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A similarity index based on the concept of an information distance is evaluated for a series of diatomic molecules. The results show that the momentum space information distance is a good indicator of the extent of charge separation present in a molecule. The Shannon entropy in position space is shown to decrease with increasing charge separation and as such is presented as a measure of the structure or extent of electron localization in a system. The concept of a local Shannon entropy over an atomic basin is introduced and it is shown how this quantity may be used to examine the local behavior of electron densities.