Rotational tunneling in molecular crystals revisited: Realization of pocket states

Abstract

Pocket states have been widely used for analyzing tunneling spectra of XH3- and XH4-groups (X = C, N) in molecular and ionic crystals. The present approach consists in realizations of these pocket states based on exact solutions of the Mathieu equation, both for potentials of 2-fold and 3-fold symmetry. With Gaussians decorated by trigonometric functions quantitative values for the overlap matrix elements h, the overlap g and effective transition matrix elements heff are obtained. For potentials not too small, heff agrees very well with the exact solution hM from the Mathieu equation. Potential dependent results provide a better view on both, advantages and limitations of the pocket state formalism. For 2-fold symmetry, pocket states can be fitted to both ground state functions. A combination of the two solutions leads to an increased agreement between heff and hM. For 3-fold symmetry a more direct access to experimental data is reached, particularly for small tetrahedral molecules like CH4. The overlap g which can be deduced from observed tunnel splittings, is predicted within the pocket state formalism. Experimental data for solid CH4 II are well reproduced.