Understanding Electrons

The Nature Of Electrons

Electrons are believed by many to be point particles with no substructure. They are also believed to be much smaller than a proton, but in the hydrogen atom, for example, the electron is the size of the atom. In the solid state, electrons can actually be many times larger than an atom (see Misconception Series).

The work of Dr. John G. Williamson, Dr. Martin B. van der Mark, and Dr. Vivian Robinson has elucidated the substructure of the electron. An electron is formed when a photon of the appropriate energy makes two complete revolutions for every one wavelength, forming a stationary wave of toroidal topology that defines the particle.

A photon (left) and the Williamson-van der Mark electron snapshot (right)

The snapshot of the electron (above, right) can be misleading because it is really two images combined. The toroidal (donut) shape represents the phase-locked path of the rotating photon in momentum space. In order to conserve angular momentum, the toroid will also tumble in space like a spinning ring. The sphere in the center represents the result of this — a projection onto normal 3-dimensional space of the electron’s charge distribution, which manifests as a sphere. An isolated electron is thus a knot of concentrated energy traveling around itself at the speed of light. (CLICK HERE to see one of John Williamson’s lectures on the subject.)

This revolutionary work explains (and unifies) the electron’s shared particle and wave nature, and it similarly — and notably — bridges the gap between the quantum and classical realms. While an electron is a particle, it is made out of a photon, which itself has both wave and particle properties.

Electrons are harmonic stationary waves that have electric charge, magnetic field, and angular momentum, and they are affected by the charge, field, and spin of other particles in their vicinity. As a result, when multiple electrons interact in the same atom or molecule, they produce orbital regions that are symmetrical, phase-locked, resonant, coherent, spherically-harmonic, stationary electron waves. These stationary waves represent the lowest energy and maximum symmetry state of the system, incorporating regions of positive and negative wave interference. The entire system also forms a single, coherent, harmonic quantum state. Each electron within this state can no longer be seen as an individual particle but as an essential component of the harmonic electron stationary wave. Any addition or subtraction of energy or electrons will cause the entire system to snap into its next most stable harmonic state. Electrons can therefore only be considered to be discrete particles when they are isolated “free” electrons, but within an atom, molecule or ion, they form part of the continuous energy flow of the system, and can therefore no longer be considered separate from it.

A vibrating (rotating) string (video link).

The image above is made with a rotating string, and it evokes the idea of a resonant wave in the linear direction.

This image represents the first 5 shells of the barium (Ba) atom, and it seeks to evoke the idea of the spherical resonance wave, a series of concentric harmonics constituting the single multi-electron state of the atom. Nodal boundaries separate each shell, as well as each orbital “slice” within each shell.

The Hierarchy of Electron Forces

Let us now look at atomic electron interactions as a Hierarchy of Forces. (See Sub-Quantum Chemistry for more detail.)

From strongest to weakest, they are:
(1) Total Di-electron Inclusion (TDI)
(2a) Pauli Field Exclusion
(2b) Parallel Spin Sharing (PSS)
(3a) Linear Spin Sharing (LSS)
(3b) Partial Di-electron Inclusion (PDI)

0: Nuclear Attraction

Electrons are present because they are attracted into the positive charge well of the nuclear protons. As electrons arrive, they will try to approach and envelop the nucleus with a simple spherical symmetry. If there is already a spherical di-electron shell, new electrons will not be able to approach the nucleus. They will therefore cluster around the core electrons in a symmetrical fashion, forming a second shell around the first. We see this in the first four atoms — hydrogen (H), helium (He), lithium (Li) and beryllium (Be) (shown below).

Spherical electron clouds of (left to right) hydrogen, helium, lithium and beryllium.

If additional electrons are competing for the privilege of approaching the nucleus, the volume of the outer shell will become subdivided in a symmetrical fashion, and electrons will find their positions in the resulting orbital resonance by submitting to the relative strengths of their interactions. Electron orbital geometry is therefore a function of distance from the nucleus, as well as charge (vector), field (bi-vector), and spin (tri-vector) interactions. (See more below.)

