Quantum Effects of Methyl-Group Rotations in Magnetic Resonance: ESR Splittings and Linewidths

Abstract

The effects of internal rotations of methyl groups on ESR hyperfine lines are analyzed in terms of a quantum‐mechanical description of the motion. The classical description of rotational averaging is replaced by (1) spin—rotational coupling from a hyperfine operator, and (2) rotational relaxation by thermal collisions. In the absence of collisions, the effects of (1) lead to a static set of splittings whose values depend upon the relative magnitudes of the hyperfine‐versus‐tunneling frequencies. In the presence of frequent collisions, represented by a strong‐collision model, the effects of (1) lead to line broadening, the detailed nature of which also depends on the hyperfine‐versus‐tunneling frequencies. In general, results predicted from a classical treatment of the motion are obtained when the hyperfine frequency is significantly greater, while quantum effects become important for relatively larger tunneling frequencies. The results are illustrated by application to relevant experimental observations. In the Appendix, the strong‐collision relaxation theory is generalized to apply to the present case where the spin—rotational coupling connects states of different nuclear spin symmetry.