Benzene on the basis of the three-electron bond.
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Bezverkhniy Volodymyr (viXra): http://vixra.org/author/bezverkhniy_volodymyr_dmytrovychhttp://vixra.org/pdf/1710.0326v4.pdf
https://dx.doi.org/10.2139/ssrn.3065288
https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=2828345
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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 (138 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/1710.0326v4.pdf
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3065288
Notes 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.
Notes 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.
The Pauli exclusion principle and the chemical bond.
The Pauli exclusion principle \u2014 this is the fundamental principle of quantum mechanics, which asserts that two or more identical fermions (particles with half-integral spin) can not simultaneously be in the same quantum state.
Wolfgang Pauli, a Swiss theoretical physicist, formulated this principle in 1925 [1]. In chemistry exactly Pauli exclusion principle often considered as a ban on the existence of three-electron bonds with a multiplicity of 1.5, but it can be shown that Pauli exclusion principle does not prohibit the existence of three-electron bonds. To do this, analyze the Pauli exclusion principle in more detail.
According to Pauli exclusion principle in a system consisting of identical fermions, two (or more) particles can not be in the same states [2]. The corresponding formulas of the wave functions and the determinant are given in the reference (this is a standard consideration of the fermion system), but we will concentrate our attention on the derivation: "... Of course, in this formulation, Pauli exclusion principle can only be applied to systems of weakly interacting particles, when one can speak (at least approximately on the states of individual particles) "[2]. That is, Pauli exclusion principle can only be applied to weakly interacting particles, when one can talk about the states of individual particles.
But if we recall that any classical chemical bond is formed between two nuclei (this is a fundamental difference from atomic orbitals), which somehow "pull" the electrons one upon another, it is logical to assume that in the formation of a chemical bond, the electrons can no longer be regarded as weakly interacting particles . This assumption is confirmed by the earlier introduced notion of a chemical bond as a separate semi-virtual particle (natural component of the particle "parts" can not be weakly interacting).
Representations of the chemical bond given in the chapter "The Principle of Heisenberg's Uncertainty and the Chemical Bond" categorically reject the statements about the chemical bond as a system of weakly interacting electrons. On the contrary, it follows from the above description that in the chemical bond, the electrons "lose" their individuality and "occupy" the entire chemical bond, that is, the electrons in the chemical bond "interact as much as possible", which directly indicates the inapplicability of the Pauli exclusion principle to the chemical bond. Moreover, the quantum-mechanical uncertainty in momentum and coordinate, in fact, strictly indicates that in the chemical bond, electrons are a system of "maximally" strongly interacting particles, and the whole chemical bond is a separate particle in which there is no place for the notion of an "individual" electron, its velocity, coordinate, energy, etc., description. This is fundamentally not true. The chemical bond is a separate particle, called us "semi-virtual particle", it is a composite particle that consists of individual electrons (strongly interacting), and spatially located between the nuclei.
Thus, the introduction of a three-electron bond with a multiplicity of 1.5 is justified from the chemical point of view (simply explains the structure of the benzene molecule, aromaticity, the structure of organic and inorganic substances, etc.) is confirmed by the Pauli exclusion principle and the logical assumption of a chemical bond as system of strongly interacting particles (actually a separate semi-virtual particle), and as a consequence the inapplicability of the Pauli exclusion principle to a chemical bond.
1. Pauli W. Uber den Zusammenhang des Abschlusses der Elektronengruppen in Atom mit der Komplexstruktur der Spektren, - Z. Phys., 1925, 31, 765-783.
2. A.S. Davydov. Quantum mechanics. Second edition. Publishing house "Science". Moscow, 1973, p. 334.
Heisenberg's uncertainty principle and chemical bond.
