Volodymyr Bezverkhniy.

Review. Benzene on the basis of the three-electron bond. Theory of three-electron bond in the four works with brief comments (review). 2016.

Volodymyr Dmytrovych Bezverkhniy,2017

Vitaliy Volodymyrovich Bezverkhniy, ,2017



Iexpress my deep gratitude tomy son, Bezverkhniy Vitaliy Volodymyrovich, for participation inthe development ofthe theory (some parts as aco-author), and for his invaluable contribution tothe English translation.

Abstract: Using the concept ofthree-electron bond we can represent the actual electron structure ofbenzene and other molecules, explain specificity ofthe aromatic bond and calculate the delocalization energy. Gives theoretical justification and experimental confirmation ofexistence ofthe three-electron bond.

It was shown, that functional relation y = a+ b/x +c/x2fully describes dependence ofenergy and multiplicity ofchemical bond from bond distance.

Keywords: benzene, three-electron bond, semi-virtual particle, fermion, entangled quantum state, Interfering Universe.


Chemical bond has been always abasis ofchemistry. Advancement ofchemical science can be considered as evolution, development ofconcepts about chemical bond. Aromatic bond is fundamental basis oforganic chemistry. Concept ofthree-electron bond inbenzene molecule enable toexplain specificity ofaromatic bond. It also becomes apparent, why planar molecules with 6, 10etc. electrons (according toH?ckel rule 4n +2) must be aromatic, and planar molecules with 4, 8etc. electrons cannot be aromatic bydefinition.

Description ofchemical bond, that is given byquantum theory, especially interms ofmethod ofmolecular orbitals, is just amathematical model. This model is an approximate representation ofmolecules and its bonds, whereas quantum-mechanical calculations oforganic molecules require considerable simplifications and are extremely complicated.

Concept ofthree-electron bond and developed mathematical relations inthis work are rather simple, illustrative and give exact results ofdifferent values (bond multiplicity, chemical bound energy, delocalization energy ofbenzene). One must clearly imagine, that three-electron bond is joint interaction ofthree electrons with relative spins, that resultsinnew type ofchemical bond (A A(+ +), A B (+ +)). This bond type, three-electron bond, makes possible todescribe real molecules oforganic and inorganic compounds without invoking virtual structures, which do not exist inreal terms.

Using ofthree-electron bond before description ofbenzene molecule enables todetermine delocalization energy ofbenzene inan elementary way, understand why multiplicity of- bond ofbenzene is more than 1.5and tounderstand the main point ofaromatic bond ingeneral, which is appeared tobe rather illustrative.

Besides, for determination ofdelocalization energy it is not required toselect reference structures. Delocalization energy follows from the concept ofaromaticity ofbenzene and its structure on the basis ofthree-electron bond.

Inote that the three-electron bond todescribe the benzene molecule used W.O.Kermak, R. Robinson and J. J.Thomson at the beginning ofthe 20th century [5,6].

Benzene molecule with three-electron bond (W.O.Kermak and R. Robinson, J. J.Thomson).

But since it is not taken into account the spin ofelectrons, have already started cyclooctatetraene problems and therefore the description ofthe benzene molecule byathree-electron proved unsuccessful. Using the three-electron bond with multiplicity of1.5and take account ofthe spin ofeach electron leads tovery good results inthe description ofthe benzene molecule and explain the aromaticity ingeneral. With the help ofthree-electron bond with multiplicity of1.5can be represented byareal formula ofmany organic and inorganic molecules without the aid ofvirtual structures.

