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, $V_3$ , at very low temperatures. For $V_3\text{\hspace{0.17em}≲\hspace{0.17em}3}{\mathrm{kcal\; mole}}^{\text{−\hspace{0.17em}1}}$ , $M_2$ is one‐quarter of its rigid‐lattice value. However, as $V_3$ increases from ∼3 kcal mole^− 1, $M_2$ does not increase monotonically to its rigid‐lattice value. $M_2$ 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 $M_2$ at helium temperatures, then it should stay reduced down to ∼10^− 2 °K.