For further analysis of chemical bond, let us consider the Compton wavelength of an electron:
\u03bbc.\u0435. = h/(me*c)= 2.4263 * 10^(-12) m
The Compton wavelength of an electron is equivalent to the wavelength of a photon whose energy is equal to the rest energy of the electron itself (the standard conclusion is given below):
\u03bb = h/(m*v), E = h*\u03b3, E = me*c^2, c = \u03b3*\u03bb, \u03b3 = c/\u03bb
E = h*\u03b3, E = h*(c/\u03bb) = me*c^2, \u03bbc.\u0435. = h/(me*c)
where \u03bb is the Louis de Broglie wavelength, me is the mass of the electron, c, \u03b3 is the speed and frequency of light, and h is the Planck constant.
It is more interesting to consider what happens to an electron in a region with linear dimensions smaller than the Compton wavelength of an electron. According to Heisenberg uncertainty in this area, we have a quantum mechanical uncertainty in the momentum of at least m*c and a quantum mechanical uncertainty in the energy of at least me*c^2 :
\u0394p \u2265 m\u0435*c and \u0394E \u2265 me*c^2
which is sufficient for the production of virtual electron-positron pairs. Therefore, in such a region the electron can no longer be regarded as a "point object", since it (an electron) spends part of its time in the state "electron + pair (positron + electron)". As a result of the above, an electron at distances smaller than the Compton length is a system with an infinite number of degrees of freedom and its interaction should be described within the framework of quantum field theory. Most importantly, the transition to the intermediate state "electron + pair (positron + electron)" carried per time ~ \u03bbc.\u0435./c
\u0394t = \u03bbc.\u0435./c = 2.4263 * 10^(-12)/(3*10^8) = 8.1*10^(-20) s
Now we will try to use all the above-mentioned to describe the chemical bond using Einstein's theory of relativity and Heisenberg's uncertainty principle. To do this, let's make one assumption: suppose that the wavelength of an electron on a Bohr orbit (the hydrogen atom) is the same Compton wavelength of an electron, but in another frame of reference, and as a result there is a 137-times greater Compton wavelength (due to the effects of relativity theory):
\u03bbc.\u0435. = h/(me*c) = 2.4263 * 10^(-12) m
\u03bbb. = h/(me*v)= 2*\u03c0*R = 3.31*10^(-10) m
\u03bbb./\u03bbc.\u0435.= 137
where R= 0.527 \u212b, the Bohr radius.
Since the De Broglie wavelength in a hydrogen atom (according to Bohr) is 137 times larger than the Compton wavelength of an electron, it is quite logical to assume that the energy interactions will be 137 times weaker (the longer the photon wavelength, the lower the frequency, and hence the energy ). We note that 1 / 137.036 is a fine structure constant, the fundamental physical constant characterizing the force of electromagnetic interaction was introduced into science in 1916 year by the German physicist Arnold Sommerfeld as a measure of relativistic corrections in describing atomic spectra within the framework of the model of the N. Bohr atom.
To describe the chemical bond, we use the Heisenberg uncertainty principle:
\u0394x * \u0394p \u2265 \u045b / 2
Given the weakening of the energy interaction 137 times, the Heisenberg uncertainty principle can be written in the form:
\u0394x* \u0394p \u2265 (\u045b * 137)/2
According to the last equation, the quantum mechanical uncertainty in the momentum of an electron in a chemical bond must be at least me * c, and the quantum mechanical uncertainty in the energy is not less than me * c ^ 2, which should also be sufficient for the production of virtual electron-positron pairs.
Therefore, in the field of chemical bonding, in this case, an electron can not be regarded as a "point object", since it (an electron) will spend part of its time in the state "electron + pair (positron + electron)", and therefore its interaction should be described in the framework of quantum field theory.
This approach makes it possible to explain how, in the case of many-electron chemical bonds (two-electron, three-electron, etc.), repulsion between electrons is overcome: since the chemical bond is actually a "boiling mass" of electrons and positrons, virtual positrons "help" overcome the repulsion between electrons. This approach assumes that the chemical bond is in fact a closed spatial bag (a potential well in the energy sense), in which "boiling" of real electrons and also virtual positrons and electrons occurs, and the "volume" of this potential bag is actually a "volume" of chemical bond and also the spatial measure of the quantum-mechanical uncertainty in the position of the electron.
