In my last post I presented the concept of a molecular knot. In it I showed to knotted orbitals side by side and noted that the existing knots cannot just be pushed together. Rather, all of the four arcs have to be part of the same helix.
So, what does this twisted knot of four helical arcs look like? If one takes four strings (or rods) and twist them by one turn, one would get this shape, if at the end of the turn the strings would continue as circular arcs (simplified shape of the helical arcs above). While the shape seems reasonable, the problem is that the string no longer bends in the original direction, but rather 90 degrees in excess.
This just means that the strings need to be twisted a bit less. Like this:
I decided to use just two colors to illustrate the the strings come from two separate, but knotted orbitals.
This spider with eight legs seems like a very strong candidate for the molecular bond. For me the next logical question is whether the equation for the atomic knot still applies.
A clue to this comes from removing half of the helices from the image like this:
It doesn’t look like a ‘natural shape’. That is, the two additional helices do seem to affect the shape. So, the molecular knot probably needs its own equations.
My hunch is that figuring out the equations require one to match the curvature of the dots in the knot and the dots outside of the knot. That is, there can be more refraction in the knot, leading to the strings twisting more, but there cannot be an altered angle of refraction. The dots entering the knot are analogous to light entering a medium with a higher refractive index. Also, in this case the curvature of the arc of dots remains unaltered, but the higher refractive index introduces a rotational component. A very similar rotational component causes four strings of dots to twist together.
However, these are still rather preliminary ideas. I will only know whether I’m correct by trying to come up with the equations for the shape. I already have some ideas, but ideas are cheap. Only testing these ideas will show whether they are any good.
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