Classical and semiclassical studies of the hydrogen molecule

The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is studied classically as an extension of the helium atom. Several types of orbits were found for two-fixed-centers system (hydrogen molecule) starting from some known orbits for one-fixed center one (helium atom), e.g., one dimension orbits as pendulum and axial and also Bohr and Langmuir's orbits. The classical stability and the single quantization of some one-dimensional periodic orbits are shown. These orbits are used to make a global quantization of that molecular chaotic system. We discuss the importance of those periodic orbits in the comprehension of the nature of chemical bond.