Two-Dimensional Hydrogen Molecule and Its Ions

The lowest four states of two-dimensional (2D) hydrogen molecule H₂ and the lowest two states of its ions H⁺₂ and H^-₂ are calculated with an applicable 2D hydrogen anion wave function properly chosen. The results are compared with their three-dimensional correspondents. It becomes possible to calculate transitions between states of clusters containing two shallow impurities in semiconductor thin films.