Spherical Li-atom; Exchange correction



This is an artists (Peter Maisenbacher) view of a Li atom. The inside shows a Kimball Li atom with external Li(2s) cloud. In order to simulate the observed spherical symmetry the artist makes use of the fact, that we do not know into which part of the "twelve-winded sky" the outer cloud is "looking". Therefore, he provides an embedding supersphere assuming that the outer cloud moves so rapidly around the central core that its effect corresponds to the larger sphere. However, this is not giving a correct collision cross section of the atom and the necessary kinetic energy for the roaming of the outer cloud does not exist in our Universe - s-electrons do not have an observed angular momentum (Niels Bohr's model of H(1s) and ns orbits of other atoms is wrong)!
In the output of the computed Li atom, lower left, we show the correct ratio of the Li(1s2) core and outer radii. Of course, the artists imagination does not know this. His 1s2 core is far too large.
The pictures on the left correspond to L.M. Kleiss' LiH model (PhD thesis, loc.cit. 1952). She does not show a model of the Li atom used. H.R. Westerman (PhD thesis, loc.cit. 1952) computed a spherical Li atom, similar to the Mathematica plot, below right. He painstakingly constructed "orthogonal clouds", a central 1s2 cloud embedded into a tangent spherical shell of a 2s electron cloud. This scheme avoided an exchange correction, but 3D (density-)clouds are never "orthogonal" in the sense of orthogonal orbitals. In the model computed below we assume overlapping clouds, and, therefore, have to evaluate an exchange correction to obey Pauli's exclusion principle. This is very small here, because the overlap volume is so tiny. The energy of the model below is practically equal to that of Westerman, when using the same screening constant for the core.-
The spherical Li atom radius is a bit smaller than the sum R1s + 2*R2s on the left, as you can see in the two diagrams at the same scale. Comparison between these two varieties is similar to our comments in regard to LiH and Li2.- Kimballs atom with an external cloud is meant to describe the capability of Li to form molecules with one chemically bonded ligand, not to represent the atoms physical state. This is certainly spherical as shown below and contains the exchange energy.