Report on the Real Structure of Benzene Molecules and the Thickness of Graphene

The problem of the benzene molecular structure has not been solved for a long time. This research proposes a new concept of covalent bonds based on the existing theory: each electron shared by the nucleus corresponds to a half-valent bond, and a half-valent bond can be formed between interval carbon atoms of the benzene ring. A new theory was established. results can quantitatively explain experimental results, such as the hydrogenation heat and ultraviolet spectroscopy of benzene. It has solved more than one hundred years of difficult problems. The design of the new structural forms of benzene molecules shows half-valent bonds with dotted lines, which have a wide range of adaptability, and shows the structural forms and reaction formulas of more than dozens of benzene homologs and derivatives. Under the guidance of the new theory, the stacked three-dimensional structure of benzene was explored. The thickness of the three-layer benzene tube is calculated to be almost equal to the thickness of the graphene. Therefore, it is speculated that graphene may be a three layer structure.


Introduction
Since Kaikule proposed the benzene molecular plane structure of cyclohexatriene, which was inconsistent with the experimental results, many people have also proposed some related structures, which were also unsuccessful. In particular, the experimental results of the hydrogenation heat and the ultraviolet spectrum of benzene that cannot be quantitatively explained are called the mystery of a century 1,2,3. Solving the problem of benzene molecular structure must follow the valence bond theory of chemical bonds 4,5 . The nature of chemical bonds is that the nuclei share electrons. In the existing valence bond theory, the nucleus shares a pair of opposite spin electrons to form one valence bond 6 . This definition is not suitable for the reality of benzene and some other molecules. Moreover, the theory does not prove that the shared electrons must be paired and the spins must be reversed 7,8 . Therefore, here is an attempt to discard the above two insufficient and nonessential conditions. In new theory, it is defined as the atom nucleus share every electron all counted as a half-valent bond. In this way, the theory can be adapted to all molecular structures.
According to the existing molecular orbital theory, the 2s and 2p orbitals of every carbon atom in the benzene ring may be hybridized into a 3 sp 2 orbital and a pz orbital alone. Six sp 2 orbitals in 6 carbon atoms form a regular hexagonal ring using 6 σ bonds. The other 6 σ bonds are connected outside the ring to the hydrogen atom. The remaining 6 unhybridized pz orbitals are linearly combined into 6 molecular orbitals. The molecular structural energy is low, so the structure is stable 9,10 . The 6 carbon nuclei of the benzene ring share 6 electrons, forming 6 half-valent π bonds and connected into a large half-valent π bond ring. It is the ground state of the benzene molecule.
When getting energy outside the system, 1 electron in each bonding orbital transitions to the anti-bonding orbital and occupies it. All electrons become the same spin 11 . The active electrons increase the mutual repulsion between adjacent pz orbital electrons, and the steric hindrance effect 9 causes one of the pz orbitals to turn to the opposite phase of the benzene ring plane. Since then, the positive and negative phases each have three interval carbon atom pz orbitals, forming a new neighboring relationship of triangular rings. In each phase, there are three interval carbon nuclei sharing three electric π electrons, forming three half-valent π bonds and their bond rings. This is the excited state of the benzene molecule. Only in the excited state can molecules participate in chemical reactions.Such a valence bond follows the tetravalent requirement of carbon, so it satisfies the saturation of the covalent bond 4 .
The half-valent bond ring of the benzene molecule the movement of electrons produces a ring current and its induced magnetic field to make the molecular structure more stable.
This series of concepts formed a new theory of the planar structure of benzene molecules. When the ring planes of the excited states of two benzene molecules are flipped and stacked, these two rings are completely symmetrical. The 3 pz orbital of the interval carbon atoms of the benzene ring can be completely docked, and the electron cloud overlaps to form 3 σ bonds. A two layer ring structure can be synthesized out. However, this two-layer structure is unstable, and it is also easy to form a three-layer benzene tube. The top and bottom of this three-layer benzene tube are exactly the same as a benzene molecular structure, so it is a stable three-dimensional structure. It can be called a three layer unit benzene tube. It is even possible to form a multilayer benzene tube.Surprisingly, the thickness of the three-layer unit benzene tube is equivalent to the thickness of a layer of graphene.
Given that the structure of graphene is similar to a fused ring compound of benzene, referring to the general physical and chemical properties of graphene, it is suspected that graphene may have a three-layer structure.

