Quantum mechanics of local mode A B A triatomic molecules

Abstract

The quantum mechanics of the vibrational stretching dynamics in ’’local mode’’ triatomic molecules is examined. A model for H2O is taken as a prototype. The quantum analysis exploits the corresponding classical analysis of the companion paper, in which an approximate but accurate Hamiltonian is derived via the techniques of nonlinear mechanics. Quantization of this Hamiltonian gives H2O vibrational energies in excellent agreement with direct quantum calculations. The corresponding overtone-combination spectrum of the H2O model is analyzed in terms of local and normal mode behavior with the aid of the twofold hindered rotor perspective provided by the Hamiltonian. The splittings in the spectrum are related to the quantum dynamics of energy transfer. A semiclassical WKB analysis is also used to relate the splittings to classical energy transfer rates and quantum dynamical tunneling and reflection probabilities.