{3}\)的情况-杂化原子，这在常见的氮氧化物自旋标签中很重要。对于转子-转子耦合哈密顿量的简单形式，我们提供了一种方法，该方法允许该系统的密度算子计算具有 1152 个量子态，计算量适中。我们发现，在转子-转子耦合和旋转势垒之间的比率远小于统一的情况下，三脉冲 ESEEM 和超精细解耦 ESEEM 仅取决于隧道分裂，而不取决于该比率。这一发现可以简化甲基与 sp \(^{3}\)杂化原子结合的系统中隧道诱导的电子退相干的处理。