Abstract
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.
Highlights
Methyl groups are ubiquitous in materials and biopolymers as well as in many organic solvents
For rotor-rotor couplings much smaller than the rotation barrier, the 1192-quantum state problem of two tunnel-split methyl groups in the vicinity of an electron spin can be solved with moderate computational effort
The numerical solution indicates that, in this regime, the coupling changes only the tunnel splitting compared to the case with the same rotation barrier in the absence of coupling
Summary
Methyl groups are ubiquitous in materials and biopolymers as well as in many organic solvents. Such treatment is of interest for understanding electron spin decoherence due to internal methyl groups of nitroxide spin labels at low temperatures [10], as common nitroxides contain two pairs of geminal methyl groups. We show that with approximate solutions for these operators in hands, it is feasible to predict the outcome of any pulse EPR experiment on such a system by density operator formalism We illustrate this approach by computations for rotation barriers and coupling potentials that lead to tunnel frequencies in the ESEEM range. We conclude with a general assessment of the information that can and cannot be obtained by such experiments on the quantum-rotor system
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