Strictly speaking, with such a consideration, the electron no longer has a certain energy, momentum, coordinates, and is no longer a "point particle", but actually takes up the "whole volume" of chemical bonding. It can be argued that in the chemical bond a single electron is depersonalized and loses its individuality, in fact it does not exist, but there is a "boiling mass" of real electrons and virtual positrons and electrons that by fluctuate change each other. That is, the chemical bond is actually a separate particle, as already mentioned, a semi-virtual particle. Moreover, this approach can be extended to the structure of elementary particles such as an electron or a positron: an elementary particle in this consideration is a fluctuating vacuum closed in a certain spatial bag, which is a potential well for these fluctuations.
It is especially worth noting that in this consideration, electrons are strongly interacting particles, and therefore the Pauli principle is not applicable to chemical bond (for more details, see the section "The Pauli Principle and the Chemical Bond") and does not prohibit the existence of the same three-electron bonds with a multiplicity of 1.5.
The above is easy to demonstrate with the example of a chemical bond of 1 A length. Then the wavelength of Broglie is written in the form (the length of the chemical bond is L = 2 * \u0394x):
\u03bb = 2*\u03c0*\u0394x
and the Heisenberg uncertainty ratio takes the form:
\u0394x * \u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / 2
from which we get:
L * \u0394p \u2265 \u045b * 137 * 2 * \u03c0
where L is the length of the chemical bond, and \u0394p is the quantum mechanical uncertainty of the momentum of each electron in a given chemical bond.
Whence, we obtain a formula for determining the uncertainty of the momentum in a chemical bond:
\u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / L
Having made the necessary calculations for a length of 1 A, we obtain:
\u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / 10 ^ (-10)
\u0394p \u2265 9.078 * 10 ^ (-22) kg * m / s
That is, the uncertainty in the pulse is greater than me * c
(me * c = 2.73 * 10 ^ (-22) kg * m / s)
(it is clear that the uncertainty of the electron velocity will be greater than the speed of light), which should be based on our assumptions.
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:
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 lengt
The Pauli exclusion principle \u2014 this is the fundamental principle of quantum mechanics, which asserts that two or more identical fermions (particles with half-integral spin) can not simultaneously be in the same quantum state.
Wolfgang Pauli, a Swiss theoretical physicist, formulated this principle in 1925 [1]. In chemistry exactly Pauli exclusion principle often considered as a ban on the existence of three-electron bonds with a multiplicity of 1.5, but it can be shown that Pauli exclusion principle does not prohibit the existence of three-electron bonds. To do this, analyze the Pauli exclusion principle in more detail.
According to Pauli exclusion principle in a system consisting of identical fermions, two (or more) particles can not be in the same states [2]. The corresponding formulas of the wave functions and the determinant are given in the reference (this is a standard consideration of the fermion system), but we will concentrate our attention on the derivation: "... Of course, in this formulation, Pauli exclusion principle can only be applied to systems of weakly interacting particles, when one can speak (at least approximately on the states of individual particles) "[2]. That is, Pauli exclusion principle can only be applied to weakly interacting particles, when one can talk about the states of individual particles.
But if we recall that any classical chemical bond is formed between two nuclei (this is a fundamental difference from atomic orbitals), which somehow "pull" the electrons one upon another, it is logical to assume that in the formation of a chemical bond, the electrons can no longer be regarded as weakly interacting particles . This assumption is confirmed by the earlier introduced notion of a chemical bond as a separate semi-virtual particle (natural component of the particle "parts" can not be weakly interacting).
