2. Structure of the benzene molecule on the basis of the three-electron bond
2.1. Results and discussion
Supposing that the chemical bond between two atoms can be established by means of three electrons with oppositely oriented spins (↑↓↑) the structure of the benzene molecule can be expressed as follows (see figure 1 and figure 2):
benzene molecule on the basis of the three-electron bond, spin
It is interesting to point out that spins of central electrons on opposite sides have an opposite orientation (see figure 2). Now let us consider in detail the interaction of six central electrons between themselves. They will be itemized as shown in figure 2. As the spin of electron 1 and those of electrons 2 and 6 are oppositely oriented (see figure 2) (1 (+), 2 (-), 6 (-)), electron 1 will be attracted to electrons 2 and 6 respectively. Let’s indicate that the distance between electrons 1 and 6 or 1 and 2 is equal to 1.210 Å which can be easily shown taking into account the distance between atoms of carbon in benzene to be 1.397 Å and the angle between carbon atoms amount to 120 degrees. Let us compare the distance between electrons 1 and 6 and 1 and 2 bond lengths in ethane, ethylene and acetylene [7]:
bond lengths in ethane, ethylene, acetylene and distance between electrons (1 and 2) in benzene
As we observe, the distance between central electrons 1 and 2 and 1 and 6 of the benzene molecule is approximately equal to that between carbon atoms in the acetylene molecule, therefore, the interaction between electrons 1 (+) and 2 (-) and 1 (+) and 6 (-) has to be rather considerable. Let us express the attraction with arrows. According to summing up vectors the resultant vector will be directed to the centre, which means that electron 1 under the influence of electrons 2 and 6 will move to the centre (figure 3):
benzene on the basis of the three-electron bond, summing up vectors
If we take a look at electron 4 we see the similar situation with it (figure 4) and it will also move to the centre and, more importantly, its spin and that of electron 1 will 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 1 and 4 in benzene is equal to 2.420 Å. It is interesting, that this distance is twice as much than distance between electrons 1 and 2, or between electrons 1 and 6 (1.210 Å ∙ 2 = 2.420 Å). This interaction through the cycle constitutes the essence of the delocalization of electrons, of course together with a three-electron bond. Since besides the three-electron bond in the benzene molecule there is an interaction through the cycle, meaning that the benzene nucleus undergoes a kind of compression it is clear that the c-c bond multiplicity in benzene will exceed 1.5.
So, the aromatic system is a cyclic system with three-electron bonds where an interaction of central electrons through the cycle is observed. In the benzene molecule there are three interactions through the cycle-pairwise between electrons 1 (+) and 4 (-), 2 (-) and 5 (+), 3 (+) and 6 (-), as shown in figure 5:
benzene on the basis of the three-electron bond, interaction through the cycle
Carbon atoms in benzene are sp²-hybridized. The three-electron bond between carbon atoms in the benzene molecule can be represented as follows:
Carbon atoms in benzene have an octet equal to 8 (3 +3 +2 = 8). It should be pointed out that due to the largest distance from the atoms nuclei the central electrons of the three-electron bond are supposed to be the most mobile compared to other electrons of the three-electron bond. The interaction of central 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 in cyclobutadiene 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. In cyclobutadiene at the expense of small distance it causes the appearance of antiaromatic properties, and in cyclooctatetraene there is a possibility of formation of non-planar molecule, where interaction of central electrons becomes impossible and molecule losing the interaction through the cycle loses also three-electron bonds, that results in a structure, in which single and double bonds alternate.
Explanation, that cyclooctatetraene is non-aromatic, because it is non-planar and does not hold water, insomuch as dianion of cyclooctatetraene is aromatic and has planar structure [8], [9].
Planar
X-ray crystal structure analysis determined crystal structure of potassium salt of dianion 1,3,5,7-tetramethylcyclooctatetraene [10], [11].
Octatomic cycle is planar with lengths of С-С bonds nearly 1.41 Å.
Planar
From the mentioned above we can make a conclusion: cyclooctatetraene conforms to the shape of bath tub not because of high angular pressure (15°) at planar structure, but because by interaction through the cycle central electrons of three-electron bonds have equal spin and will push away. Thus for energy reduction cyclooctatetraene conforms to the shape of bath tub and becomes non-planar, that disables interaction of central electrons.
Cyclobutadiene represents rectangular high reactivity diene [8, p. 79].
It is also interesting to observe cyclodecapentaene (cis-isomer [10] -annulene).
cyclodecapentaene (three-electron bond)
cyclodecapentaene, distance
Whereas central electrons of three-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 Å if accept Lс-с = 1.400 Å for regular decagon), angular pressure is high (24°) and that’s why stabilization at the expense of interaction through the cycle at such long distance will be low and cannot cover energy consumption for creation of planar molecule.