Why are antiaromatic compounds less stable than aromatic compounds?

[avistein]

In aromatic compounds ,it is stabled because $\pi$ electrons are delocalised.But why in antiaromatic compounds delocalisation of $\pi$ electrons destablizes the compound and make it less stable than the corresponding single chain compound also. Should not the delocalisation have stabled it?

 

[DrDu]

Delocalization also stabilizes anti-aromatic compounds, however, the statilization is not as large as in aromatic compounds. You also have to take in mind not only the absolute stability but also the stability relative to deformations leading away from equal bond lengths. For this, what is most relevant is the sigma system, not only the pi system.
There exists voluminous literature on that topic, a nice read is e.g.:

http://onlinelibrary.wiley.com/doi/10.1002/jcc.20470/full

 

[avistein]

. For this, what is most relevant is the sigma system, not only the pi system.

That means delocalisation of $\pi$ electrons in sigma system does not stablize the system?

 

[DrDu]

It does stabilize the system energetically but not necessarily geometrically.