Hydrogenic near-degeneracy

In the 1960s, this identification was based on two features of electronic structure The hydrogenic near-degeneracy (H-ND), with prototypical example, the Be ls 2s S state and the dissociation near-degeneracy (D-ND), with prototypical example, the H21 cr + state. Both cases require a simple, yet crucial, 2 X 2 CL The former depends mildly (essentially linearly) on the nuclear charge Z, and the latter depends critically on the internuclear distance R. 

The hydrogen atom and one-electron ions are the simplest systems in the sense that, having only one electron, there are no inter-electron repulsions. However, this unique property leads to degeneracies, or near-degeneracies, which are absent in all other atoms and ions. The result is that the spectrum of the hydrogen atom, although very simple in its coarse structure (Figure 1.1) is more unusual in its fine structure than those of polyelectronic atoms. For this reason we shall defer a discussion of its spectrum to the next section. 

Within each (n +1) manifold, the dependence on n (or l) can also be readily understood. The hydrogen-like tendency toward near-degeneracy of l values, but strong dependence on n, tends to persist even in many-electron atoms. As a result, the orbital energies continue to depend much more strongly on n than on l. The lowest-energy orbital of the (n + l) manifold is therefore that of lowest n (or, equivalently, highest i), e.g.,... 

Near degeneracies between the ground states for D > 5 and certain D = 3 excited intrashell states are particularly striking [47,79]. In analogy to the hydrogenic case, we find that D D + 2L identifies non-S excited states that lie close to a ground Is S state of... 

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