Proton second moment of an isolated tunneling methyl group

Abstract

In an attempt to find an explanation for the reduced proton second moments in methyl-bearing compounds at low temperatures, the rather simple model of an isolated methyl group has been considered. By taking account of the quantization of the molecular motion, an energy-level scheme is obtained for the nuclear spin system which is different from that obtained if the molecular motion is treated as a classical rotation. The intramolecular methyl contribution, M 2, to the second moment of the proton spectrum is calculated from the energy-level scheme for various barrier heights, V3, at very low temperatures. For V3≲3 kcal mole-1, M2 is one-quarter of its rigid-lattice value. However, as V3 increases from ∼3 kcal mole-1, M2 does not increase monotonically to its rigid-lattice value. M2 decreases to about one-fifth of the rigid-lattice value in the region of 3.5 kcal mole-1 before increasing to its full value for barriers, probably in the region of 5 kcal mole-1. If the barriers are assumed to be temperature independent, it follows that if the energy-level scheme predicts a reduced M2 at helium temperatures, then it should stay reduced down to ∼10-2 °K.