2.Structure ofthe benzene molecule on the basis ofthe three-electronbond

2.1. Results and discussion

Supposing that the chemical bond between two atoms can be established bymeans ofthree electrons with oppositely oriented spins (???) the structure ofthe benzene molecule can be expressed as follows (see figure 1and figure2):

benzene molecule on the basis ofthe three-electronbond,spin

It is interesting topoint out that spins ofcentral electrons on opposite sides have an opposite orientation (see figure 2). Now letus consider indetail the interaction ofsix central electrons between themselves. They will be itemized as shown infigure 2. As the spin ofelectron 1and those ofelectrons 2and 6are oppositely oriented (see figure 2) (1(+), 2(-), 6(-)), electron 1will be attracted toelectrons 2and 6respectively. Lets indicate that the distance between electrons 1and 6or 1and 2is equal to1.210? which can be easily shown taking into account the distance between atoms ofcarbon inbenzene tobe 1.397? and the angle between carbon atoms amount to120degrees. Letus compare the distance between electrons 1and 6and 1and 2bond lengths inethane, ethylene and acetylene[7]:

bond lengths inethane, ethylene, acetylene and distance between electrons (1and 2) inbenzene

As we observe, the distance between central electrons 1and 2and 1and 6ofthebenzene molecule is approximately equal tothat between carbon atoms inthe acetylene molecule, therefore, the interaction between electrons 1(+) and 2(-) and 1(+) and 6(-) has tobe rather considerable. Letus express the attraction with arrows. According tosumming up vectors the resultant vector will be directed tothe centre, which means that electron 1under the influence ofelectrons 2and 6will move tothe centre (figure3):

benzene on the basis ofthe three-electron bond, summing up vectors

If we take alook at electron 4we see the similar situation with it (figure 4) and itwillalso move tothe centre and, more importantly, its spin and that ofelectron 1will be oppositely oriented, i.e. electron 1(+) and electron 4(-) will be attracted through the cycle. Electrons 6(-) and 3(+) and electrons 2(-) and 5(+) will interact similarly. The distance between electrons 1and 4inbenzene is equal to2.420?. It is interesting, that this distance is twice as much than distance between electrons 1and 2, or between electrons 1and 6(1.210? ? 2= 2.420?). This interaction through the cycle constitutes the essence ofthe delocalization ofelectrons, ofcourse together with athree-electron bond. Since besides the three-electron bond inthe benzene molecule there is an interaction through the cycle, meaning that the benzene nucleus undergoes akind ofcompression it is clear that the c-c bond multiplicity inbenzene will exceed1.5.

So, the aromatic system is acyclic system with three-electron bonds where an interaction ofcentral electrons through the cycle is observed. Inthe benzene molecule there are three interactions through the cycle-pairwise between electrons 1(+) and 4(-), 2(-) and 5(+), 3(+) and 6(-), as shown infigure5:

benzene on the basis ofthe three-electron bond, interaction through the cycle

Carbon atoms inbenzene are sp?-hybridized. The three-electron bond between carbon atoms inthe benzene molecule can be represented as follows:

Carbon atoms inbenzene have an octet equal to8(3+3+2= 8). It should be pointedout that due tothe largest distance from the atoms nuclei the central electrons ofthe three-electron bond are supposed tobe the most mobile compared toother electrons ofthe three-electron bond. The interaction ofcentral electrons with opposite spins through the cycle can easily explain why cyclobutadiene and cyclooctatetraene are not aromatic compounds:

cyclobutadiene and cyclooctatetraene (three-electron bond)

As we see both incyclobutadiene and cyclooctatetraene, electrons interacting through the cycle have the same spins and, clearly, will be repulsed, therefore there will be no interaction through the cycle and the molecule will not be aromatic. Incyclobutadiene at the expense ofsmall distance it causes the appearance ofantiaromatic properties, and incyclooctatetraene there is apossibility offormation ofnon-planar molecule, where interaction ofcentral electrons becomes impossible and molecule losing the interaction through the cycle loses also three-electron bonds, that results inastructure, inwhich single and double bonds alternate.

Explanation, that cyclooctatetraene is non-aromatic, because it is non-planar and does not hold water, insomuch as dianion ofcyclooctatetraene is aromatic and has planar structure [8],[9].


X-ray crystal structure analysis determined crystal structure ofpotassium salt ofdianion 1,3,5,7-tetramethylcyclooctatetraene [10], [11].

