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Complex rotational fine structure of semi-rigid spherical, symmetric, and asymmetric top molecules can be clearly related to semi-classical trajectories on rotational energy (RE) $surfaces.^{1}$ The RE surface pictures provide ways to visualize the possibilities for complex rotational dynamics of polyatomic rotors and to interpret fine and superfine energy level patterns. An analogy can be made between RE surface dynamics and the dynamics on harmonic on or anharmonic vibrational PE $surfaces.^{2}$ The concept of a coherent or minimum uncertainty wavepacket state is one key to this analogy. The RE surface picture can be extended to treat general rovibronic energy levels which involve multiple nested RE surfaces or a multi-valued RVE $surface.^{3}$ For this an analogy can be made to the study of vibronic interactions using multi-valued PE surfaces for the Jahn-Teller or Renner effects. Some examples of scalar and tensor Coriolis interactions in $\nu_{3}$-like spherical top levels with high J provide a clear and detailed picture of how a molecule can move in various extremes of Hund's cases as well as in between these extremes. From the examples studied so far it appears that complex rovibronic Hamiltonians can have revealing ``pictures'' made of them. The pictures and semi-classical calculations based on them can elucidate molecular dynamics as well as spectra associated with rotational, vibrational, electronic, and nuclear orbital or spin angular momentum coupling effects. Pictures of RE and RVE surfaces will be shown in color using 3D stereo projection if time and equipment permit it.


1. W.G. Harter, and C.W. Patterson, J. Chem. Phys. (in press). 2. W.G. Harter, Mario Blanco, and E.J. Heller (manuscript in preparation). 3. W.G. Harter, J. Statistical Physics-Conference Proceedings on Fractal Structure in Physics (in press). $^{\ast}$ Research supported in part by NSF grant PHY-8207150.
Author Institution: Theoretical Division T-12 MS-J569, Los Alamos National Laboratory