Staggered alkanes

1987 Dr. Evi Honegger (Chemistry Department, Univ. of Bern) had a project for documenting additive properties in organic chemistry. She deduced them by quantum chemistry and hoped to compile a whole system of "lego"-like objects suitable for quantitatively modelling almost any organic molecule with minimal computer expenses, see Evi Honegger, 'Systematic regularities of molecular SCF energies', Theor.Chim.Acta, 73(1988)317-322. This project, unfortunately, rests unfinished.
I refer to her computed series CnH2n+2 with n = 1...10, i.e. CH4 to C10H22 (from C2H6 explicitely in staggered conformation) with Gaussian82(TM) using the model chemistry RHF/4-31G. The C10 hydrocarbon was the largest manageable with our computer resources at the time. She found an interesting linear relation (equ. (5) of loc.cit.):
E_tot(n) = -(1.1621±0.0004)-(38.9767±0.0131)*n Eh and a standard error of s=0.0003. This has been an ab initio computation with a well known basis set. It showed that a building block |CH2| exists.

This motivated me to try the same thing with Kimball's model. I calibrated the model with the experimental heats of formation (0 K) of the first 8 saturated, normal hydrocarbons and wrote the Pascal program which produces the output of the image in ethene.htm for n = 1...141(or 194). After the first few members of the CnH2n+2 series (see complete dataset), the total energy per CH2 group began to change very slowly with n as shown in the linear relationship:

E_tot(n) = -(1.1771±0.000152)-(39.2952±0.000013)*n Eh relating to the series n = 1...26, with R²=-1.000000. Interestingly, |CH2| is also an additive building block within Kimball's model. Since CnH2n+2 = n*CH2 + H2 it is amazing that Etot(H2) = -1.1771 Eh (or -1.1621 by Honegger) follows as extrapolation from the series of hydrocarbons and is nearly the perfect groundstate energy of gaseous H2. The difference between Honegger and Kimball is irrelevant and caused by my calibration procedure, making good some of the defects of the RHF computation, which neglects most of correlation energy. Take note of the fact, that Kimball produces a total energy for the series of hydrocarbons equivalent to an RHF/4-31G computation, using seconds instead of hours.

Another point is remarkable: In hydrocarbons the CH-cloud radii are within a couple of percents equal to the CC-cloud radii. This happens nowhere in molecular chemistry over the whole periodic table between two different atoms. It means that the average electronic density between C-H and C-C is almost equal and, certainly, is the main reason for the inert character of hydrocarbons and high molecular weight synthetics like polyethylene and polypropylene. Even the unmatched stability of large chains of carbon-hydrogen compounds, the concatenation ability of carbon, may be caused by these unique properties. This is a remarkable insight, coming from such a simple model.