Semiclassical electronic eigenvalues for charge asymmetric one-electron diatomic molecules: general method and sigma states Original Research Article

The primitive semiclassical method is applied to the motion of the electron in an asymmetrically charged one-electron diatomic molecule in the fixed nucleus approximation. Using the Einstein-Keller-Brillouin rules, semiclassical approximations to the eigenvalues are found for planar motion (σ states). The general method is applied to the one-electron diatom HeH2+. The agreement between the classical approximations and the quantum eigenvalues is qualitatively good and often quantitatively good, to within a fraction of a percent. For the two stable states considered, the semiclassical results fail at the onset of chemical bonding, emphasizing the importance of tunnelling. In contrast to the charge symmetric molecules, for some non-bonding states the primitive semiclassical results are good for all internuclear separations. An interesting scaling law is derived between states of a molecule with a common ratio of quantum numbers: (2n + 1)2 En(Rn) = (2m + 1)2 Em(Rm), where (2m + 1)2 Rn = (2n + 1)2 Rm.