In my last post I raised the idea that the dots in a molecular orbital are sort of a gamma-ray laser, where gamma ray photons are linked back-to-back into a closed loop. When I had the idea, I was thinking of stretched spring, where the loops of dots would be well separated. This idea stemmed from the initial idea of the orbital being knotted string, which turned into a helix when I realized that the dots couldn’t push the neighboring dots, but would rather move out of the way.
Having thought about the concept for three days, I realized that the only conceivable shape the gamma rays within the orbital could take would be with the loops not just being connected at the ends, but the loops themselves should touch. What this means is that the orbital looks less like a knotted string, but more like knotted tube.
But there is a catch. The inner circumference of the tube is smaller than the outer circumference, just by definition. This means that the string of dots would need to be thinner in the inner bend and thicker in the outer bend. But if the dots are always the same size, how could this be? This we can solve with rather simple geometry. Below left, you can see a square lattice of dots, with each dot surrounded by four other dots. There the packing is tight. Below right you see a hexagonal lattice of dots, with a hole in the middle of each hexagon, with each dot surrounded by three other dots. I could bore you with the details, but you can calculate exactly how much thicker the string is in this case.
Except this was my first idea, which after some reconsideration doesn’t look as likely as my second idea. In this second iteration the outer bend still has a hexagonal alignment of dots, but there are no unexplainable holes between the strings.
What this means that while the general concept of gamma-ray laser still holds, the actual shape of the orbital looks more like a tube with a continuous surface of dots in a lattice pattern shifting from square to hexagonal.
Now we’re getting really close to a proper explanation of the atomic orbital. Next I have to revisit my electron model based on this concept. I have a feeling that I’ll be surprised again.
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