Van der Waals forces

This post is a further thought to an earlier post on sphere packing.

It may mean something important...... 

"As a geometist I remain intrigued by the attached diagram which I drew a long while ago. I endeavored to draw eight circles around a larger circle so that all the circumferences touched.

 By rough measurement it appeared that the ratio of the diameters of the smaller circles to the diameter of the larger centre circle was very close to the Golden Section. A good friend and mathematician advised me that it was close but no coconuts were to be won."

That man was Kimo King, a truly brilliant man and good friend, who sadly passed over a number of years ago.I asked Kimo to calculate if the golden section was present as my rough measurements had hinted at. 

I recently read over his calculations and rough drawings that he did for me. 

This has set me back to wondering as to why the relationship of the smaller circle to the larger circle is so close to Phi.

The actual difference is 0.6194 less 0.618 = 0.0014.

Let us now think three-dimensional.

Well I'm musing that we now imagine these circles to be spheres at molecular level and, as such, are subjected to Van der Waals forces which draw the smaller spheres to the larger single sphere yet minutely repel each other when they get close.They don't touch!  
Van der waals forces are when a molecule attracts an object from a distance and as they come closer, they repel from each other. Such as a magnet, they attract from a distance and then as they come close they repel. You can find more information here:

http://antoine.frostburg.edu/chem/senese/101/liquids/faq/h-bonding-vs-london-forces.shtml

I welcome all deep thinkers to offer their thoughts.
Could the volume of the spheres be used to calculate the forces acting on them and then calculate the distance they would be repelled from one another?


Here are Kimo's proofs:

A partial construct of eight smaller spheres tangentially encircling a larger sphere. The  ratio of the diameters of the smaller sphere to the larger is 1.6194.. A mere difference of  0.0014 separates this ratio from the Golden section.
Why?