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.
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. The sphere in the center represents a projection into normal 3-dimensional space of the electron’s charge distribution, which manifests as a sphere. (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 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.
The Hierarchy of Electron Forces
Let us now look at atomic electron interactions as a Hierarchy of Forces.
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)
2.0: 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, as we see in the atoms of hydrogen (H), helium (He), lithium (Li) and beryllium (Be) (shown below).
If the electrons are competing with other repulsive electrons for the privilege of approaching the nucleus, they will have to find their positions in the resulting orbital resonance by submitting to the relative strengths of their interactions. If electrons already surround the nucleus, new electrons will not be able to approach the nucleus and will therefore cluster around the core electrons in a symmetrical fashion. Electron positions are therefore a function of distance from the nucleus, spatial geometry, as well as charge (vector), field (bi-vector), and spin (tri-vector) interactions. It is these interactions that give rise to the shapes of the orbitals. (See more below.)
- TOTAL DI-ELECTRON INCLUSION (TDI):
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 results in maximum magnetic field cancellation, lowering 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 gives rise to the di-electron state that is the helium (He) atom’s 1s2 shell. The 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 field cancellation is the attractive force that holds the atoms together.
2a. PAULI FIELD EXCLUSION:
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.
2b. PARALLEL SPIN SHARING (PSS):
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, all 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. Degeneracy — spin sharing — compensates for the energy increase of field 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 ones, and are therefore weaker than atomic electron forces 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 stabilize otherwise unpaired electrons into a coherent quantum state.
3a. LINEAR SPIN SHARING (LSS):
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 stabilizes them by lowering energy, and results in an attractive force and a shortening of molecular bond lengths. This effect can also 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 aligned fields of linear electrons overlap.
3b. PARTIAL DI-ELECTRON INCLUSION (PDI):
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.
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.
Orbitals & Orbital Hybridization
Electron orbitals are phase-locked, spherical, stationary waves. Each electron occupies one discrete region within (and at the same time constitute) this single coherent atomic 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 property. It does not arise from orbiting the nucleus.)
Atomic orbitals are essentially regions of electron density that are held in place by a combination of nuclear attraction and the repulsion of other electrons. These regions 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 one or two electrons, which is confined to its symmetrical volume by fixed nodal boundaries. These 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. Adding to or removing electrons (or photons) from this resonance state causes it to snap into the next (either higher or lower energy) stable resonance state. The difference in energy between those resonance states represents the amount of energy arriving or leaving the atom during the transition.
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 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 boundaries. The orbitals do not extend all the way to the nucleus but are confined to the thickness of their shell by the shell within (shown below).
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.
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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