On the crossing of electronic energy levels of diatomic molecules at the large-D limit

Analytical and numerical results are presented for the intersection of electronic energies of the same space symmetry for electrons in the field of two Coulomb centers in D-dimensions. We discuss why such crossings are allowed and may be less ‘‘exceptional’’ than one could think because even for a diatomic molecule there is more than one parameter in the electronic Hamiltonian. For a one electron diatomic molecule at the large-D limit, the electronic energies are shown analytically to diverge quadratically from the point of their intersection. The one electron two Coulomb centers problem allows a separation of variables even when the charges on the two centers are not equal. The case of two electrons, where their Coulombic repulsion precludes an exact symmetry, is therefore treated in the large-D limit. It is then found that, in addition to the quadratic intersection, there is also a curve crossing where the energies diverge linearly. © 2001 American Institute of Physics. @DOI: 10.1063/1.1372181#