Nonlinear dynamical behavior of a hydrogen molecular ion and similar three-body Coulomb systems

We investigate the classical dynamical stability of a hydrogen molecular ion beyond the Born-Oppenheimer approximation. We study both the coplanar and collinear arrangements. Results show that invariant structures exist in phase space, including a quasiperiodic zone surrounding the antisymmetric stretching periodic orbit. Outside this zone, bound chaotic orbits exist which correspond to a hybrid motion between two types of motion, quite different from the normal quasiperiodic or chaotic motion. We extend the dynamical stability study to several other three-body Coulomb systems, similar to the hydrogen molecular ion, and present results of primitive semiclassical quantization of the quasiperiodic zone of the collinear hydrogen molecular ion. These semiclassical results suggest that the ground electronic state of the hydrogen molecular ion is stable. [S1050-2947(99)05301-9].