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The quantitative
G.N.Lewis Model


  Miscellaneous: In preparation


Intermolecular and Van der Waals interactions, Dipole Moments, Vibrations

Stable Kimball molecules like BH3, AlH3, AlCl3 dimerize in the way we know from experiment. The dimers are more stable than twice the energy of monomers. This has been shown by L.M. Kleiss, diss.loc.cit. Since Kimball's clouds are assumed not to penetrate between different monomers, van der Waals interaction happens exclusively through dipole-dipole (perhaps dipole-induced dipole) interaction. Kleiss has shown, that the special dipole interaction connected to H-bond formation can be computed between NH3, H2O, HF molecules and any mixture of these. CH4 pairs do not show any interaction when touching. The numeric values are not good, since Kimballs model overestimates dipole moments by about a factor of 2, due to the unphysical charge distribution which does not model the density cusps near nuclei. For the same reason, vibrational frequencies are too high and energy
barriers for internal rotation, e.g. in ethane, too low but qualitatively correct. You can select the computation of dipole moments and vibrational frequencies/force constants in Perego's Kimball.exe and check these terse statements.

Positronium, Myonium and friends

By simply adding reduced mass one can include the motion of nuclei and their kinetic zero point energy for computing the ground state of molecules. Changing the mass of the electron allows to model molecules with heavier electrons. A special case is positronium, where the nucleus of the H atom is replaced by a positive electron. Since this has the same kinetic zero point energy as the electron with the same +/- interaction energy as for the H atom, the ground state energy is correctly determined as one half of that of the H atom, -1/4 Eh. Similarly all other short lived aggregates of matter-antimatter particles can be computed with Kimballs model (E.Schumacher, unpublished, 1961).

Excited states

Referring to pp. 23-26 of the (german) Tutorial and to Slater-type-orbitals, it is clear, that Kimball's model can correctly compute all levels of the H atom spectrum depending on the principal quantum number n alone, without fine structure, of course. More interesting is the following table, showing the excitation
He(1s,2p) <- He(1s2)


The last three columns show, that the experimental values are almost perfectly reproduced without any parametrization, except the He(1s2) screening constant which has been set to Slater's value of 0.3. Finetuning this could lower the error limits even further.
This is an indication that the chosen model for the 2p-state can be usefully applied.
Other trials for excited states have been published in Perego's diploma thesis (loc.cit.). He has been able to successfully model the UV/Vis shift of the absorption band of polymethine and polyene dyes. ES has modeled chemical shifts for NMR spectra.

Ionization Potentials, Electron Affinities, Ionic Radii

Atomic ionization potentials and electron affinity values can be similarly predicted. Another application, perhaps later more extensively demonstrated, are ionic radii. W.Heinzelmann (loc.cit. 1963) has shown that these follow the empirical values of the literature almost perfectly. This opens the way to model a large body of (ionic) solids hitherto almost entirely based on empirical data as known from mineralogy.

Mechanical Properties

With a reasonable, although crude, model of electronic structure, one can easily model mechanical properties of matter. We have e.g. successfully computed compressibilities of solids, densities and stress tensors of macroscopic matter, based on the kinetic zeropoint energy of Kimballs electron clouds imbedded into the Coulomb interactions of ionic and metal lattices. (E. Schumacher, unpublished, 1961).