CLASSICAL AND QUANTUM PHASE SPACES FOR A MOLECULE WITH INTERNAL ROTATION

Abstract

For several years we have been exploring the use of analytical methods based on classical mechanics to understand the torsio-rotation quantum energy level structure of acetaldehyde-like molecules. We reported last $year^{1}$ on an investigation of unquantized and semi-classically quantized trajectories on rotational energy $surfaces^{2}$ to treat torsion-rotation levels well below the barrier, an energy regime in which each rotational energy surface can be considered separately. Above the barrier the adiabatic separation between rotation and torsion breaks down, leading to a situation where various rotational energy surfaces touch each other. In this energy regime the validity of a procedure based on a single rotational energy surface is, to say the least, not clear. Another problem, namely the complete destruction of all quantum numbers other than the total energy and total angular momentum (associated at the most elemental level with eigenvector labeling problems) could arise because of the existence of classically chaotic regions. Following a suggestion by W. Reinhardt, we have used classical treatments of four-dimensional phase space (two coordinates, two conjugate momenta) in the literature to construct Poincare surfaces of section for torsion-rotation energies above the barrier. Our preliminary results suggest that classically chaotic regions appear at unexpectedly low energies for the acetaldehyde torsion-rotation problem. In similar surface-of-section studies of other systems the connection between classical and quantum mechanics is accomplished by using the coherent state concept, which allows construction of a quantum mechanical phase space. We are presently attempting to carry out such a treatment for the acetaldehyde torsion-rotation system.