Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle

Abstract

The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.

Nonexponential Solid State 1H and 19F Spin–Lattice Relaxation, Single-crystal X-ray Diffraction, and Isolated-Molecule and Cluster Electronic Structure Calculations in an Organic Solid: Coupled Methyl Group Rotation and Methoxy Group Libration in 4,4′-Dimethoxyoctafluorobiphenyl

“…The transition from the low-temperature quantum mechanical tunneling regime to the high-temperature semiclassical hopping regime is well understood. [16][17][18]20,23,25 Experimental Methods X-ray Crystallography. The sample of compound 1, 4,4'-dimethoxyoctafluorobiphenyl, (99%, mp 85-88 O C) was purchased from Acros.…”

“…The transition from the low-temperature quantum mechanical tunneling regime to the high-temperature semiclassical hopping regime is well understood. [16][17][18]20,23,25 2), c = 12.6056(4) Å, V = 1302.90(7) Å 3 . A total of 3645 reflections (R int = 0.0345) were collected (1128 unique) over θ = 6.57 to 67.99°.…”

“…Below approximately 80 K in most solids, methyl group rotation is better described by quantum mechanical tunneling. The transition from the low-temperature quantum mechanical tunneling regime to the high-temperature semiclassical hopping regime is well understood. − ,,, …”

Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation

“…At temperatures below approximately 80 K in most solids, the models for methyl group dynamics involve quantum mechanical tunneling [1][2][3][4][5][6][7][8][9] and the idea of the classical rotation of a triangle of spin-1/2 protons makes no sense. Indeed, the concepts of instantaneous position and speed have no place in the fundamental quantum mechanics of bound systems.…”

“…We note that the transition from the low-temperature quantum mechanical tunneling regime to the high-temperature classical hopping regime is well understood. 2-4, 10, 11, 13 We do note an interesting 1 H spectroscopy study in a single crystal of partially deuterated methylmalonic acid [CDCH 3 (COOD) 2 ] where, for spectra in the range 69-104 K, using a quantum-mechanical model for methyl group rotation gave a better fit of the data than the classical hopping model. 21 In the end, the tests of the validity of a model are (1) whether or not it is consistent with a wide variety of experimental results and (2) that it has a reasonably small number of adjustable parameters, all of which can be determined uniquely by the experiment.…”