Octatomic cycle is planar with lengths of- bonds nearly 1.41?.


From the mentioned above we can make aconclusion: cyclooctatetraene conforms tothe shape ofbath tub not because ofhigh angular pressure (15) at planar structure, but because byinteraction through the cycle central electrons ofthree-electron bonds have equal spin and will push away. Thus for energy reduction cyclooctatetraene conforms tothe shape ofbath tub and becomes non-planar, that disables interaction ofcentral electrons.

Cyclobutadiene represents rectangular high reactivity diene [8, p.79].

It is also interesting toobserve cyclodecapentaene (cis-isomer [10] -annulene).

cyclodecapentaene (three-electron bond)

cyclodecapentaene, distance

Whereas central electrons ofthree-electron bonds have opposite spins, then interaction through the cycle is possible. But distances between central electrons on opposite sides, which interact through the cycle, are extremely long (4.309? if accept L- = 1.400? for regular decagon), angular pressure is high (24) and thats why stabilization at the expense ofinteraction through the cycle at such long distance will be low and cannot cover energy consumption for creation ofplanar molecule.

Cyclodecapentaene was received inthe form ofcrystalline substance at 80. On spectrums ??-NMR and ?-NMR it was determined, that compound is non-planar and is olefin, that is logical on the basis oflong distance between central electrons [8, p. 84], [12].

Lets draw our attention tothe fact that ingoing from benzene tocyclooctatetraene and tocyclodecapentaene distance increases not only between central electrons on the opposite sides (interaction through the cycle), but also between neighboring central electrons.

Lets show it on figure.

benzene on the basis ofthe three-electron bond, distance between electrons (benzene, cyclooctatetraene, cyclodecapentaene)

As we can see distance between neighboring central electrons 1and 2inbenzene makesup 1.210?, inregular octagon 1.303?, and inregular decagon 1.331? (almost as distance between carbon atoms inethene molecule). That is bygoing from benzene toregular octagon and decagon not only angular pressure (0, 15, 24) and distance between central electrons increase, which are situated on the opposite sides (2.420?; 3.404?; 4.309?), as well as distance between neighboring central electrons 1and 2(1.210?; 1.303?; 1.331?), that causes considerable weakening ofinteraction through the cycle inregular decagon. Thats why regular hexagon (benzene) is ideal aromatic system. As angular pressure is equal tozero, distances between central electrons both neighboring and situated on the opposite sides are minimal (accordingly 1.210? and 2.420?). I.e. interaction through the cycle will be maximal. Bygoing toregular decagon these advantages will be lost. Thats why cyclodecapentaene is olefin.

Letus note for comparison that if we take Lc-c = 1.400? for the planar cyclooctatetraen, we will have L (15) = 3.380?, L (12) = L (81) = 1.293? which vary just slightly from the above mentioned distances between the central electrons at L- = 1.410?.

Bymeans ofthe interaction through the cycle together with the three-electron bond, aromaticity ofcoronen, [18] -annulene, naphthalene and other organics substances can be explained (see conclusion).

Now lets pass tothe definition ofdelocalization energy ofbenzene. It is easy toshow, that relation multiplicity = f (L) and = f (L), where multiplicity is multiplicity ofbond, L length ofbond in?, Š energy ofbond inkj/mole will be described byfunction y = a+ b/x + c/x? for any types ofbond (C-C, C-N, C-O, C-S, N-N, N-O, O-O, C-P).

We shall consider ethane, ethylene and acetylene tobe initial points for the c-c bond.

For lengths ofbonds letus take the date[7]:

bond lengths inethane, ethylene and acetylene

As usual, the - bond multiplicity inethane, ethylene and acetylene is taken for 1, 2,3.

For energies ofbonds letus take the date [7, p. 116]:

energies ofbonds inethane, ethylene and acetylene

The given bond energies (according toL. Pauling) are bond energy constants expressing the energy that would be spent for an ideal rupture ofthese bonds without any further rebuilding ofthe resulting fragments. That is, the above mentioned energies are not bond dissociation energies.