Method
To verify the correctness of the new theory of the benzene molecular structure, an equivalent electronic model of the benzene ring was established, carrying out the coordinate table transformation and over to a hydrogen atom model. Then, the equivalent electronic wave function and wave equation are established. The variational method was used to solve the energy eigenvalues of the equation and calculate the equivalent electron energy levels and transition energies 7,12,13 The equivalent electronic ground state and excited state transition energy are used to quantitatively explain the hydrogenation heat and ultraviolet spectrum of benzene, as well as the bond length of the benzene ring. The calculated value is compared with the experimental result to verify the correctness of the new theory of the planar structure of the benzene molecule. The comparison of the calculated thickness of the three-layer benzene tube with the thickness of the graphene documented in the data shows the basis for suspicion that graphene is also a three-layer structure.

Quantitative interpretation of the hydrogenation heat of benzene
In the benzene ring, 6 pz electrons revolve around the carbon nucleus where they are located, and the movement of each electron has an arc in the same direction along the benzene ring. They will be connected in an arc to form a circle. The overall behavior is similar to a circular motion of an equivalent electron along the circumscribed circle of a benzene ring. Generate the pulse loop current and orresponding magnetic field.
The ground state and the excited state are the two energy levels of the equivalent electron. In this way, an equivalent electronic model of benzene was established. To make the model transition to the hydrogen-like atom model 7 and determine its kinetic energy and potential energy, the wave function and Schrodinger equation 12 were established. However, the kinetic energy of the equivalent electron is not known. The only amount that can be inferred is the work done by the electron to circumscribe a circle around the benzene ring.
The question is whether it is possible for WH to be seen as kinetic energy. First, the certain distance of a circle around it, that is, when the perimeter is written in the form of integral, and the force is also written in the form of differential: It seems that at the end point of the circle, WH and kinetic energy Ek can be equal It can also be said that at this point, it is possible to change the equivalent electron model to a hydrogen atom-like model. Similarly, at this point, the kinetic energy EK and the potential energy VH of the electrons outside the hydrogen nucleus are also equal.
Obviously, it has the following relationship with the general form of force in the hydrogen atom mode: Comparing (6) with (7), the force of the rotation of work done along the benzene ring is less than the force of the electromagnetic field, To make the force of the former equal to the latter, the only way to change the radius is. If is set  (8) and g has nothing to do with r. We get This clearly shows that the difference between the two expressions of force is mainly reflected in the radius r. If r in (9) is regarded as a coordinate transformation, this transformation can make the equivalent electron model further transition to the hydrogen-like atom mode 13 .
With reference to (7), (8) and (9), the potential energy of the equivalent electron can also be written more in the general form 14 In (10), VB is the equivalent electronic potential energy of the benzene ring, e is the electronic charge, and ε0 is the vacuum permittivity. Therefore, as the equivalent electronic coordinate transformation of the benzene ring, refer to (9) and (10), which can be written as a general transformation form: Based on the abovementioned equivalent electrons, a reciprocating circular motion is made along the benzene ring, and the abovementioned conditions are met only at the end of a circle. Therefore, in the new coordinate system, it is reasonable to set the motion period to 2nπ. According to these conditions, resimulate the Schrodinger wave function 7 , from (4) (10) (11), Planck's formula and De Broglie's formula 7 , establish the equivalent electronic wave function. then

