State-by-state assignment of the bending spectrum of acetylene at 15 000 cm−1: A case study of quantum-classical correspondence

Abstract

Techniques of quantum, semiclassical, and nonlinear classical mechanics are employed to investigate the bending dynamics of acetylene, as represented by a recently reported effective Hamiltonian [J. Chem. Phys. 109, 121 (1998)], with particular emphasis on the dynamics near 15 000 cm−1 of internal energy. At this energy, the classical mechanics associated with the bending system is profoundly different from that at low energy, where normal mode motions (trans and cis bend) dominate. Specifically, at 15 000 cm−1, classical chaos coexists with stable classical motions that are unrelated to the normal mode motions; these high-energy stable bending motions include those that we call “local bend” (one hydrogen bending) and “counter-rotation” (the two hydrogens undergoing circular motion at opposite ends of the molecule), as well as more complicated motions which can be considered hybrids of the local bend and counter-rotation motions. The vast majority of the bending quantum eigenstates near 15 000 cm−1 have nodal coordinates which coincide with the stable periodic orbits, and thus can be assigned semiclassical quantum numbers representing the number of nodes along the stable classical motions.