benzene on the basis of the three-electron bond 2.3, spin
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The present work shows the inapplicability of the Pauli principle to chemical bond, and a new theoretical model of the chemical bond is proposed based on the Heisenberg uncertainty principle. See pp. 88 - 104 Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdfNotes on the chemical bond.
If we analyze the formation of the chemical bond (one-electron, many-electron) strictly theoretically, then it is difficult to understand the cause of the formation of the chemical bond. There are several problems here:
1. When a chemical bond is formed, when the domain of "existence" of electrons actually decreases (the "volume" of the chemical bond (MO) is much smaller than the "volume" of the corresponding AO, this was emphasized by L. Pauling) in comparison with the original AO ((in other words , that the electron distribution function in a diatomic molecule is much more concentrated than in the case of atoms), the repulsion between electrons inevitably must increase significantly. And then according to Coulomb's law (F=f(1/r ^ 2)) this repulsion can not be compensated in any way This is also noted by L. Pauling, and we assume (pp. 88 - 89, Review. Benzene on the Basis of the Three-Electron Bond. (The Pauli Exclusion Principle, Heisenberg's Uncertainty Principle and Chemical Bond). http://vixra.org/pdf/1710.0326v2.pdf) that he therefore analyzed the interaction of the hydrogen atom and the proton in the entire range of lengths (admitted that the hydrogen atom and H + are retained when approaching) and showed that the connection is not formed in this case (since there is no exchange interaction or Pauling resonance.) This actually showed that even a one-electron bond can not be explained only by the electro-magnetic interaction (that is, the classical approach), and if we go to many-electron bond (two-electron bond, three-electron bond, etc.) and take into account the repulsion between the bonding electrons, it becomes evident that the classical explanation (the electromagnetic approach) can not even provide a qualitative explanation of the cause of the formation of a chemical bond. It inevitably follows that the cause of the formation of a chemical bond can only be explained by quantum mechanics. Moreover, the chemical bond is a "pure" quantum-mechanical effect, in principle this is strictly indicated by the exchange interaction introduced by quantum mechanics, but not having the physical justification, that is, the exchange interaction is a purely formal, mathematical approach, which makes it possible at least some results. The fact that the exchange interaction has no physical meaning can be confirmed by the fact that the exchange integral essentially depends on the choice of the basis wave functions (more precisely, the overlap integral of the basis functions), and therefore, when choosing a certain basis, it can be less modulo, and even change sign on the reverse, which means that two atoms can not be attracted but repelled. In addition, the exchange interaction by definition can not be applied to the one-electron coupling, since there is no overlap integral since we have one electron (but Pauling's resonance can be applied to explain the one-electron bond).
2. In addition, using A. Einstein's theory of relativity, it can be shown that, in the motion of electrons, the field in a molecule can not by definition be a conservative field (pp. 90 - 92, http://vixra.org/pdf/1710.0326v2.pdf). When describing the behavior of electrons in atoms or molecules, it is often (more precisely, almost always) assumed that the motion of electrons is in the average conservative field. But this is fundamentally not true (based on the theory of relativity), and therefore further assumptions are not theoretically rigorous. Moreover, this case (application of the theory of relativity to a chemical bond) directly indicates that it is only possible to explain the cause of the formation of a chemical bond by using jointly quantum mechanics and the theory of relativity of A. Einstein, which we will try to do (see below).
3. It is also especially worth noting that when analyzing the Pauli principle (pages 103-105, http://vixra.org/pdf/1710.0326v2.pdf), it turned out that it can not be applied to chemical bonds, since the Pauli principle can be applied only to systems of weakly interacting particles (fermions), when one can speak (at least approximately on the states of individual particles). Hence it inevitably follows that the Pauli principle does not forbid the existence of three-electron bonds with a multiplicity of 1.5, which has a very important theoretical and practical significance for chemistry. In chemistry, a three-electron bond with a multiplicity of 1.5 is introduced, on the basis of which it is easy to explain the structure of the benzene molecule and many organic and inorganic substances (pp. 6-36, 53-72, http://vixra.org/pdf/1710.0326v2.pdf).
4. It is shown (pp. 105 \u2014 117, http://vixra.org/pdf/1710.0326v2.pdf) that the main assumption of the molecular orbitals method (namely, that the molecular orbital can be represented like a linear combination of overlapping atomic orbitals) enters into an insurmountable contradiction with the principle of quantum superposition. It is also shown that the description of a quantum system consisting of several parts (adopted in quantum mechanics) actually prohibits ascribe in VB method to members of equation corresponding canonical structures.
