benzene on the basis of the three-electron bond 2.5., formula
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benzene on the basis of the three-electron bond, formula.
So, the aromatic system is a cyclic system with three-electron bonds where an
interaction of central electrons through the cycle is observed. In the benzene molecule
there are three interactions through the cycle-pairwise between electrons 1 (+) and 4 (-),
2 (-) and 5 (+), 3 (+) and 6 (-), as shown in figure 5.
We can simply and clearly explain the increase in the multiplicity of benzene from 1.5 to 1.67. by MO method calculations give a value of 1.67, but Pauling from resonant structures, which is logical (2 and 4 of the electron) gave 1.5.
If the multiplicity is greater than 1.5 (eg 1.67), since the communication multiplicity in classical chemistry correlates with the amount of the bonding electrons (even if it is average) like:
2 electrons multiplicity 1;
4 electrons multiplicity 2;
6 electrons multiplicity 3;
thene in benzene at a multiplicity of 1.67 in six (6) aromatic bonds as it further appears 1 electron:
1.67 - 0.17 = 1.5
6 * 0.17 = 1.02
At the three-electron bond in benzene and interaction through a simple explanation of the cycle - the cycle just a little compressed.
Theoretical justification of three-electron bond with multiplicity of 1.5 which can be explained by the structure of the benzene molecule and many other organic and inorganic compounds.
Justification of three-electron bond given here:
1. pp. 4-6 http://vixra.org/pdf/1606.0151v1.pdf
2. pp. 1-5 http://vixra.org/pdf/1606.0150v1.pdf
Quantum mechanics defines what such a chemical bond. Without quantum mechanics it is impossible. Classical concepts to explain what the chemical bond is impossible (and this despite the existence of four fundamental interactions: the electromagnetic (most important for chemistry), strong, weak, gravity). It is obvious that when the chemical bond formation quantum effects are important. That is, to form a chemical bond is not enough to have two specific atoms with unpaired electrons and the four fundamental interactions, but still need these two atoms placed at a certain distance where quantum effects "help" form a chemical bond. Without quantum effects these baselines (atoms and fundamental interactions) is not enough to form a chemical bond. It is obvious that when the chemical bonds forming, important not only the properties of atoms and fundamental interactions but also the structure of the space-time at distances of several angstroms (scale chemical bond). Quantum effects of the space-time begin to affect the interaction of atoms (the house begins to affect the interaction between residents), without it, explaining the formation of a chemical bond is impossible.
"Now the question is how to explain the existence of the three-electron bond in benzene and other molecules and ions from the point of view of quantum theory. It stands to reason that any placement of three electrons on the same atomic or molecular orbital is out of the question. Therefore it is necessary to lay the existence of three-electron bond in molecules in reality as an axiom. In this case the three-electron bond in benzene can be actually considered a semi-virtual particle. A real particle, such as an electron, exists in the real world for indefinitely long time. Virtual particles exist for the time which is insufficient for experimental registration (strong interactions in atomic nuclei). So we shall call the three-electron bond which really exists for indefinitely long time only in molecules and ions a semi-virtual particle. The three-electron bond as a semi-virtual particle has certain characteristics: its mass is equal to three electronic masses, its charge is equal to three electronic charges, it has half-integer spin (plus, minus 1/2) and a real spatial extension. That is, our semi-virtual particle (the three-electron bond) is a typical fermion. Fermions are particles with half-integer spin; they follow the Fermi-Dirac statistics, and have appropriate consequences, such as the Pauli exclusion principle etc. An electron is a typical fermion, and therefore such distribution in atomic and molecular orbitals is accepted (calculated). It follows that the three-electron bond in benzene is a real fermion in benzene, so quantum calculations can be extended to the molecule of benzene (and other systems) with the use of corresponding fermion (i.e. three-electron bond as a particle) instead of the electron in calculations. Then everything shall be made as usual: the Pauli exclusion principle, distribution in MO, binding and disintegrating MO, etc."
"\u2026The interaction of two three-electron bonds in a molecule of benzene at a distance of 2.42 A (on opposite sides) can be explained if we consider these two three-electron bonds as two particles (two fermions) in an entangled quantum state [1, p. 4-11]. That is, these two fermions are in an entangled quantum state. Quantum entanglement is a quantum mechanical phenomenon, in which the quantum states of two or more fermions or bosons prove to be interconnected [2-6]. And surprisingly, this interconnection remains at virtually any distance between the particles (when there are no other known interactions). It should be realized that the entangled quantum system is in fact an "indivisible" object, a new particle with certain properties (and the particles of which it is composed should meet certain criteria). And most importantly, when measuring the spin (or other property) of the first particle we will automatically unambiguously know the spin (property) of the second particle (let's say we get a positive spin of the first particle, then the spin of the second particle will always be negative, and vice versa). Two particles in an entangled state prove to be bound by an "invisible thread", that is, in fact, they form a new "indivisible" object, a new particle. And this is an experimental fact. As for the benzene molecule [1, p. 2-11], if we consider the interaction of all six three-electron bonds as an entangled quantum state of six fermions (three-electron bonds), then the definition of the spin of one of the fermions automatically implies the knowledge of all the spins of the other five fermions, and in closer inspection it means the knowledge of the spins of all 18 benzene electrons that form all the six C-C bonds. In fact, on this basis, the benzene molecule can be used to study the entangled quantum states of electrons (fermions).
