Pi bond formation energy of allyl cation

[freedom856]

Homework Statement

The cation [CH2=CH-CH2]+ has a delocalized pi network that can be described using Huckel Molecular Orbital Method. Calculate the pi bonding formation energy



2. The attempt at a solution
Using matrix, energy = alpha, alpha + root2 beta , alpha-root2 beta

The pi electron bonding energy(Ebf) is equal to pi electron bonding energy(Epi)-N (alpha), where N is number of carbon atom in the molecules so

Ebf = 2(alpha+root2 beta)-3alpha
but, the suggested answer is N=2 can anyone tell me why N is 2 but not 3

 

[nate808]

?

Hello!

The reason why N is considered to be 2 in this case is because the cation [CH2=CH-CH2]+ has a delocalized pi network that includes only two carbon atoms. The third carbon atom is not included in the pi network and does not contribute to the pi bonding formation energy. Therefore, N=2 is the correct value to use in this calculation.

I hope this helps clarify your question. Let me know if you have any further doubts.