5. See pp. 116 \u2013 117, Quantum-Mechanical Analysis of the MO Method and VB Method from the Position of PQS. http://vixra.org/pdf/1710.0326v2.pdf
b...Therefore, in order to "restore" the chemical bond in the corresponding equations and to exclude the inconsistency with the quantum superposition principle, it is necessary to not express MO in members of a linear combination of AO, but postulate the existence of MO as a new fundamental quality that describes a specific chemical bond and is not derived from simpler structural elements. Then we will "return" the chemical bond to the calculation methods and possibly significantly simplify the quantum chemical calculations. This is due to the fact that the energy of the chemical bonds is well known, and since the MO will describe the chemical bond (and the chemical bond energy is known), it will be easy to calculate the MO energy simply by substraction the chemical bond energy from the AO energy.
\tSince the chemical bond is the result of the interaction of fermions and they interact [84] according to the Hückel rule (4n + 2) (or 2n, n - unpaired), we can schematically depict molecular orbitals similarly to atomic orbitals. The number of electrons according to Hückel's rule will be: 2, 6, 10, 14, 18, \u2026
Accordingly, the molecular orbitals of the chemical bond are denoted as follows:
\tMO (s) is a molecular s-orbital, 1 cell, can contain up to 2 electrons.
\tMO (p) is a molecular p-orbital, 3 cells, can contain up to 6 electrons.
\tMO (d) - molecular d-orbital, 5 cells, can contain 10 electrons.
\tMO (f) is a molecular f-orbital, 7 cells, can contain up to 14 electrons.
\tMO (g) is a molecular g-orbital, 9 cells, can contain up to 18 electrons.
\tThen the usual single bond will be described by the molecular s-orbitale (MO(s)).
To describe the double bond, we need to assume that it is formed from two equivalent single bonds (as pointed out by L. Pauling [85]), and is then described by two molecular s-orbitals (2 MO(s)).
\tThe triple bond will be described by a molecular p-orbital (MO (p)), then all six electrons of the triple bond will occupy one molecular p-orbit, which very well explains the difference between acetylene and ethylene (meaning C-H acidity).
\tIn benzene 18 - electronic cyclic system can occupy one molecular g-orbital (MO(g))...\u00bb.
\tTaking into account the above reasoning about the chemical bond, we can say that modern concepts of the chemical bond can not be strictly theoretically fair, but rather qualitative with empirical quantitative calculations. Using quantum mechanics, namely the Heisenberg uncertainty principle and A. Einstein's theory of relativity, one can explain the reason for the formation of a chemical bond (pp. 92 - 103 http://vixra.org/pdf/1710.0326v2.pdf), and understand how electrons form a chemical bond , and how the binding process itself in the molecule. It should be noted that the chemical bond is in fact a separate particle (a fermion or a boson depending on the number of electrons), which we called a semi-virtual particle (pp. 41 - 43, http://vixra.org/pdf/1710.0326v2.pdf) , which exists indefinitely long in a particular molecule.
If we analyze the formation of the chemical bond (one-electron, many-electron) strictly theoretically, then it is difficult to understand the cause of the formation of the chemical bond. There are several problems here:
1. When a chemical bond is formed, when the domain of "existence" of electrons actually decreases (the "volume" of the chemical bond (MO) is much smaller than the "volume" of the corresponding AO, this was emphasized by L. Pauling) in comparison with the original AO ((in other words , that the electron distribution function in a diatomic molecule is much more concentrated than in the case of atoms), the repulsion between electrons inevitably must increase significantly. And then according to Coulomb's law (F=f(1/r ^ 2)) this repulsion can not be compensated in any way This is also noted by L. Pauling, and we assume (pp. 88 - 89, Review. Benzene on the Basis of the Three-Electron Bond. (The Pauli Exclusion Principle, Heisenberg's Uncertainty Principle and Chemical Bond). http://vixra.org/pdf/1710.0326v2.pdf) that he therefore analyzed the interaction of the hydrogen atom and the proton in the entire range of lengths (admitted that the hydrogen atom and H + are retained when approaching) and showed that the connection is not formed in this case (since there is no exchange interaction or Pauling resonance.) This actually showed that even a one-electron bond can not be explained only by the electro-magnetic interaction (that is, the classical approach), and if we go to many-electron bond (two-electron bond, three-electron bond, etc.) and take into account the repulsion between the bonding electrons, it becomes evident that the classical explanation (the electromagnetic approach) can not even provide a qualitative explanation of the cause of the formation of a chemical bond. It inevitably follows that the cause of the formation of a chemical bond can only be explained by quantum mechanics. Moreover, the chemical bond is a "pure" quantum-mechanical effect, in principle this is strictly indicated by the exchange interaction introduced by quantum mechanics, but not having the physical justification, that is, the exchange interaction is a purely formal, mathematical approach, which makes it possible at least some results. The fact that the exchange interaction has no physical meaning can be confirmed by the fact that the exchange integral essentially depends on the choice of the basis wave functions (more precisely, the overlap integral of the basis functions), and therefore, when choosing a certain basis, it can be less modulo, and even change sign on the reverse, which means that two atoms can not be attracted but repelled. In addition, the exchange interaction by definition can not be applied to the one-electron coupling, since there is no overlap integral since we have one electron (but Pauling's resonance can be applied to explain the one-electron bond).