Having performed all necessary calculations we obtain the equation:



From these equations we find:

cc benzene multiplicity (L = 1.397?) = 1.658

cc graphite multiplicity (L = 1.42?) = 1.538?1.54

Ecc benzene (L = 1.397?) = 534.0723kj/mole

Ecc graphite (L = 1.42?) = 503.3161kj/mole

Being aware that the benzene has the three-electron bonds and also the interaction through the cycle, we can calculate the interaction through the cycle energy.

benzene on the basis ofthe three-electron bond, interaction through the cycle


from the equation we find L = 1.42757236?.

So, if the benzene molecule had aclean three-electron bond with a1.5multiplicity the c-c bond length wouldbe L = 1.42757236?.

Now letus determine the energy ofthe clean three-electron bond with a1.5multiplicity knowing its length L = 1.42757236?:

Ec c (L =1.42757236?) = 493.3097kj/mole

Taking into account that the benzene c-c bond energy with a1.658multiplicity is equal toEc-c benzene = 534.0723kj/mole, the difference will make:

?E = 534.0723kj/mole 493.3097kj/mole = 40.7626kj/mole.

40.7626kj/mole is the energy ofinteraction through the cycle per one c-c bond. Therefore, the energy ofinteraction through the cycle will be two times higher:

E1 = 40.7626kj/mole ? 2= 81.5252kj/mole (19.472kcal/mole)

It is clear that the three interactions through the cycle present precisely the working benzene delocalization energy whichis:

E = 3E1 = 3? 81.5252kj/mole = 244.5756kj/mole (58.416kcal/mole)

benzene on the basis ofthe three-electron bond, delocalization energy

It is also possible tocalculate the benzene molecule energy gain incomparison withthecurved cyclohexatriene (letus assume that energy ofC-H bonds inthese molecules is similar). For this we calculate the sum ofenergies ofsingle and double c-c bonds incyclohexatriene:

E2 = 3Ecc +3Ec?c = 2890.286kj/mole

The energy ofsix benzene c-c bonds with a1.658multiplicity is equalto:

E3 = 6 534.0723kj/mole = 3204.434kj/mole

Therefore, the gain energy ofbenzene compared tocyclohexatriene will amountto:

E = E3 E2 = 3204.434kj/mole 2890.286kj/mole = 314.148kj/mole (75.033kcal/mole).

2.2. Experimental

Lets show more detailed calculation ofratios for our mathematical relations. Lets consider relation Multiplicity = f (L) and E = f (L) for - bonds, where multiplicity is multiplicity ofbond, L length ofbond in?, Š energy ofbond inkj/mole.

As initial points for the given bonds we will use ethane, ethene and acetylene. For the length ofbonds letus take the findings[7]:

bond lengths inethane, ethylene and acetylene

As usual, the - bond multiplicity inethane, ethylene and acetylene is taken for 1, 2, 3. For the energy ofbonds letus take the findings [7, p. 116]:

energies ofbonds inethane, ethylene and acetylene

If we have two variants and we received the set ofpoints and we marked them on the plane inthe rectangular system ofcoordinates and if the present points describe the line equation y = ax + b that for choose the coefficients aand b with the least medium-quadratic deflection from the experimental points, it is needed tocalculate the coefficients aand b bythe formulas:



n-the number ofgiven values x ory.

If we want toknow how big is the derivative, it is necessary tostate the value ofagreement between calculated and evaluated values y characterized bythe quantity:


The proximity ofr2 toone means that our linear regression coordinates well with experimental points.

Letus find bythe method ofselection the function y = a+ b/x + c/x2 describing the dependence multiplicity = f (L) and E = f (L) inbest way, ingeneral this function describes this dependence for any chemical bonds.

Letus make some transformations for the functiony = a+ b/x + c/x2, we accept

X =1/x,

than well receive: Y = b1 + cX, that is the simple line equality,than



nthe number ofgiven valueY.

