Classical, semi-classical, and quantum dynamics of uni-axial and multi-axial floppy rotors

The theory of frame transformation relations connecting body oriented angular (BOA) momentum states and lab weakly coupled (LWC) momentum states have been extended from rotor-electron to rotor dimer systems. Coupling schemes are analyzed for weak and strong cases of correlation between lab and two different rotor body frames. It is shown that the frame transformation relation is a purely quantum effect at low angular momentum but approaches a classical limit for high J. In addition, a symmetry analysis of the frame transformation is compared to eigensolutions of model coupling Hamiltonian.;We investigate how a single rotor quantum state results from merging two coupled rotors and consider consequences of a frame transformation relation between the constituent rotors. We also outline a procedure to determine the range of coupling constants for which K quantum numbers are good and relate Body vs. Lab states by introducing the LWC and BOA bases for rotor-rotor dimer systems.;A theory for transformation between Body Oriented Angular (BOA) states and Lab Weakly Coupled (LWC) states was introduced by Chang and Fano for treating the interacting electron-diatomic rotor model of molecular hydrogen Rydberg ions. We have extended this model in order investigate more general rotor-excitation dynamics involving three frames (or four if the Lab is counted) that may be understood using classical, semi-classical and quantum approaches. It is found that a third frame emerges when the coupling between rotors becomes very strong. The theory was extended to include the dynamics of symmetry effects in connecting LWC and BOA limits. Symmetry relations also help to understand the energy level and state frame transformation effects due to a "locking" or correlation of two rotors. These includes unitary tableau schemes for finding the rovibronic statistical weights for the nuclear spin states and permutational properties of the individual nuclei in either the LWC or BOA limit as well as in between where most states exist.;Moreover, we consider a classical and semi-classical approach to understand the dynamics of rigid coupling. For instant, molecules carrying more or less freely turning rotors have classical and quantum rotational properties that are more difficult to calculate and visualize than those of a semi-rigid molecule. To help unravel the many dynamical and spectral possibilities, a semi-classical analysis involving rotational energy surfaces RES may be used to elucidate both classical and quantum modeling. We consider the simplest models of single uniaxial rotor, such as a methyl group, attached to a larger rigid or semi-rigid molecule, and compare (RES) geometry to eigenvalue solutions.