2. In addition, using A. Einstein's theory of relativity, it can be shown that, in the motion of electrons, the field in a molecule can not by definition be a conservative field (pp. 90 - 92, http://vixra.org/pdf/1710.0326v2.pdf). When describing the behavior of electrons in atoms or molecules, it is often (more precisely, almost always) assumed that the motion of electrons is in the average conservative field. But this is fundamentally not true (based on the theory of relativity), and therefore further assumptions are not theoretically rigorous. Moreover, this case (application of the theory of relativity to a chemical bond) directly indicates that it is only possible to explain the cause of the formation of a chemical bond by using jointly quantum mechanics and the theory of relativity of A. Einstein, which we will try to do (see below).
3. It is also especially worth noting that when analyzing the Pauli principle (pages 103-105, http://vixra.org/pdf/1710.0326v2.pdf), it turned out that it can not be applied to chemical bonds, since the Pauli principle can be applied only to systems of weakly interacting particles (fermions), when one can speak (at least approximately on the states of individual particles). Hence it inevitably follows that the Pauli principle does not forbid the existence of three-electron bonds with a multiplicity of 1.5, which has a very important theoretical and practical significance for chemistry. In chemistry, a three-electron bond with a multiplicity of 1.5 is introduced, on the basis of which it is easy to explain the structure of the benzene molecule and many organic and inorganic substances (pp. 6-36, 53-72, http://vixra.org/pdf/1710.0326v2.pdf).
4. It is shown (pp. 105 \u2014 117, http://vixra.org/pdf/1710.0326v2.pdf) that the main assumption of the molecular orbitals method (namely, that the molecular orbital can be represented like a linear combination of overlapping atomic orbitals) enters into an insurmountable contradiction with the principle of quantum superposition. It is also shown that the description of a quantum system consisting of several parts (adopted in quantum mechanics) actually prohibits ascribe in VB method to members of equation corresponding canonical structures.
5. See pp. 116 \u2013 117, Quantum-Mechanical Analysis of the MO Method and VB Method from the Position of PQS. http://vixra.org/pdf/1710.0326v2.pdf
b...Therefore, in order to "restore" the chemical bond in the corresponding equations and to exclude the inconsistency with the quantum superposition principle, it is necessary to not express MO in members of a linear combination of AO, but postulate the existence of MO as a new fundamental quality that describes a specific chemical bond and is not derived from simpler structural elements. Then we will "return" the chemical bond to the calculation methods and possibly significantly simplify the quantum chemical calculations. This is due to the fact that the energy of the chemical bonds is well known, and since the MO will describe the chemical bond (and the chemical bond energy is known), it will be easy to calculate the MO energy simply by substraction the chemical bond energy from the AO energy.
\tSince the chemical bond is the result of the interaction of fermions and they interact [84] according to the Hückel rule (4n + 2) (or 2n, n - unpaired), we can schematically depict molecular orbitals similarly to atomic orbitals. The number of electrons according to Hückel's rule will be: 2, 6, 10, 14, 18, \u2026
Accordingly, the molecular orbitals of the chemical bond are denoted as follows:
\tMO (s) is a molecular s-orbital, 1 cell, can contain up to 2 electrons.
\tMO (p) is a molecular p-orbital, 3 cells, can contain up to 6 electrons.
\tMO (d) - molecular d-orbital, 5 cells, can contain 10 electrons.
