Knot Shaped
Atomic Orbitals
Claimed by B. Vincent Crist.
Defined in 2005 as discussed w R. Joshi
I claim that all current models of atomic orbitals are wrong and grossly misleading by indicating that a “diffuse” cloud-shaped electron can tunnel from one “lobe” through the atomic nucleus (with its massive protons and neutrons) and end up on the opposing side.
The force required to tunnel through a nucleus is huge so a tiny electron can not tunnel from one side to the other. If you supposed that it actually does or could tunnel then most electron (orbitals) have a corresponding orbital electron which would have to either simultaneously transfer in the other direction, or be excited to a different orbital / state.
By having holes in the center of all atomic orbitals the electron does not need to tunnel through a massive nucleus. Please review the shapes shown below. I claim that all atomic (electron) orbitals actually have a large hole in their centers, and that the orbital path is chiral forming the chiral KNOT shapes shown below. Knots are a form of Topological structures that have been ignored in atomic physics and QED.
These KNOT shapes allow us to rethink the simple s, p, d and f orbitals. In chiral knot forms, the p, d, and f orbitals now have simpler interactions with the nucleus and the other electrons. Much needs to be rethought and tested.
These KNOT orbitals are quite elastic in a manner that we now define as “HYBRID” orbitals. We may not need to consider HYBRIDS.
The super-elastic nature of these KNOT orbitals explains how electrons absorb all ranges of EM albeit for a short time period after which the EM wave (photon) is re-emitted. This structure helps us to understand the infinite number of EM photos being “simultaneously” absorbed and release (emitted) with time periods ranging from 10(-25) sec to seconds. Again EM is being simultaneous absorbed and emitted from each orbital-nucleus interaction.
I suggest that it is all EM absorption or interaction is due to a Dipole Pair Interaction that involves both the Nucleus (as the positive +) and the Electron (as the negative -).
Just now I suggest that the electron “particle” as it orbits the nucleus at near light speed must involve the “orbital” path constituting the angular momentum as now known.
Shape of all “s” Atomic Orbitals
Atomic Orbital structure is knot-shaped and chiral:
d and l, r and s, + and –


Shape of all “p” Atomic Orbitals
“Trefoil” is Chiral:
d and l, r and s, + and –

Electron and Positron if p-shaped
Shape of all “d” Atomic Orbitals
“Penta-knot”is Chiral:
d and l, r and s, + and –

Electron and Positron if d-shaped
Shape of all “f” Atomic Orbitals
“Septa-knot” is Chiral:
d and l, r and s, + and –

Electron and Positron if “f” shaped
(c) 2025 All rights reserved, B. Vincent Crist, PhD
