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The energy level diagram for the π-molecular orbitals of the cyclic C3H3 radical is given below.

The delocalization energy of the molecule in the ground state (in units of β, where β is Hückel's constant for interaction energy) is
  • a)
    3
  • b)
    1
  • c)
    0
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The energy level diagram for the π-molecular orbitals of the cyclic...
Cyclopropenyl System:
In case of cyclopropenyl, N=3.

The corresponding energy level diagram is given below:
  • Cyclic C3H3 radical contains a total of 3 electrons. Out of which 2 electrons are present in Eo and 1 in E1.
  • The total π electron energy (E) of cyclic C3H3 radical is given by,
  • Now, Another related term is π bond formation energy which is the energy released when a π bond is formed.
  • Since the contribution of α is the same in the molecules as in the atoms, so we can consider the energy of two electrons, each one in isolated and non-interacting atomic orbitals as 2α, then the π bond formation energy becomes,
Eπ(bond formation) = E - nα
where, n is the number of C atoms.
  • For, cyclic C3H3 radical (n=3) π bond formation energy is
​Eπ(bond formation) = 3α+3β - 3α
= 3β
  • ​The delocalization energy of the molecule in the ground state is,
= 3β−2β (2β is the total π bonding energy on the formation of the ethylene molecule)
= β 
Hence, the delocalization energy of the molecule in the ground state (in units of β, where β is Hückel's constant for interaction energy) is 1.
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The energy level diagram for the π-molecular orbitals of the cyclic C3H3radical is given below.The delocalization energy of the molecule in the ground state (in units of β, where β is Hückels constant for interaction energy) isa)3b)1c)0d)2Correct answer is option 'B'. Can you explain this answer?
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