23. Vanadium

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Below: Electron Shell, Bonding & Ion Formation, Magnetic Properties

Vanadium is the 23^rd element on the periodic table. It has 23 protons and 28 neutrons for a mass of 51 amu, and 23 electrons.

Electron Shell

DISCLAIMER: The following reflects the sub-quantum mechanics approach to electron interactions and hybridization. Some details may therefore differ somewhat from traditional quantum chemistry:

Vanadium is the third element to feature electrons in the d–orbital. Building upon the pd-hybridization [ref] we introduced in regard to scandium (Sc) and titanium (Ti), it is proposed that vanadium has a 3^rd shell containing 3 di-electrons and 3 unpaired electrons in a p³d³-hybridized, octahedral symmetry (see image below). The 3 di-electron and the 3 unpaired electron sets are each planar arrangements, and they lie orthogonal (90⁰) to one another in making up the octahedral electron geometry.

This pd-hybridization does not need to involve the 3s-orbital electrons, and they can return to their preferred spherical di-electron state, within which (or upon which) the hybrid orbitals will resonate like harmonics upon a fundamental.

In such a configuration, the 4 tetrahedral di-electrons in the 2^nd shell will align themselves with two di-electrons roughly opposite two of the unpaired electrons in the 3^rd shell, allowing the other di-electrons to orient their directions roughly between one another, in order to minimize repulsion between shells.

NOTE: The small spheres in the image above simply indicate the directions of maximum electron density. The 3^rd shell hybrid orbitals themselves will assume a spherical octahedral structure that divides the 3^rd shell into six roughly equal volumes, with two 3-way symmetries, one of di-electrons and the other of unpaired electrons. Each shell segment will be filled with electron density. It will be highest at the center of the face of each orbital (as in the traditional hybrid orbital lobe shapes) and will decrease toward the nodal regions between orbitals — as wave structures usually do — where electron density will be lowest (though not zero).

NOTE ALSO: Even though it is often useful to talk about these orbitals as separate, they are all — the entire atom is — part of a single, coherent, harmonic, resonant, phase-locked, spherically-symmetrical quantum wave state, and it is all electromagnetic at the root-energy level. Orbitals and their ‘boundaries’ can be seen as nothing more than nodes and antinodes in this harmonic wave structure

It is also proposed that the stronger repulsion and larger charge density of the three di-electrons will constrict the three unpaired electron orbitals, bringing these three degenerate electrons into closer proximity. It is conceivable that this might even increase the coherence of the parallel spin bonding between them. (See Magnetic Properties below.)

As in the case of scandium and titanium, vanadium’s 3^rd shell p³d³-hybrid orbitals exist within the added sheath of the 3s²-orbital di-electron, since it is not needed for hybridization. They are superimposed within it as a harmonic frequency coincides with its fundamental frequency in a resonance. It is proposed that the 3s² di-electron gives additional stability to the electron configuration within it, even though it contains 3 unpaired electrons. The other elements in the d-block will also experience this 3s-orbital stabilization phenomenon, since they also achieve at least 4-directional symmetry with only their p– and d-orbitals.

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Bonding & Ion Formation

The 4s²-orbital di-electron shell completes the atom. When forming a metallic crystal, the 4s² electrons delocalize to form the metallic bond, and when forming a 2+ ion, they are removed. In both cases, the core electron geometry remains the same. (A third ionization, would either leave the 2 remaining di-electrons in linearly opposite positions — if one of the di-electrons is ionized — or if it loses an unpaired electron, it will change it to the geometry of the previous element, titanium.)

(In a few cases, such as chromium (Cr) and copper (Cu), the 4s-orbital outer shell contains only 1 electron, since the other joins the 3rd shell hybridization within in order to help it achieve 8-directional symmetry.)