\tMO (f) is a molecular f-orbital, 7 cells, can contain up to 14 electrons.
\tMO (g) is a molecular g-orbital, 9 cells, can contain up to 18 electrons.
\tThen the usual single bond will be described by the molecular s-orbitale (MO(s)).
To describe the double bond, we need to assume that it is formed from two equivalent single bonds (as pointed out by L. Pauling [85]), and is then described by two molecular s-orbitals (2 MO(s)).
\tThe triple bond will be described by a molecular p-orbital (MO (p)), then all six electrons of the triple bond will occupy one molecular p-orbit, which very well explains the difference between acetylene and ethylene (meaning C-H acidity).
\tIn benzene 18 - electronic cyclic system can occupy one molecular g-orbital (MO(g))...\u00bb.
\tTaking into account the above reasoning about the chemical bond, we can say that modern concepts of the chemical bond can not be strictly theoretically fair, but rather qualitative with empirical quantitative calculations. Using quantum mechanics, namely the Heisenberg uncertainty principle and A. Einstein's theory of relativity, one can explain the reason for the formation of a chemical bond (pp. 92 - 103 http://vixra.org/pdf/1710.0326v2.pdf), and understand how electrons form a chemical bond , and how the binding process itself in the molecule. It should be noted that the chemical bond is in fact a separate particle (a fermion or a boson depending on the number of electrons), which we called a semi-virtual particle (pp. 41 - 43, http://vixra.org/pdf/1710.0326v2.pdf) , which exists indefinitely long in a particular molecule.
See pp. 88 - 104 Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdf
Benzene on the basis of the three-electron bond:
Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdf
1. Structure of the benzene molecule on the basis of the three-electron bond.
http://vixra.org/pdf/1606.0152v1.pdf
2. Experimental confirmation of the existence of the three-electron bond and theoretical basis ot its existence.
http://vixra.org/pdf/1606.0151v2.pdf
3. A short analysis of chemical bonds.
http://vixra.org/pdf/1606.0149v2.pdf
4. Supplement to the theoretical justification of existence of the three-electron bond.
http://vixra.org/pdf/1606.0150v2.pdf
5. Theory of three-electrone bond in the four works with brief comments.
http://vixra.org/pdf/1607.0022v2.pdf
6. REVIEW. Benzene on the basis of the three-electron bond. http://vixra.org/pdf/1612.0018v5.pdf
7. Quantum-mechanical aspects of the L. Pauling's resonance theory.
http://vixra.org/pdf/1702.0333v2.pdf
8. Quantum-mechanical analysis of the MO method and VB method from the position of PQS.
http://vixra.org/pdf/1704.0068v1.pdf
9. Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdf
Bezverkhniy Volodymyr (viXra): http://vixra.org/author/bezverkhniy_volodymyr_dmytrovych
Benzene on the basis of the three-electron bond:
Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdf
1. Structure of the benzene molecule on the basis of the three-electron bond.
http://vixra.org/pdf/1606.0152v1.pdf
2. Experimental confirmation of the existence of the three-electron bond and theoretical basis ot its existence.
http://vixra.org/pdf/1606.0151v2.pdf
3. A short analysis of chemical bonds.
http://vixra.org/pdf/1606.0149v2.pdf
4. Supplement to the theoretical justification of existence of the three-electron bond.
http://vixra.org/pdf/1606.0150v2.pdf
5. Theory of three-electrone bond in the four works with brief comments.
http://vixra.org/pdf/1607.0022v2.pdf
6. REVIEW. Benzene on the basis of the three-electron bond. http://vixra.org/pdf/1612.0018v5.pdf
7. Quantum-mechanical aspects of the L. Pauling's resonance theory.
http://vixra.org/pdf/1702.0333v2.pdf
8. Quantum-mechanical analysis of the MO method and VB method from the position of PQS.
http://vixra.org/pdf/1704.0068v1.pdf
9. Review (135 pages, full version). Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). http://vixra.org/pdf/1710.0326v3.pdf
Bezverkhniy Volodymyr (viXra): http://vixra.org/author/bezverkhniy_volodymyr_dmytrovych
Bezverkhniy Volodymyr (Scribd):
https://www.scribd.com/user/289277020/Bezverkhniy-Volodymyr#
https://www.amazon.com/Volodymyr-Bezverkhniy/e/B01I41EHHS/ref=dp_byline_cont_ebooks_1
benzene on the basis of the three-electron bond
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 f
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