Letus find afrom the equality:

?y = na + b? (1/x) + c? (1/x2),(9)

when n =3.

Letus find now multiplicity = f (L) for C?C, C?C,C?C.

Table 1. Calculation ofratios for relation Multiplicity = f(L).

1/x1 = 0.64808814, x1 = 1.543, y1 =1

? (1/x2) = 1.66729469, ? (1/x) = 2.22534781when n =3

c = 11.28562201,

b = 5.67787529,

a= 0.06040343

Letus find from the equation:

Multiplicity CC (ethane) =1.

Multiplicity C?C (ethylene) =2.

Multiplicity C?C (acetylene) =3.

Multiplicity CC (graphite) (L = 1.42?) = 1.538? 1.54.

Multiplicity CC (benzene) (L = 1.397?) = 1.658.

As we can see the multiplicity CC ofbenzene bond is 1.658it is near the bond order of1.667calculated bythe method MO [8, p.48].

It should be noted that the , b, coefficients for this y = a+ b/x + c/x? function incase ofusing three pairs ofpoints (1, 1), (2, 2) and (3, 3) are defined explicitly; actually, they (the coefficients) are assigned tothese points. Inthat way we find these coefficients for working further with the equation. For making certain that this dependence y = a+ b/x + c/x? describes well the Multiplicity = f (L) and E = f (L) functions it will take only toperform correlation for four or more points. For example, for the dependence Multiplicity = f (L) for C-C bonds we should add afourth point (Lcc = 1.397?, Multiplicity = 1.667) and obtain an equation with r? = 0.9923and the coefficients = 0.55031721, b = 4.31859233, = 10.35465915.

As it is difficult, due toobjective reason, todefine four or more points fortheMultiplicity = f (L) and E = f (L) equations for aseparate bond type, we will find the , b, coefficients using three points (as arule they are the data for single, double and triple bonds). The dependences obtained insuch away give good results as regards the bond multiplicity and energies.

Well find the dependence E = f (L) for the CC bonds

b1 = b + c/x1, Y = b1 +cX

As usual:



nthe number ofgiven valueY.

Letus calculate afrom the equation

?y = na + b? (1/x) + c? (1/x2),(9)

when n =3.

Table 2. Calculation ofratios for relation E = f(L).

1/x1 = 0.64808814, x1 = 1.543, y1 = 347.9397

? (1/x2) = 1.66729469, ? (1/x) = 2.22534781when n =3

c = 1699.18638789,

b = 5065.62912191,

a= 2221.34518418


Letus calculate from the equation:

Ecc (ethane) = 347.9397kj/mole

Ec?c (ethylene) = 615.4890kj/mole

Ec?c (acetylene) = 812.2780kj/mole.

2.3. Conclusion

As we can see, three-electron bond enables toexplain aromaticity, find delocalization energy, understand aromatic bonds specificity. Aromatic bond inbenzene molecule is simultaneous interaction ofthree pairs ofcentral electrons with opposite spins through the cycle. But whereas central electrons are the part ofthree-electron bond, then it is practically interaction ofsix three-electron bonds between themselves, that is expressed inthree interactions through cycle plus six three-electron bonds. We shouldnt forget inthis system about important role ofsix atom nucleuses, around which aromatic system is formed. Properties ofnucleuses especially their charge will influence on properties ofaromatic system.

Finally, postulates ofthe three-electron bond theory (TBT) can be presented:

1) Achemical bond between two atoms may be established bymeans ofthree electrons with oppositely oriented spins (???).

A A(???)

A B (???)

2) The electron shell ofeach atom inthe stable molecule, ion, radical should have such anumber ofelectrons which corresponds tothe octet. Adeviation from the octet results inan instability ofaparticle.

3) The state ofthe three-electron bond is determined bythe octet rule.

4) The number ofelectrons participating inthe chemical bond should be maximal and its then that the energy ofthe system will be minimal. Taking into consideration para 5and2.

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