Torsional ground state splitting for tetrahedral molecules

Abstract

With improved neutron scattering and nuclear magnetic resonance techniques it has been possible to observe the splitting of the torsional ground state—commonly referred to as tunnel splitting—of a number of high symmetry molecules in various crystal fields. The tunnel splitting depends nearly exponentially on the strength of the potential experienced by a molecule as it rotates in the crystal. Tunneling spectroscopy may thus be developed into a sensitive probe for measuring rotational potentials once the relation between the potentials and the tunnel splitting is known. We have used the pocket state formalism to calculate the splitting for tetrahedral molecules in tetrahedral fields. With increasing potentials the wave function becomes smaller in the overlap region making an accurate prediction of the tunnel splittings more difficult. Our calculation provides reliable results for splittings from 200 μeV down to about 1 μeV. Detailed predictions are made for the isotope effect in solid methane and for the pressure dependence of the energy levels with special reference to (NH4+)2 SnCl6−−. Tunneling experiments under pressure are well suited for providing information about the distance dependence of intermolecular forces.