* WILLIAM G. HARTER* AND ALVASON ZHENHUA LI, Department of Physics, University of Arkansas, Fayetteville, AR 72701.

Quantum revivals or “super-beats” are predicted to occur when angularly localized symmetric tops states are free to evolve. Similar types of dynamics are expected to involve spherical top superfine and superhyperfine level clusters that are labeled by induced representations of octahedral or tetrahedral symmetries for XY_{4}, XY_{6}, and related molecules. A considerably more complicated set of effects are expected for the icosahedral molecule C_ 60 and its related isotopomers. An important difference for icosahedral symmetry is that its superfine splitting ratios are most-irrational (Golden-ratio) fractions that preclude perfect Poincare recurrence of quantum phase while the octahedral splitting ratios are rational.