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The quantitative
G.N.Lewis Model

G.N.Lewis' and G.E.Kimball's Model

Gilbert N. Lewis, Prof. of Physical Chemistry at U.C. Berkeley, 1912-1946, has published seminal papers about the chemical bond, and 1916, the famous book "The Atom and the Molecule". His model is now 100 years old and has changed little over time. It is a structural tool. Lewis tried in vain to give it quantitative significance.
George E. Kimball, Prof. of Physical Chemistry at Columbia University, NY, 1947-1956, is a.o. well known to the older generation of physical chemists through his co-authorship of H.Eyring, J.Walter & G.E.Kimball: "Quantum Chemistry", J.Wiley, N.Y., 1944.
1957 Kimball and G.F. Neumark [1] proposed to describe the observable three-dimensional electron density of a ground state molecule or extended structure using only s-type functions i with different expectation radii R(i). These "free clouds" have been studied for the first time during the thesis research of G.F. Neumark [2] as a simple computational tool with modest requirements of computer power. They are occupied by at most two electrons of opposite spin, each. For the valence electrons they play the roles of Lewis' electron double dots or dashes, but endowed with computable properties: One determines the sum of the kinetic zero point energies of all clouds (QM-part), Ekin, and the potential energy (classical): From the electrostatic attraction of nuclei-clouds Vne, the repulsion between clouds Vee, and between nuclei Vnn. A unique molecular structure is obtained by minimizing this sum Etot = Ekin+Vne+Vee+Vnn as a function of the R(i). Repulsions of electrons in the same cloud i are included in Vee. For other than linear molecules angles between two and dihedrals between more than two bond directions, and non centric positions of nuclei, especially of protons in X-H clouds, may be additional variables of the minimum energy problem. Pauli's exclusion principle, the Hellmann-Feynman electrostatic and the Virial theorems are valid in the optimized molecule. All this and more is described in five PhD theses, supervised by Kimball [2], and in two papers [1],[3].
[1] J.Chem.Phys.26(1957)1285
[2] G.F. Neumark,1951, CA 46(1952)1867b;
L.M. Kleiss,1952, CA 49(1955)3584e;
J.L. Birman,1952, CV; H.R. Westerman,1952, CA 49(1955)7303d; J.D. Herniter,1956, CA 52(1957)9285g [3] G.E. Kimball & E.M. Loebl,J.Chem.Educ.36(1959)233

From Wikipedia: G.E. Kimball died 1967, only 61 years old. He had left his professorship at Columbia 1956 to work full-time as a pioneer in Operations Research for Arthur D. Little, from 1961 as Vice President.-
It is a pity that Kimball's work with his Columbia doctorands is only marginally documented in the literature. This has led to a proliferation of qualitative "Kimball" and "Tangent Sphere" models of dubious quality by authors who have not understood the basic theory. The model must exclusively be used in a quantitative context.
The aim of these pages is to restore awareness for the original quantitative Kimball model applied a.o. to Lewis' structures.