# 21.5: Application of the MO Method to 1,3-Butadiene


To treat the $$\pi$$-electron system of 1,3-butadiene by simple MO theory, we combine the four $$p$$ carbon orbitals of an atomic-orbital model, such as $$17$$, to obtain four molecular orbitals:

We can estimate a stabilization energy for butadiene from heats of hydrogenation, and it is useful to compare the values obtained with the calculated delocalization energy. Thus the heat of hydrogenation of 1,3-butadiene is $$57.1 \: \text{kcal}$$, whereas that of ethene is $$32.8 \: \text{kcal}$$ and of propene $$30.1 \: \text{kcal}$$. If ethene is used as the model alkene, the stabilization energy of 1,3-butadiene is $$\left( 2 \times 32.8 - 57.1 \right) = 8.5 \: \text{kcal}$$, whereas with propene as the model, it would be $$\left( 2 \times 30.1 - 57.1 \right) = 3.1 \: \text{kcal}$$. The bond energies (Table 4-3) in combination with the heat of formation at $$25^\text{o}$$ $$\left( 26.33 \: \text{kcal} \right)$$ give a stabilization energy of $$5.0 \: \text{kcal}$$.