The acetylene bending spectrum at similar to 10000 cm(-1): Quantum assignments in the midst of classical chaos

A combination of quantum mechanics, semiclassical mechanics, and nonlinear classical dynamics is used to extract the detailed internal molecular motio ns that underly the quantum eigenstates of acetylene with 16 quanta of tota l bend excitation. No potential energy surface is used; rather, the states are represented by an algebraic effective Hamiltonian that has been extensi vely refined against experimental data. The classical mechanical analysis r eveals widespread chaos, but the quantum mechanical structure is surprising ly regular. Specifically, all 81 quantum states can be assigned a pair of s emiclassical quantum numbers that reveal the underlying classical motions a ssociated with each state. These classical motions range continuously betwe en limiting-case motions that we refer to as local bend (one hydrogen bendi ng) and counter-rotation (the two hydrogens undergoing circular motions in planes perpendicular to the CC axis). The first reason that the regularity in the quantum structure was previously undetected is that the identificati on of regular nodal coordinates, if any exist, of quantum wave functions in a multidimensional (i.e., greater than two dimensions) space is generally a difficult task; our success here was made possible by the identification in a reduced two-dimensional (2D) space of two families of periodic orbits (dynamic modes) which evolve with energy. Every quantum state reflects the quantization of the two dynamic mode system. The second reason for the unde tected regularity is that the regular sequences of quantum levels that we h ave identified are interspersed among each other in energy, thus giving the appearance of a complex, unassignable spectrum.