Why does fusion to a benzene ring reduce the acidity of a cyclopentadiene ring?
For example, acidity decreases going from cyclopenta-1,3-diene to indene and to fluorene:
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Clar's rule states that (Solà, 2013):
The Kekulé resonance structure with the largest number of disjoint aromatic π-sextets, i.e., benzene-like moieties, is the most important for characterization of properties of polycyclic aromatic hydrocarbons (PAHs).
Applying Clar's rule to the the question, we would realise that in the indenyl and fluorenyl anions, the resonance structures where there are 6 π-electrons delocalised exclusively within the fused benzene rings would contribute more to the actual structure than the resonance structures where the π-electrons are delocalised along the 5-membered ring. In the major resonance structure for the fluorenyl anion, we would have the negative charge concentrated on the carbon atom, without delocalisation.
In the cyclopentadienyl anion, the negative charge is completely delocalised, as shown below in the resonance structures. Thus, it is the most stable among them. In the indenyl and fluorenyl anions, the negative charge is not as delocalised and thus, these are less stable.
Due to this, the π-electrons in the 5-membered ring experiences the most delocalisation and achieves most aromatic stabilisation in the cyclopentadienyl anion, and this gradually decreases going to the indenyl and fluorenyl anions.
Solà, M. (2013). Forty years of Clar's aromatic π-sextet rule. Frontiers in Chemistry, 1(22). doi:10.3389/fchem.2013.00022
When you deprotonate cyclopentadiene you make the ring aromatic, bringing all five carbon atoms and six pi electrons into an aromatic cycle. When you deprotonate indene, you again make the five-atom ring aromatic, but ... in this case part of the ring had already been aromatic by being incorporated into the benzenoid ring. You don't add as much to the aromatic conjugation and thus the impact of aromaticity on the deprotonation is less. Add another fused benzenoid ring in fluorene and you get another decrement in the net effect of aromaticity.