When cyclohexane successively loses H2 to form cyclohexene and cyclohexadiene, the C-C and C=C bond lengths do not change appreciably from one molecule to another. When one more H2 is lost, benzene is formed and it is found that the six CC bond lengths are equal and almost an average between an ordinary C-C and C=C bond length.

If benzene has kept its name and has not been named 1,3,5-hexatriene, it is because benzene behaves differently than the unsaturated cyclohexenes. We explore here the consequences of changes in structure, especially bond lenth on the energies of molecules. The following diagram gives the molar standard enthalpies of formation of cyclohexane, cyclohexene, 1,3-cyclohexadiene, and benzene. These are used to calculate standard enthalpies of successive dehydrogenation reactions.

A 'gedunken' or 'thought' experiment is performed in order to see the effects of resonance energy. Let us suppose that reaction 2 forms a "decoupled" or "nonconjugated" cyclohexadiene. In that case, we consider this new reaction 2' to be just twice the enthalpy of reaction 1; or, reaction2' is just a sum of two simple dehydrogenations.

Comparing 'gedunken' reaction 2' to the 'real' reaction 2, the latter is lower in energy by 3 kcal/mol. This arbitrary stabilization energy can be called "resonance energy". We can compare the 'real' reaction 3 to reaction 3' which is just three times reaction 1, and expect perhaps two or three times as much resonance energy, or 6-10 kcal/mol. This is not the case. The stabilization energy is 36 kcal/mol. This is called energy of aromaticity.

A theoretical aromatic energy can be calculated using the theoretical methods in GausView. Optimize the geometry of each of the five molecules involved. You will be assigned a particular theoretical method for the optimizations. Record the energy of each optimized molecule. If you want, you can do this for the AM1 method and compare your results to mine.

Cyclohexane -0.0616005 atomic units (au)
cyclohexene -0.016199
cyclohexadiene 0.0277032
benzene 0.0349417
hydrogen -0.0082606

1 au = 627.5095 kcal/mol

In the same manner in which Hesse's Law is used to calculate reaction energies, we can use the electronic energies in place of the enthalpies of formation:
Reaction 1 energy: [ (-0.016190 + -0.0082606) - (-0.0616005)] = 37.15au = 23.31 kpm
Reaction 2 energy : [(0.0277032 + 2(-0.0082606)) - (-0.0616005)] = 72.78au = 45.67kpm
Reaction 3 energy : [(0.0349417 + 3(-0.0082606)) - (-0.0616005)] = 71.76au = 45.03kpm

Reaction 2' energy : 2*23.31 kpm = 46.61 kpm
2' - 2 = 46.61 kpm -45.67kpm = 1 kpm. This is sometimes called the "resonance energy".

Reaction 3 energy : 3*23.31 kpm = 69.93 kpm
3' - 3 = 69.93 kpm - 45.03kpm = 25 kpm

This compares with 36kpm for the experimantal value of "aromatic energy".

(You might want to verify for yourself that the values for the H2 are not needed for the differences, just as when we 'adjust' the heats of formation of elements to zero.)

You can continue with various mono-substituted benzenes

1) -NO2 nitro (in the 1 position, thus in conjugation with the ene and diene systems)

nitrocyclohexane  -0.057571
nitrocyclohexene  -0.013751
nitrocyclohexadiene +0.030572
nitrobenzene +0.040066
(-0.50; +21.)

2) -NH2 amino (in the 1 position, thus in conjugation with the ene and diene systems; lone pair in conjugation; axial position in cyclohexane)

aminocyclohexane  -0.050990
aminocyclohexene  -0.018287
aminocyclohexadiene +0.023663
aminobenzene +0.032473
(-5.8; +9.2)