  
In the wave function (12), n is a natural number, λ is the wavelength, ν is the frequency, r is the radius of the benzene ring, h is the Planck constant, p is the electron momentum, m is the static mass of the electron, u is the electron velocity, EK is the kinetic energy, E is the total energy, and V is the potential energy. With reference to (10), (12) and Schrodinger's equation 7,12 , the three-dimensional wave equation of the equivalent electron can be obtained: Substitute (10) into (13) to get Equation (14) is converted to the spherical coordinate equation To solve the energy eigenvalue E in equation (15), the Lagrange undetermined coefficient method is applied 13,14 . The Hamiltonian operator 14 is used in the algorithm, which must meet the following conditions: In (16) and (17), H is the Hamiltonian quantity, E is the energy eigenvalue, and η is the undetermined coefficient. Since only the r part of (15) Suppose: the variational function is ψ= e -ar , and a is a positive real number.
Through (16), (17) and (18), the undetermined coefficient η can be calculated by the variational method as follows: by (16), (17)and (19) Substituting (20) into (19), the coefficient η to be determined is From (16), (17), (18), (19) and (21), the calculated energy eigenvalue 14 is In formula (22), E is the eigenvalue of the equivalent electron energy, but it is still not clear that it is the lowest value. It can be calculated only after turning it into an energy level formula.
In (23), EH is the lowest energy level of extranuclear electrons of hydrogen atom 7 . En is the energy level of the equivalent electron. n is number of energy levels. It is also the two states of the benzene molecule. When n = 2, the energy level is E2 and is the lowest energy level. It is the ground state and cannot participate in chemical reactions.
When n = 1, the energy level is E1, which must be an excited state. Can participate in chemical reactions? When in an excited state, the electrons further increase their energy, benzene hydrogenates to form cyclohexane, the electrons escape, and the benzene ring does not exist. If you regard it as an extreme state of energy level, it can only be n=0, and the energy level is E0= 0. These energy levels are as follows:

Its transition energy should be
where ΔE2 is the transition energy of the ground state. ΔE1 is the transition energy of the excited state. If the tiny b is not counted, the hydrogenation heat of benzene is a constant composed entirely of basic physical constants 12 , denoted as BH.
In (30), the ground state transition energy ΔE2 is related to the ultraviolet light energy absorbed by the benzene molecule, and combined with (27) and (28), the Rydberg constant R∞ can also be calculated.

Quantitatively explains of the ultraviolet spectrum of benzene
General benzene UV spectrum 15,16 image, superimposed image of a large number of benzene molecules. It shows a strong single peak at 184 nm, a strong dentate peak at 203-212 nm, and a weak dentate peak at 230-270 nm. In the infrared spectrum, there are skeleton vibration peaks at 6250 nm and 6670 nm and C-H stretching vibration peaks at 3230 nm and 3300 nm.
To interpret these spectra, first use the Planck formula Calculate the energy corresponding to the wavelength. In (31), E is the energy, λ is the wavelength of the absorption peak, h is the Planck constant, and c is the speed of light.
Substituting the value in, the calculation results are shown in Table 1. Table 1 The energy corresponding to the peak wavelength of the infrared and ultraviolet spectra of benzene
Simplified calculation by Huckel's 7,17 molecular orbital theory, the wave function and energy level of the benzene molecular orbital are: According to the new theory of benzene molecular structure, combining (27) and (28), ground state and excited state energy levels, the corresponding (32) is (27) In (36), the Coulomb integral α coincides with the negative value of the half-valent π bond energy between the carbon atoms in the benzene ring. Moreover, both α and β are constants composed of basic physical constants, which are composed of (36) and (37), and the relationship between the two is obtained In Table 1, the infrared spectrum 7,17 shows that the benzene ring skeleton vibration is the basic molecular vibration, and the energy average value is E6460=0.192 eV. C-H flexural vibration can be regarded as the characteristic of benzene ring resonance that makes the ring expand and shrink. The average value of resonance energy is E3265=0.380 eV. -β is used to judge the energy corresponding to the wavelength of the ultraviolet spectrum to briefly define and quantitatively explain the ultraviolet spectrum of benzene (see Table 2).   Table 1, Table 2 The wave function is When a free particle moves in a circle along a ring with a radius of r (like an equivalent electron), for the wave function to satisfy the single value condition, the wavelength λ must satisfy 13 2 , 0,1, 2 hr q pq

Design methods of new plane structural forms of benzene molecule
In the design of the planar structural form of the benzene molecule, the dotted line represents the half-valent bond. The simple form of the ground state is a double ring of a regular hexagon. The outer circle is a solid line, and the inner circle is a dashed line. The outer ring of the excited state is the same as the ground state, and the inner ring is composed of two dashed equilateral triangles that are inverted from each other.
The positive triangle represents the positive phase, and the inverted triangle represents the negative phase (see Figure 1).

