Semiclassical analysis of spin-lattice relaxation of a tetrahedrally coordinated four-spin-12system

A semiclassical calculation of the proton spin-lattice relaxation of a tetrahedrally coordinated four-spin-$\frac{1}{2}$ group is presented. In this calculation, the nuclear spins are treated quantum mechanically, while the random reorientations are treated classically. The relaxation mechanism considered is the thermally activated reorientation of the spin group simultaneously about its twofold and threefold symmetry axes. The reorientation rates around the twofold and threefold axes are assumed to be different. On this basis, the temperature dependence of the relaxation is calculated, and it is shown that double extrema in the $T_1$ temperature dependence can occur semiclassically as well as by tunneling.