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 Bezverkhniy
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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.
Cyclodecapentaene was received in the form of crystalline substance at – 80°С. On spectrums ¹³С-NMR and ¹Н-NMR it was determined, that compound is non-planar and is olefin, that is logical on the basis of long distance between central electrons [8, p. 84], [12].
Lets draw our attention to the fact that in going from benzene to cyclooctatetraene and to cyclodecapentaene 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 of the three-electron bond, distance between electrons (benzene, cyclooctatetraene, cyclodecapentaene)
As we can see distance between neighboring central electrons 1 and 2 in benzene makes up 1.210 Å, in regular octagon 1.303 Å, and in regular decagon 1.331 Å (almost as distance between carbon atoms in ethene molecule). That is by going from benzene to regular 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 Å; 3.404 Å; 4.309 Å), as well as distance between neighboring central electrons 1 and 2 (1.210 Å; 1.303 Å; 1.331 Å), that causes considerable weakening of interaction through the cycle in regular decagon. That’s why regular hexagon (benzene) is ideal aromatic system. As angular pressure is equal to zero, distances between central electrons both neighboring and situated on the opposite sides are minimal (accordingly 1.210 Å and 2.420 Å). I.e. interaction through the cycle will be maximal. By going to regular decagon these advantages will be lost. That’s why cyclodecapentaene is olefin.
Let us note for comparison that if we take Lc-c = 1.400 Å for the planar cyclooctatetraen, we will have L (1—5) = 3.380 Å, L (1—2) = L (8—1) = 1.293 Å which vary just slightly from the above mentioned distances between the central electrons at Lс-с = 1.410 Å.
By means of the interaction through the cycle together with the three-electron bond, aromaticity of coronen, [18] -annulene, naphthalene and other organics substances can be explained (see conclusion).
Now let’s pass to the definition of delocalization energy of benzene. It is easy to show, that relation multiplicity = f (L) and Е = f (L), where multiplicity is multiplicity of bond, L – length of bond in Å, Е – energy of bond in kj/mole will be described by function y = a + b/x + c/x² for any types of bond (C-C, C-N, C-O, C-S, N-N, N-O, O-O, C-P).
We shall consider ethane, ethylene and acetylene to be initial points for the c-c bond.
For lengths of bonds let us take the date [7]:
bond lengths in ethane, ethylene and acetylene
As usual, the С-С bond multiplicity in ethane, ethylene and acetylene is taken for 1, 2, 3.
For energies of bonds let us take the date [7, p. 116]:
energies of bonds in ethane, ethylene and acetylene
The given bond energies (according to L. Pauling) are bond energy constants expressing the energy that would be spent for an ideal rupture of these bonds without any further rebuilding of the resulting fragments. That is, the above mentioned energies are not bond dissociation energies.
Having performed all necessary calculations we obtain the equation:
(1)
(2)
From these equations we find:
c—c benzene multiplicity (L = 1.397 Å) = 1.658
c—c graphite multiplicity (L = 1.42 Å) = 1.538 ≈ 1.54
Ec—c benzene (L = 1.397 Å) = 534.0723 kj/mole
Ec—c graphite (L = 1.42 Å) = 503.3161 kj/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 of the three-electron bond, interaction through the cycle
(3)
from the equation we find L = 1.42757236 Å.
So, if the benzene molecule had a «clean» three-electron bond with a 1.5 multiplicity the c-c bond length would be L = 1.42757236 Å.
Now let us determine the energy of the «clean» three-electron bond with