    When two electrons envelop a nucleus, they will prefer to snap into an antiparallel relationship because this allows them to superimpose completely upon one another. This causes their magnetic fields to be oppositely aligned at every point, resulting in maximum magnetic field cancellation, which lowers both energy and angular momentum significantly. At such close distances, the attraction of magnetic field cancellation overwhelms electrostatic charge repulsion since the magnetic force is about two orders of magnitude (102) stronger than the electric force at very close range.
TDI (left) yields the di-electron (boson) state (right)

TDI gives rise to the di-electron state that is the helium (He) atom’s 1s2 shell. This di-electron is a boson state, which is a distinct state from that of two individual electrons.

When two electrons on adjacent atoms have antiparallel spin, they can be attracted into this superimposed di-electron state, giving rise to a single covalent bond, as in the hydrogen molecule (H2). The lowering of energy from electron field cancellation is the attractive force that holds the atoms together. The two proton nuclei remain suspended within the di-electron by the attraction of charge cancellation, but remain a distance apart from one another due to the field intensification of proton charge repulsion. A molecule can thus be thought of as a discrete crystal-like unit.

Helium’s 1s2 di-electron (left) and the hydrogen molecule’s bonding di-electron (right)


If the spherical s-orbitals are full, new electrons must resonate as non-spherical p-orbitals (or higher). This no longer allows the electron density to achieve spherical symmetry around the spherical atomic core. Since the electrons can no longer superimpose as a result of geometric constraints, asymmetry raises resonance energy and decreases coherence. Electrons therefore seek symmetry by venturing into the slightly higher energy state of parallel spin.

Since they are no longer at immediately close range, electrostatic repulsion returns to primacy. This is because the stronger (dipole) magnetic force drops off as the inverse cube of distance whereas the (monopole) electric charge drops off as the inverse square of distance. This means that, since the electric force drops off more slowly than the magnetic force, it is stronger at distance.

Since their magnetic fields no longer cancel perfectly, the increase in energy from constructive magnetic interference causes the electrons to repel each other in search of a lower energy state. In addition, quantum spins are oriented in conflicting directions in the region between the electrons.

The sum of these interactions causes the electrons to move as far from each other as their atomic geometry will allow.

However, the energy of these electrons is now higher than it would be if they were in a superimposed, di-electron state (under TDI). This necessitates a lowering of energy in order to compensate, and this is possible through the following quantum spin interactions.

According to Sub-Quantum Chemistry, a new theory of electron quantum coherence, once electrons with parallel spin achieve the maximum allowed distance from one another, the forces of field repulsion are in balance. The electrons will then be able to link their spin states into a single, larger, coherent, multi-electron quantum spin state. This lowers energy and pseudo-stabilizes these otherwise unpaired electrons, in a similar way that gyroscopes can be spin-linked. (In their internal structure electrons are extremely powerful, light-speed gyroscopes.)

Degenerate electrons that are unable to superimpose therefore preferentially assume parallel spin states, creating a more favorable energy condition, with spin sharing, out of one that is otherwise less stable than the preferred (antiparallel) di-electron state. This is what occurs during hybridization. In the sp2 hybridization of boron (B), for example, the 2s2 electrons uncouple from their di-electron state and elevate their energies, so that the single p-electron can lower its energy. The three electrons can then find symmetry and coherence as a set of trigonal planar, degenerate, spin-sharing electrons — a tri-electron state. Spin sharing compensates for the energy increase of electrostatic repulsion by lowering energy through the stabilization of quantum angular momentum linkage.

The Pauli Exclusion Principle thus embodies the process of field exclusion in concert with Parallel Spin Sharing in order to create the next most favorable energy state after the di-electron state.

Electrons in Molecules

Molecular electron interactions generally occur at greater distances than atomic electron interactions, and are therefore weaker in the hierarchy. Once magnetic, electrostatic, and spin forces at close range have been satisfied, they come into play at greater distances. These effects can be meaningful.

The theory of Sub-Quantum Chemistry introduces the idea that unpaired electrons on adjacent atoms in a molecule can experience quantum interactions, and that these interactions pseudo-stabilize otherwise unpaired electrons into a coherent quantum state.

