This paper describes an approach to molecular similarity using a Gaussian expansion for the density which simplifies the calculation of the Carbo-type molecular similarity index. In addition, we introduce the notion of a local similarity index. The local index uses the fragment density of a molecule to compute the index and allows parts of molecules to be compared to one another. Our approach to similarity is tested on a variety of small test cases; benzene and substituted benzenes,water, the water dimer, and complexes such as H2O-F- and H2O-Cl-. The results of these calculations are in qualitative agreement with previous calculations, and one’s general intuition of chemical similarity. Finally, we point out that the results obtained here suggest that our approach can be applied to more complex systems to study questions involving biological activity and the binding of inhibitors to proteins.