Flip-flop motion and spin symmetry conversion of methyl groups

It is commonly supposed that hindered methyl groups in solids undergo phonon induced rotations through +or-120. This may be symbolized (1) to (2) or (1) to (3) where (1), (2) and (3) indicate equivalent orientations of the group. The authors show both theoretically and experimentally that a second type of motion may be more important. In this motion a transition to a mixed state occurs: (1) to 2 / 3 ((2)+(3)- 1 / 2 (1)). The operator which converts (1) to the mixed state converts the latter back to (1) so the motion involves two states only and may be described as flip-flop motion. It may be distinguished experimentally from rotation because it does not modulate matrix elements between pairs of states of E symmetry. Both the rotation and flip-flop rates are measured for the 4-methyl group in 4-methyl-2,6-ditertiarybutylphenol (MDBP) between 10K and 50K. The flip-flop rate is six times greater than the rotation rate. The measurement technique combines proton spin-lattice relaxation measurements with a novel way of determining the rate of conversion between proton spin symmetry species.