Basic structural forms of fused ring aromatics of benzene design example
The new structure of polycyclic aromatic hydrocarbons (PAHs) is not formed by splicing the same Kekule style before. The internal structure of each benzene ring in the structural form is different. However, these changes are not arbitrary but are determined by the internal structure. The structure is unique. Moreover, each ring conforms to the overall structure. Such a structural form can truly record the chemical reaction process (see Figure 2).

Naphthalene Anthracene Phenanthrene
Pyrene Guanidine   PAHs carcinogenic effects. These newly designed structural forms (see Figure 4) found 3 of the strong carcinogenic PAHs all contain one double bond. See Table 3.  The results in Table 3 show that the newly designed PAH structural formula is helpful for judging the carcinogenicity intensity. Of course, there are many carcinogenic factors, and it is not enough to judge by the molecular structure alone 19 .

Structure and reaction design of homologs and derivatives of benzene
The types of homologues and derivatives of benzene are many and complex, which test the universality and practicability of the new design method. Not only can the structural formula be easily designed, but it can also be used to record chemical reaction formulas.

Phenylbenzene structural forms and reaction formula
Phenyl 2 is a special molecular structure composed entirely of a benzene ring. It is not like the fused ring compound of benzene tightly joined together but the structural forms connected to each other through bouds (see Figure 5).

Design examples of structural forms of benzene homologs and derivatives
Design examples of the planar structure form of benzene homologs and derivatives (see Figure 6 The design method of forming a half-valent bond between the carbon atoms of the benzene ring has a wide range of simplicity and versatility (see Figure 7).

Toluene to benzoic acid reaction
Reaction of salicylic acid to aspirin The benzene ring participates in the free radical 1,5-rearrangement reaction In the study of the three-dimensional structure of benzene, it was found that the thickness of the three-layer unit benzene tube was almost equal to the thickness of the graphene data 2,20 . Calculation method This total thickness of the three-layer benzene tube is easy to calculate. The three layers are connected by two σ bonds, the top and bottom pz orbitals are in the same direction, and only one pz orbital length is counted, that is, the 0.5 σ bond length. The total thickness of the three-layer structure is 2.5 times the σ bond length (see Figure 8).
The length of this σ bond, calculated according to the effect of the relevant bond force, will not exceed the bond length of the benzene ring. With a benzene ring bond length of 0.1397 nm, the total thickness of the three-layer structure is 2.5 times the σ bond length, that is, 0.349 nm. .The thickness of graphene is 0.334-0.335 nm, which is very close. Therefore, the total thickness of the three layer unit benzene tube will not exceed 0.349 nm.
The energy required to synthesize a multilayer benzene tube can be calculated.
Except for each half of the benzene ring structure in the top and bottom layers, the others are all cyclohexane-type single ring laminated benzene tubes, which release (n-1) times the heat of hydrogenation, that is, (n-1) BH. At the same time, 3 (n-1) times the energy for C-C bond synthesis must be obtained from outside the system.
According to the general C-C bond energy of 3.590 eV (346 kJ/mol) 11 , the total energy required to form an n layer benzene tube is =8.605(n-1)eV (5-1) When n=2, the total energy of the 3 C-C σ bonds between the two layers is only 8.605 eV, which is much weaker than the total energy of 6 σ bonds in each ring. Therefore, the interlayer structural energy is much smaller than the structural energy of the layer itself. It is the foundation that tends to be twisted, tilted or broken. It is conceivable that honeycomb benzene, which is composed of a fused ring compound of benzene, can be torn into a single layer with tape such as graphene 20,21 .
The study of the real structure of benzene molecules has greatly broadened the thinking on the structure of benzene and graphene. Imagine that if graphene is truly a single layer structure, the pz orbitals of the carbon atoms spaced on the six-carbon ring 21 are vertical. Single-layer graphene with the same phase is stacked on a flip surface so that the pz orbitals are completely symmetrical. Under certain conditions (high temperature, high pressure, catalyst), it will be linked by bonds to form a double layer three-dimensional structure. The relatively stable three-layer structure has many characteristics similar to the one-layer structure. In addition, stable, like the honeycomb benzene mentioned above.
Many data indicate that the thickness of single-layer graphene 20 is 0.334-0.335 nm. There are more estimated to be 0.34-0.35 nm or thicker. However, to date, there is no conclusive evidence that graphene must be a single layer structure. What is puzzling is that the thickness of these single-layer graphene data is equivalent to the thickness of a three-layer benzene tube. The benzene ring bond length is 0.1397 nm, and the calculated three-layer similar structure thickness is 2.5 times the benzene ring bond length, which is 0.349 nm. When the graphene superlattice constant 22 of benzene is 0.246 nm, the calculated side length of the hexagonal carbon ring (or the vertical σ bond length between two layers) is 0.142 nm. It is recognized that the bond length of the C-C bond in the graphite crystal is also 0.142 nm. Its 2.5 times is 0.355 nm. All these calculations are basically consistent with the recognized thickness of graphene.
However，The thickness of graphene is questionable. According to the graphene superlattice constant of 0.246 nm, the diameter of the six carbon rings is also less than 0.3 nm, and the thickness of a single layer is the thickness of carbon atoms of 0.334 nm. It is impossible for the thickness of one carbon atom to be larger than the diameter of a ring formed by 6 carbon atoms.
At present, it is generally recognized that graphene is a two-dimensional structure. When two layers of graphene are stacked together, the interaction between them is regarded as a van der Waals heterostructure. This may be related to the opposite of the top and bottom magnetic fields.
In addition to the inconsistencies with these calculated thicknesses, graphene also exhibits highly stable chemical properties, physical properties, solid structure, good electrical conductivity and thermal conductivity, high hardness and toughness, etc., which are similar to metal lattices 22 . Therefore, it also shows that graphene is not a single-layer structure, so graphene is more like a three-dimensional structure.
If a three-dimensional benzene tube and honeycomb graphene exist, their crystal lattice can hold a large number of electrons and can conduct electricity. A large number of regular hexagonal carbon rings form the line at the center of the tube. If there is no deflection or distortion 22 , it is likely to become an undisturbed channel for superconducting electrons and is an ideal superconducting structural material.