Representations of the chemical bond given in the chapter "The Principle of Heisenberg's Uncertainty and the Chemical Bond" categorically reject the statements about the chemical bond as a system of weakly interacting electrons. On the contrary, it follows from the above description that in the chemical bond, the electrons "lose" their individuality and "occupy" the entire chemical bond, that is, the electrons in the chemical bond "interact as much as possible", which directly indicates the inapplicability of the Pauli exclusion principle to the chemical bond. Moreover, the quantum-mechanical uncertainty in momentum and coordinate, in fact, strictly indicates that in the chemical bond, electrons are a system of "maximally" strongly interacting particles, and the whole chemical bond is a separate particle in which there is no place for the notion of an "individual" electron, its velocity, coordinate, energy, etc., description. This is fundamentally not true. The chemical bond is a separate particle, called us "semi-virtual particle", it is a composite particle that consists of individual electrons (strongly interacting), and spatially located between the nuclei.
Thus, the introduction of a three-electron bond with a multiplicity of 1.5 is justified from the chemical point of view (simply explains the structure of the benzene molecule, aromaticity, the structure of organic and inorganic substances, etc.) is confirmed by the Pauli exclusion principle and the logical assumption of a chemical bond as system of strongly interacting particles (actually a separate semi-virtual particle), and as a consequence the inapplicability of the Pauli exclusion principle to a chemical bond.
1. Pauli W. Uber den Zusammenhang des Abschlusses der Elektronengruppen in Atom mit der Komplexstruktur der Spektren, - Z. Phys., 1925, 31, 765-783.
2. A.S. Davydov. Quantum mechanics. Second edition. Publishing house "Science". Moscow, 1973, p. 334.
Heisenberg's uncertainty principle and chemical bond.
For further analysis of chemical bond, let us consider the Compton wavelength of an electron:
\u03bbc.\u0435. = h/(me*c)= 2.4263 * 10^(-12) m
The Compton wavelength of an electron is equivalent to the wavelength of a photon whose energy is equal to the rest energy of the electron itself (the standard conclusion is given below):
\u03bb = h/(m*v), E = h*\u03b3, E = me*c^2, c = \u03b3*\u03bb, \u03b3 = c/\u03bb
E = h*\u03b3, E = h*(c/\u03bb) = me*c^2, \u03bbc.\u0435. = h/(me*c)
where \u03bb is the Louis de Broglie wavelength, me is the mass of the electron, c, \u03b3 is the speed and frequency of light, and h is the Planck constant.
It is more interesting to consider what happens to an electron in a region with linear dimensions smaller than the Compton wavelength of an electron. According to Heisenberg uncertainty in this area, we have a quantum mechanical uncertainty in the momentum of at least m*c and a quantum mechanical uncertainty in the energy of at least me*c^2 :
\u0394p \u2265 m\u0435*c and \u0394E \u2265 me*c^2
which is sufficient for the production of virtual electron-positron pairs. Therefore, in such a region the electron can no longer be regarded as a "point object", since it (an electron) spends part of its time in the state "electron + pair (positron + electron)". As a result of the above, an electron at distances smaller than the Compton length is a system with an infinite number of degrees of freedom and its interaction should be described within the framework of quantum field theory. Most importantly, the transition to the intermediate state "electron + pair (positron + electron)" carried per time ~ \u03bbc.\u0435./c
\u0394t = \u03bbc.\u0435./c = 2.4263 * 10^(-12)/(3*10^8) = 8.1*10^(-20) s
Now we will try to use all the above-mentioned to describe the chemical bond using Einstein's theory of relativity and Heisenberg's uncertainty principle. To do this, let's make one assumption: suppose that the wavelength of an electron on a Bohr orbit (the hydrogen atom) is the same Compton wavelength of an electron, but in another frame of reference, and as a result there is a 137-times greater Compton wavelength (due to the effects of relativity theory):
\u03bbc.\u0435. = h/(me*c) = 2.4263 * 10^(-12) m
\u03bbb. = h/(me*v)= 2*\u03c0*R = 3.31*10^(-10) m
\u03bbb./\u03bbc.\u0435.= 137
where R= 0.527 \u212b, the Bohr radius.
