Multiwell potentials of endohedral complexes of icosahedral symmetry

Abstract

We examine multiwell potentials that correspond to the displacements of off-center ions in complexes with icosahedral symmetry (dodecahedrons, icosahedrons, fullerenes, etc.) along symmetry directions (toward vertices, midpoints of edges, and centers of faces). An expression is derived for an effective Hamiltonian, which describes the behavior of endohedral complexes with off-center ions placed in external electric fields of arbitrary strength and orientation. We find the eigenvalues of this Hamiltonian and calculate the intensities of the lines of all possible transitions between tunneling levels. We also predict and analyze the spectra of paraelectric resonances in the absence of an external static electric field (zero-field resonances) and in the presence of such a field. Finally, we provide recommendations for detecting these effects and discuss the specific features of the effects and the possibility of studying them.