The set of structures showing the correct hapticity of azulene on the basis of the 18 e^- rule, is

Concept:

• Azulene is bicyclic organic system. It consists of cycloheptatriene and cyclopentadiene rings. 
• Presence of 10 pi-electrons with sp² hybridised carbons makes it aromatic and thus shows Friedel-Crafts substitution reactions.
• The organometallic compounds follows 18e^- rules. The metal center with18 valence e^-s is considered stable.
• Aromatic systems usually can change their hapticity depending on the electron requirement for stable system.

Explanation:

Lets say, the hapticity of cyclopentadiene and cycloheptatriene rings is x and y, respectively.

Contribution of electron by each CO = 2

Valence electrons of Fe = 8

Valence electrons of Mo = 6

electron shared by other metal = 1

(a) Calculating hapticity of Fe containing Azulene based system:

applying 18 e^- rule on Fe₁ :

           8 + 4 +1 + x = 18 

                            x = 5 

applying 18 e- rule on Fe₂ :

           8 + 6 +1 + y = 18

                             y = 3

hapticity of rings should be 5 and 3 for cyclopentadiene and cycloheptatriene respectively.

(a) Calculating hapticity of Mo containing Azulene based system:          

applying 18 e- rule on Mo₁ :

​           6 + 6 + 1 + x = 18

                              x = 5

applying 18 e- rule on Mo₂ :

          6 + 6 + 1 + y =18 

                             y = 5

Hence, the hapticity of rings should be 5 for both cyclopentadiene and cycloheptatriene.

Conclusion:

The set of structures showing the correct hapticity of azulene is:

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