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I read that tendency of $\ce{ClO2}$ to form dimer is less and that of $\ce{ClO3}$ to form dimer is more.

I can understand the reason for the former because the unpaired electron is more delocalized in this case. So, if an electron is localized, i.e. it is at rest then the tendency of the molecule to form dimer will be high. Whereas if the electrons are delocalized, i.e. it is moving, then the tendency of the molecule to form dimer will be less.

I don't understand why the tendency to form dimer in the case of $\ce{ClO3}$ is high. There are vacant $\mathrm{d}$ orbitals with chlorine. Then why is that?

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