Nonadiabatic dynamics of the classical hydrogen molecular ion H2+

Classical dynamics of the hydrogen molecular ion H-2(+) is investigated, and electron dynamics involved in nonadiabatic (non-Bom-Oppenheimer) processes is clarified in the framework of nonlinear dynamics. When the electron motion is described by the action variables, J(xi) and J(eta), of the system with a fixed internuclear distance R, the electron dynamics coupled with the R motion is governed by nonlinear resonances between the (xi) and (eta) degrees of freedom. As a result, the system possesses an approximate constant of motion of the form nJ(xi) + mJ(eta), where the integers, n and m, depend on the initial condition of the trajectory. In consequence, the electronic degrees of freedom consists of (1) one degree of freedom conserved approximately and (2) the other degree of freedom corresponding to the nonadiabatic process. The latter degree of freedom exhibits stochastic-like time evolution, which is ascribable to the Arnol'd diffusion along the resonance lines.