Electrons on adjacent atoms in a molecule that are free to re-align themselves into a linear arrangement will do so in order that their magnetic fields can be perfectly aligned. This results in Linear Spin Sharing, which causes magnetic field to cancel between the electrons. This pseudo-stabilizes them by lowering energy, and results in an attractive force and a shortening of molecular bonds. This effect can concentrate quantum spin, which in turn affects an element’s magnetic properties (see below). LSS can also occur between unpaired electrons on opposite sides of a large atom when there are d– or f-orbitals present. Field cancellation will occur in the space where the fields of aligned electrons overlap.

Electrons on adjacent atoms in a molecule that have antiparallel spins will attract one another, but they will not be able to superimpose due to atomic orbital constraints. This results in a PDI force — a partial overlap and a partial cancellation of field between the electrons — which stabilizes them by lowering energy. This is also an attractive force that shortens molecular bond lengths.


Evidence that might lend support to this view might be the observed ‘quadruple bond’ in the dicarbon (C2) molecule. This fourth ‘bond’ has been measured at 55kJ/mol, which is rather weak in comparison to the strength of a C-C single bond (347kJ/mol).

When we look at the structure of dicarbon using a Quantum Lewis Dot Structure that shows relative spin states, we see that the dicarbon molecule allows for quantum interactions — either PDI or LSS — between the unpaired electrons on opposite sides of this small (linear) molecule. It is possible that this attractive force is responsible for the 55kJ/mol bonding that has been measured in experiment.

Quantum Lewis Structure of the dicarbon (C2) molecule

The Quantum Lewis Dot Structure above for dicarbon shows bonding electrons as dots on the bond, and indicates the relative spin states of electrons with a small circle versus a diamond.


When both unpaired electrons and di-electrons are present in the same shell, di-electrons will repel more strongly than unpaired electrons. This occurs due to the significant lowering of energy due to field cancellation that takes place during di-electron formation, but this energy is raised if another field is allowed to interact (and interfere) with it. This is the reason diamagnetic substances repel magnetic fields, and di-electrons will similarly repel the fields of nearby unpaired electrons more strongly than unpaired electrons will repel one another.

As a consequence, electron orbital geometry will be dominated by di-electron geometry, and unpaired electrons will be repelled into secondary positions as a result.

Orbitals & Orbital Hybridization

Electron Orbitals:

The electron orbitals in an atom are regions of electron density that result from a combination of nuclear attraction, mutual electron repulsion, and quantum electron interactions. Like-charge repulsion causes electron orbitals to space out as much as possible in order to minimize repulsion. This yields spherical geometric symmetry. These discrete regions of electron density — the orbitals — are separated by nodes of low (to zero) electron density. Each region of electron density can therefore be thought of as a stationary ‘tuft,’ containing either a single electron or a di-electron, which is confined to its symmetrical volume by fixed nodal boundaries. These tufts all form a part of a continuous spherical resonance structure — a phase-locked spherical stationary wave — that surrounds the nucleus in the most symmetrical, lowest energy state it can achieve. (An analogy in the linear case might be a resonating guitar string, where the symmetrical tufts (or bulges) in the wave remain fixed in location and are separated by nodal points of low to zero amplitude.)

Each electron or di-electron occupies one discrete region within (and at the same time constitutes) this single coherent atomic (or molecular) resonance. This implies that electrons need not “orbit” the nucleus at all in order to remain connected to it. (The conservation of electron angular momentum — spin — is an internal electron property. It does not arise from orbiting the nucleus.)

Adding to or removing electrons (or photons) from this atomic resonance state causes it to snap into the next (either higher- or lower-energy) stable resonance state. The difference in energy between these resonance states represents the amount of energy arriving or leaving the atom during the transition.

Orbital Hybridization:

Electrons strive to maximize symmetry and minimize repulsion. The way that orbitals achieve this is known as hybridization. It is when orbitals — that we normally designate as having different energies and geometries, like s– and p-orbitals — combine and rearrange themselves into a symmetrical arrangement of identical energy states. Overall, this symmetrical state has a lower energy than the sum of the individual energy states before they hybridized.

