Effective spin Hamiltonians for the quantum-rotor tunneling problem in pulse EPR.

We analyzed the spin-tunneling Hamiltonian of a quantum rotor coupled to an electron spin. Even under conditions where the rotor's nuclei are magnetically inequivalent, the symmetry between the rotor's state exchange and relabeling of nuclei holds exactly; hence, the Hamiltonian can be simplified with the help of a group theoretical approach. We demonstrated this principle on methyl-type and methane-type rotors, both in protonated and deuterated forms. We showed that the spin-tunneling problem in these cases is equivalent to solving a few spin-only problems where the tunneling interaction appears in the form of an effective spin Hamiltonian. We derived spin-operator forms of the effective Hamiltonians and discussed the application to the two-pulse electron spin echo envelope modulation experiment.