Since the De Broglie wavelength in a hydrogen atom (according to Bohr) is 137 times larger than the Compton wavelength of an electron, it is quite logical to assume that the energy interactions will be 137 times weaker (the longer the photon wavelength, the lower the frequency, and hence the energy ). We note that 1 / 137.036 is a fine structure constant, the fundamental physical constant characterizing the force of electromagnetic interaction was introduced into science in 1916 year by the German physicist Arnold Sommerfeld as a measure of relativistic corrections in describing atomic spectra within the framework of the model of the N. Bohr atom.
To describe the chemical bond, we use the Heisenberg uncertainty principle:
\u0394x * \u0394p \u2265 \u045b / 2
Given the weakening of the energy interaction 137 times, the Heisenberg uncertainty principle can be written in the form:
\u0394x* \u0394p \u2265 (\u045b * 137)/2
According to the last equation, the quantum mechanical uncertainty in the momentum of an electron in a chemical bond must be at least me * c, and the quantum mechanical uncertainty in the energy is not less than me * c ^ 2, which should also be sufficient for the production of virtual electron-positron pairs.
Therefore, in the field of chemical bonding, in this case, an electron can not be regarded as a "point object", since it (an electron) will spend part of its time in the state "electron + pair (positron + electron)", and therefore its interaction should be described in the framework of quantum field theory.
This approach makes it possible to explain how, in the case of many-electron chemical bonds (two-electron, three-electron, etc.), repulsion between electrons is overcome: since the chemical bond is actually a "boiling mass" of electrons and positrons, virtual positrons "help" overcome the repulsion between electrons. This approach assumes that the chemical bond is in fact a closed spatial bag (a potential well in the energy sense), in which "boiling" of real electrons and also virtual positrons and electrons occurs, and the "volume" of this potential bag is actually a "volume" of chemical bond and also the spatial measure of the quantum-mechanical uncertainty in the position of the electron.
Strictly speaking, with such a consideration, the electron no longer has a certain energy, momentum, coordinates, and is no longer a "point particle", but actually takes up the "whole volume" of chemical bonding. It can be argued that in the chemical bond a single electron is depersonalized and loses its individuality, in fact it does not exist, but there is a "boiling mass" of real electrons and virtual positrons and electrons that by fluctuate change each other. That is, the chemical bond is actually a separate particle, as already mentioned, a semi-virtual particle. Moreover, this approach can be extended to the structure of elementary particles such as an electron or a positron: an elementary particle in this consideration is a fluctuating vacuum closed in a certain spatial bag, which is a potential well for these fluctuations.
It is especially worth noting that in this consideration, electrons are strongly interacting particles, and therefore the Pauli principle is not applicable to chemical bond (for more details, see the section "The Pauli Principle and the Chemical Bond") and does not prohibit the existence of the same three-electron bonds with a multiplicity of 1.5.
The above is easy to demonstrate with the example of a chemical bond of 1 A length. Then the wavelength of Broglie is written in the form (the length of the chemical bond is L = 2 * \u0394x):
\u03bb = 2*\u03c0*\u0394x
and the Heisenberg uncertainty ratio takes the form:
\u0394x * \u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / 2
from which we get:
L * \u0394p \u2265 \u045b * 137 * 2 * \u03c0
where L is the length of the chemical bond, and \u0394p is the quantum mechanical uncertainty of the momentum of each electron in a given chemical bond.
Whence, we obtain a formula for determining the uncertainty of the momentum in a chemical bond:
\u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / L
Having made the necessary calculations for a length of 1 A, we obtain:
\u0394p \u2265 (\u045b * 137 * 2 * \u03c0) / 10 ^ (-10)
\u0394p \u2265 9.078 * 10 ^ (-22) kg * m / s
That is, the uncertainty in the pulse is greater than me * c
(me * c = 2.73 * 10 ^ (-22) kg * m / s)
(it is clear that the uncertainty of the electron velocity will be greater than the speed of light), which should be based on our assumptions.
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
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. 5-7 http://vixra.org/pdf/1606.0151v2.pdf
2. pp. 1-7 http://vixra.org/pdf/1606.0150v2.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 lengt
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