PERIODIC-ORBITS OF THE HYDROGEN MOLECULAR ION AND THEIR QUANTIZATION

In a classical study of the hydrogen molecular ion beyond the Born-Opp enheimer approximation (BOA), we have found that segments of trajector ies resemble that of the Born-Oppenheimer approximation periodic orbit s; The importance of this fact to the classical understanding of chemi cal bonding leads us to a systematic study of the periodic orbits of t he planar hydrogen molecular ion within the BOA. Besides introducing a classification scheme for periodic orbits, we discuss the convergence properties of families of periodic orbits and their bifurcation patte rns according to their types. Semiclassical calculations of the densit y of states based on these periodic orbits yield results in agreement with the exact quantum eigenvalues of the hydrogen molecular ion syste m.