Results
Represents the excited state transition energy of the equivalent electron of the benzene ring of the benzene molecule, which is only a coefficient b that is 0.231% different from the experimental value of the hydrogenation heat of benzene. When this coefficient is neglected, the heat of hydrogenation is a constant composed of basic physical constants. Li Debao's constant is proportional.
The energy corresponding to the wavelength peak of the ultraviolet spectrum of benzene is in the transition energy range of the equivalent electronic ground state. The transition energy is 8 times the integral of Huckel's theory. From the median wavelength peak of benzene ultraviolet spectrum, the calculated benzene ring bond length is almost equal to the benzene molecular bond length measured by Raman spectroscopy.
The half-valent bond is represented by the dashed line, and the planar structure design method that can form a half-valent bond between the carbon atoms of the benzene ring has a wide range of simplicity and versatility. In this way, more than 50 structural formulas and chemical reaction examples of benzene homologs and derivatives have been easily designed. And found that the strong carcinogenic polycyclic aromatic hydrocarbon molecules all contain double bonds.
Benzene molecules are stacked on a plane, and it is possible to form a multilayer benzene tube. The calculated energy required is 8.605 (n-1) eV. The thickness of the three-layer benzene tube is 0.349nm, which is consistent with the thickness of graphene.

Discussion
When a new concept of covalent bonds is proposed based on the nature of chemical bonds, that is, every electron shared between atomic nuclei is recorded as half valence.
There are two states of benzene molecule: ground state and excited state. It is deduced that a half-valent bond can be formed between carbon atoms in the excited state of Under the guidance of the new theory, the stacked three-dimensional structure of benzene was explored.Equivalent to the thickness of a layer of graphene.Graphene, a fully carbonized structure of fused ring aromatic hydrocarbons similar to benzene, in addition to the thickness equivalent to the three layer unit benzene tube, also has chemical stability, harder and stronger toughness than steel, and good thermal and electrical conductivity. These properties are more similar to the characteristics of a three-dimensional structure, and their properties are more similar to the characteristics of a three-dimensional structure.If graphene is determined to have a three layer structure, in which a large number of regular hexagonal carbon tubes are connected at the center, without deflection and distortion it is likely to become an undisturbed channel for superconducting electrons.