Floating Spherical Gaussian Orbitals

Arthur A. Frost mentions in his seminal first installment of FSGO [1], that he wants to extend Kimball's model with an improved representation of electronic density. The Gaussian distribution allows to approximate the density cusps at or near the nuclear positions in a molecule, thus reducing the main weakness of Kimball's model. Unfortunately, Frost had to cast his approach into the form of
wavemechanics and, hence, was forced to adopt the whole machinery of (ab initio) Quantum Chemistry, thus loosing the following of the pedagogical chemists. As basis sets the FSGO's have meanwhile been replaced by better sets in the modern arsenal of quantum chemical programs. But they have become important again for the electron Force Field method, see last paragraph.- Here are a few early publications:
[1] Arthur A. Frost, JCP 47(1967),3707,3714
[2] H.Preuss, Intern.J.Quantum Chem. 2(1968)651
[3] P.H.Blustin and J.W.Linnett, J.Chem.Soc.Faraday II 70(1974)274,327
[4] R.E.Christoffersen, Advan.Chem.Phys. 6(1972)333
[5] B.Ford, G.G.Hall and J.C.Packer, Intern.J.Quantum Chem. 4(1970)533
[6] D.F.Brailsford, G.G.Hall, N.Hemming and D.Martin, Chem.Phys.Lett. 15(1975)437


However, Arthur A. Frost was the only established chemical scientist who took Kimball's model so seriously that he worked on its improvement. This deserves admiration because he must have felt the hostility of the quantum chemical community as much as it happened to others who touched the quantitative Kimball model. Its qualitative caricatures have never been a problem because they were justly ignored by theoreticians. To be fair, I have to extend the names of scientists who seriously looked at Kimball's model:
J. P. Platt (Chicago 1961, Hdb. der Physik, 37/2, p. 258)
R. G Parr (ca. 1962 described Kimballs clouds as extraordinary functions for QC in JCP)
M.P.Teter (ca. 1990, Corning Glass Research, computed extended silica glasses with K-model)
Walter Kohn (later than 1965: looked at K-model for utilization in DFT, personal comm. of M.P.Teter)


Dr. John Beveridge, Calgary, has recently (August 2, 2013) informed me, that I have overlooked a very important and fascinating development of Prof. William A. Goddard III and his coworkers, especially Dr. Julius Su, at Caltech (among latest papers: J.Comput.Chem, 32:497-512,2011). My excuse: I just had'nt surmised that their work overlapped with any key words I was using for scanning the literature. They have invented the "electron Force Field" method which explicitly models the electrons in a molecular dynamics system using FSGO's and wavepacket dynamics. I have to study many papers from 2003 to get familiar with the new method, but am overwhelmed by the similarity of some results (and their flaws) with my Kimball work, see e.g. the ethene and diborane pages.
I thank John Beveridge for pointing my attention to this work.