Hybridizations like sp, sp2, sp3, sp3d, and sp3d2 are familiar concepts. The first instance of it occurs in the boron atom with sp2-hybridization. With five electrons, boron is the first atom to contain electrons that are in a p-orbital. This is not a sphere-shaped harmonic, and so a single electron in a p-orbital cannot find a symmetrical arrangement around a sphere by itself. Boron therefore cannot simply add its p-electron on top of the same (2s2) configuration that beryllium has, as shown below, because it would not be stable:

Each p-orbital lobe can hold 1 electron. An electron pair occupies two opposite lobes.

The asymmetry therefore causes the two electrons in the 2s orbital to uncouple from their di-electron state and form a tri-electron state with the single p-electron. Three equal-energy (degenerate) electrons can now achieve maximum stability by assuming a trigonal planar (sp2-hybridized) arrangement around the core electron shell, because this minimizes their mutual repulsion by having them as far from one another as they can get. (The wireframe indicates the boundary of the n=2 shell.)

The outer spheres above simply indicate the directions of maximum electron density. The orbitals themselves will be more like three equal longitudinal sections that can only occupy volume within their shell. Each orbital occupies one third of the volume of the shell, though not uniformly, as electron density has a maximum at the center of the orbital and decreases towards the orbital boundary. But electron density will nonetheless fill the entire shell in order to shield the positive charge of the nucleus. The orbitals also do not extend all the way to the nucleus, but are confined to the thickness of their shell by the shell within. In the case of boron, each of the three hybrid orbitals contains one electron.

Boron’s three 2sp2-orbitals surrounding a 1s2 core di-electron shell (left), with top view (right).

The sp3-hybridization that occurs in carbon, for example, allows the atom to achieve tetrahedral symmetry involving an s-orbital and three p-orbitals of the same shell. When they hybridize, the s-orbital increases in energy and the p-orbitals decrease in energy in order to produce four equivalent energy (degenerate) orbitals that will arrange themselves in a tetrahedral symmetry. Each orbital occupies one fourth of the volume of the shell, though not uniformly, as electron density has a maximum at the center of the orbital and decreases towards the orbital boundary. But electron density will nonetheless fill the entire shell in order to shield the positive charge of the nucleus. The orbitals also do not extend all the way to the nucleus, but are confined to the thickness of their shell by the shell within. In the carbon atom, each of the four hybrid orbitals contains one electron.

Four sp3 orbitals (left), and exploded view (right)

An example of sp3d-hybridization occurs when a sulfur atom, containing two unpaired valence electrons and two valence di-electrons, is approached by highly electronegative atoms like oxygen or fluorine. Their high electronegativity can induce sulfur’s valence di-electrons to uncouple, yielding 6 unpaired electrons available for bonding. This is possible for sulfur but not for oxygen because the 3rd shell contains a larger volume than the 2nd shell, which is the reason it can accommodate a d-orbital. While sulfur does not usually have electrons in its 3d-orbital, the 3rd shell has enough volume to accommodate the additional electron density. This allows sulfur’s electrons to hybridize into more electron domain directions than a 2nd row element. Sulfur can therefore make up to 6 covalent bonds (shown below), as we see in the octahedral sulfur hexafluoride (SF6) molecule.

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Since a full valence shell, for example neon (Ne) on the second row, contains 8 electrons, it could be argued that the most symmetrical and lowest energy state is achieved with 4 di-electrons in tetrahedral symmetry. If that is the case, the electron configuration of argon (Ar) (on the third row) should produce two nested spherical tetrahedra, aligned antiparallel, as shown below.

Nested tetrahedral orbital geometry (left), and with one outer orbital raised (right).

The reason that nested antiparallel tetrahedral geometries are so stable for electrons is that the region of lowest electron density on one shell lines up with the region of highest electron density on the adjacent shell, thereby minimizing repulsion. In the diagram above, the vertex where the nodes between orbitals intersect is a point of lowest electron density. It lies directly opposite the center of the face of the orbital above or beneath it, which is the point of highest electron density in that orbital. This overlap is therefore the lowest energy state.

In addition, the theory of Sub-Quantum Chemistry allows for the speculation of a new type of orbital hybridization that involves interactions between p-, d– and f-orbital electrons when they occupy the same shell. It is proposed that the resulting electron geometries help explain the magnetic properties of the transition and rare earth metals.

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