\u2026The fact that electrons during the formation of chemical bonds are in an entangled quantum state, is very important for chemistry and quantum mechanical bond calculations. For example, when calculating the two-electron chemical bond of a hydrogen molecule, it will no longer be necessary to consider the movement of two electrons in general, i.e. as independent and virtually any relative to one another. And we will know for sure that in an entangled quantum state, these two electrons can be considered actually bound by an "invisible thread" with a certain length, that is, two electrons are connected and form a new "indivisible" particle. That is, the movement of two electrons in the field of cores can be described by the movement of a point located in the middle of the "invisible thread" (or in the center of a new particle, or in the center of mass, and so on), what should greatly simplify the quantum mechanical calculations. The length of the "invisible thread" will definitely be much less than the sum of the covalent radii of hydrogen atoms, and it is this length that will determine the Coulomb repulsion between the two electrons. The length of the "invisible thread" between electrons in various chemical bonds should not greatly differ, and perhaps it will be a constant for all, without exception, chemical bonds (meaning two-electron bonds), maybe it will be another constant. The three-electron bond can also be seen as an entangled quantum state in which there are three electrons. Then the length of the "invisible thread" between electrons will be different from that of the twoelectron bond. You can also expect that for all, without exception, three-electron bonds the distance between electrons will be the same that is constant. All types of chemical bonds (two-electron, three-electron, four-electron, five-electron, six-electron, and so on) can be seen as an entangled quantum state, in which there are electrons involved in chemical bonding. And interestingly, all entangled particles behave as they should according to the quantum theory, that is, their characteristics remain uncertain until the moment of measurement. From this point of view (the quantum mechanical point), it becomes clear the cause of failure to calculate chemical bonds "on the tip of the pen" with attempts to calculate the speed and energy of electrons and other characteristics. But these characteristics of electrons of the chemical bond (a chemical bond is a quantum entangled system, which contains electrons of the bond) cannot be determined in principle, because it is so constituted the quantum world. Logically, that what is impossible to determine is impossible to calculate in principle, what is confirmed by the history of quantum chemical calculations. That is, all attempts to calculate characteristics of electron chemical bond (speed, power, and so on) were doomed to failure from the beginning. Therefore, in our opinion, it would be more correct to consider the chemical bond as a certain new "indivisible" particle, with well-defined characteristics and spatial extension, which we called a "semi-virtual particle" [14, p. 4-6.]. In particular chemical substance the chemical bond is really indivisible. In addition, such semi-virtual particle is a fermion for the three-electron bond and other bonds with an unpaired number of electrons and total half-integral spin. And the semi-virtual particle will be a boson for the two-electron bonds and other bonds with a paired number of electrons and total integral or zero spin. And the characteristics of a semi-virtual particle (as an integral), we can calculate. These are the characteristics of a semi-virtual particle, such as energy, spatial extension, length, and so on, that are very important for chemistry. Calculations of a hydrogen molecule will actually come to the solution of the movement of one point in the field of two protons, which is similar to the solution of a task for the hydrogen molecular ion H2 + [7-13]. And we can expect that finally the two-electron chemical bond will be calculated "on the tip of the pen\u201d. Besides that, an entangled quantum state clearly demonstrates that the chemical bond is real and that it is neither an abstraction, nor a convenient concept used to describe and explain. Two electrons indeed form a chemical bond (which is a new particle), and they really "know each other's spins", and are in an entangled quantum state. This means that these two electrons forming a chemical bond and connected by an "invisible thread" have their own well-defined characteristics. And this bond (or this thread) is real, but not in terms of energy (if the energy of such bond really exists and is not equal to zero, then its value cannot be compared with the energies of chemical bonds).\u201d
"...Construction of diagrams showing how electrons gravitate (in explaining the interaction through the cycle, etc.) is an attempt to explain the Quantum interaction of electrons by using methods of classical chemistry. It is clear that electrons do not gravitate towards each other (gravitational interaction is neglected), but on the contrary, if they gravitate, a force should exist, as well as an equation for the calculation of this force. In nature, there are only four fundamental interactions:
1. Gravity.
2. Electromagnetic.
3. Strong.
4. Weak.
With neglect of gravitational interaction, it is only electromagnetic interaction and broadly
speaking, Coulomb attraction and repulsion in the molecule (or rather between electrons and nuclei)."
P.S. Hückel rule (4n + 2) for aromatic systems can be written in a different form, in the form of 2n where n - unpaired number. So, we have: 2, 6, 10, 14, 18, etc. This is also true for the electron shells in the atom and aromatic systems. The principle of the interaction of fermions always one, everywhere.
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