Question

For benzene, the total π-electron energy is E_π = 6α + 8β and for 1,3,5-hexatriene it is E_π = 6α + 6.99β.

(a) Using Huckel molecular orbital theory, compare the total π-electron energy of 1,3,5-hexatriene to the energy of a molecule with 3 localized π-bonds (i.e. 3 ethene molecules). What factor leads to the lower energy of 1,3,5-hexatriene as compared to the molecule with 3 localized π-bonds? Explain.

(b) Explain why the total π-electron energies of benzene and 1,3,5-hexatriene are different even though both have 6 carbons and 6 π-electrons. Why does benzene have a lower energy? Explain.  

Answer 1

the extent of delocalization causes less energetic system or more stabilized system.

In 1,3,5-hexatriene the three double bonds are in conjugation. Conjugated double bonds are localized in nature and results to have more π-electron energy and eventually produces stable system as compared to the independent 3 localized systems (3 ethene molecules). One π-bond causes 2(α + β) diminishing in the system energy, 3 independent localized systems causes 6(α + β) π-bond energy and it is 0.99 β less than the 1,3,5-hexatriene π-bond energy.

In case of benzene, the delocalization is further more than compare to 1,3,5-hexatriene. According to Huckel (4n+2)π e^- cyclic planar systems causes more delocalization than compare to acyclic (4n+2)π e^- conjugated systems. Due to this aspect, benzene aquires more π-electron energy than compare to 1,3,5-hexatriene. Hence, benzene is more stable than 1,3,5-hexatriene.