Comparison
Method 
Etot Eh  dLiH Å  Vne Eh  Vee Eh  Vnn Eh  D0 eV 
RHF/6311G** opt  8.022475  1.5941  20.42077  3.469247  0.9959   
LiH, left model  8.02263  1.5949  20.4953  3.45468  0.9954   
LiH, right model  8.03042  1.58112  20.5058  3.44093  1.00405   
Experiment  na  1.5957  na  na  na  2.42871 
Parameters fitted
Method 
k1  k2  sigma1  sigma2  exchange correction 
LiH, left model  1.028055  1.232586  0.274383  0.299973   
LiH, right model  1.016140  0.658581  0.257422  0.229589  2.6034 mEh 
Kimball/Slater  1.0  1.0  0.3  0.3   
BeH2
We continue with "sp" type BeH2: Left image with non overlapped clouds, same size and similar energy terms as the right model:

The overlapped model has now two volumes with exchange corrections, the smaller spherical inside the lens shaped volume between the two spclouds. The lens has been exchange corrected. With Wolfram CDF Player (free plugin to your browser) you can turn the model and inspect the overlap regions:

BH3
For "sp2" like BH3 with non overlapped clouds we get a non tangent (!) model:
 and for the overlapped model we have now three exchange lenses with 8 electrons in the core region (6 excluded!) and 6 or 4 around it:

CH4
The non overlapped "sp3" like CH4 is seen from the apex on a C3 axis. It has tangent CH clouds in this parametrization. The projection into the base plane makes the CH bonds appear overlapping the core.
 The overlapped model has 6 lens shaped overlap regions and 10 electrons in the core region (8 excluded!). In the surrounding sixfold overlap 8 electrons roam about, whose cohabitation has not been allowed by Pauli! Inspect them with the Wolfram CDF Player.

For LCAOMO and Hybridization fans:
Hybridization is a tool of the computational chemists to construct symmetry adapted orthogonal orbitals from (spherical) atomic orbitals. Chemists who use "hybridization" as a qualitative visualization tool (which they shouldn't), will recognize, that the left series of Kimball model projections is similar (except for the spherical shape of the Kimball clouds) to what they construct as hybrids of atomic s and p orbitals. It is important to realize, that there is no hybridization scheme applied to Kimballs model to arrive at this similarity. This becomes obvious when you are studying the (simple!) calculations. The energy minimalization of the sum of kinetic energy and elctrostatic potential terms just leads to these results, reflecting the structure defined by the potential of the nuclear frame. It is also visible, that the equilibrium assembly of the clouds and nuclei produces an "orthogonal" set. This means that the clouds do not (or very slightly) overlap. There are, of course, no vanishing "overlap integrals" with 3D charge clouds  which penetrate each other in real space. Charge densities do not subtract! But atomic s and p orbitals are orthogonal wavefunctions and thus have vanishing overlap (= product) integrals (over all space). This does not apply to Kimballs model. The clouds are not orbitals but relate to the ψ^{2} amplitude distributions which have the same sign everywhere. I'd like to point out an important fact rarely explained in Chemistry texts and so obvious when using Kimballs model: The (crude, qualitative) LCAOMO constructions, and similarly the VBhybridization schemes used in textbooks and even in the research literature, are always shown and discussed before the compulsary antisymmetrization is done, i.e. the exclusion of Pauli forbidden multiple electron occupations. If the wavefunctions thus "constructed" (i.e. without computation!) are not checked for being orthogonal, that gives an incorrect idea about the electron density distribution in the bonding region. So, most of this sort of argumentation is worthless pseudoscience!

 