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Magnetic Properties

Vanadium has three unpaired electrons. In all elements prior to the d-block, unpaired electrons have occurred in the outer (valence) shell of the atom. Those are the electrons involved in chemical reactions. Vanadium is the third case of an atom with unpaired core electrons. They are protected from reacting (at least, until vanadium becomes a V²⁺ ion), and they are stabilized by the 3s di-electron ‘fundamental.’ We propose that it is this protection and stabilization of unpaired core electrons that allows them to interact magnetically, and that consequently determines an element’s magnetic properties.

UNPAIRED CORE ELECTRONS:
While these electrons may technically be called core electrons, for the purposes of this discussion, we recognize that in a metal, if we exclude the valence “conduction” electrons, the pd-hybrid orbital electrons do become ‘valence electrons’ in a sense. Not in the sense that they can participate in chemical reactions, but in the sense that they are now in the outermost shell of the atomic cores, which are suspended in the conduction electron matrix — the 3D electron gas — of the solid metal crystal.

PARAMAGNETISM:
In the presence of an external magnetic field, an unpaired core electron will orient its spin to align with the magnetic field. This will cause the atom to be drawn into and toward that field — via magnetic field cancellation — giving it a positive magnetic susceptibility (χ_m) value. This attractive force is called paramagnetism, and its effects only last as long as the external magnetic field is present. We might therefore presume that, the stronger the paramagnetism, the more ‘unpaired electron character’ is present. Surprisingly, this does not seem to go according the number of unpaired electrons present, as the diagram below illustrates. There must therefore be other contributing factors, which we will investigate below.

Vanadium is the second least paramagnetic metal of the 3d row — excluding the diamagnetic copper and zinc — even though it has three times as many unpaired electrons as scandium, the second most paramagnetic.

As described above, it is proposed that vanadium has three unpaired electrons arranged in a planar arrangement within an octahedral electron structure. Due to the orbital constriction by the 3 di-electron orbitals in the same shell, the 3 unpaired electron orbitals should be compressed (and concentrated) into a slightly narrower wedge-like section of the spherical system.

The images below are intended to represent the orientation of these 3 electrons in an external (or adjacent atom’s) magnetic field (whose north pole is pointing upwards). (The purple arrows inside the atom represent the unpaired electrons and the black dots represent the relative positions of the di-electrons.)

While vanadium has three unpaired electrons — three times as many as scandium — it has a slightly lower magnetic susceptibility value of χ_m = +285, though still higher than titanium (with χ_m = +151). It is here proposed that this is due to the parallel spin bonding and field cancellation that occurs between its three unpaired electrons, given their proximity, degeneracy, and orbital constriction.

When unpaired electrons align linearly, as in the case of titanium (Ti), it was proposed that field cancellation occurs between them due to destructive interference, and that in ‘spin-space,’ the linear spin bonding reduces the magnetic signature of the electrons — their effective magnetic electron count (EME). In the case of vanadium, there are three electrons spin bonding together, but this time they are parallel spin bonding adjacent to one another. We might expect that this would increase the coherence of the spin bonding and decrease EME. On the other hand, the unpaired electrons are also being compressed together by the repulsion of 3 di-electron orbitals in the same shell, which should increase their EME. As such, it makes sense that each of vanadium’s electrons might contribute a diminished EME, though not quite as diminished as in the case of titanium.

If we consider scandium’s single unpaired electron to have an EME ≈ 1e^– (with χ_m = +295), and titanium’s 2 linear spin bonding electrons to have an EME ≈ 0.51e^– (with χ_m = +151), then vanadium’s 3 spin bonding electrons would have an EME ≈ 0.97e^–. That equates to about 0.32e^– of electron signature contributed per electron.

PARAMAGNETIC STRENGTH ANALYSIS:
The following diagram shows the relative paramagnetic strengths of the transition metals, along with their proposed hybrid orbital geometries. (See paramagnetic strength trend analysis for more detail.)

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OTHER PARAMAGNETIC 3d METALS: Scandium, Titanium, Vanadium, Chromium (also antiferromagnetic), Manganese
FERROMAGNETIC 3d METALS: Iron, Cobalt, Nickel
DIAMAGNETIC 3d METALS: Copper, Zinc

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