We propose a new similarity measure operating in an abstract space spanned by properties evaluated at bond critical points defined by the theory of Atoms in Molecules. Consequently, we represent molecules compactly and reliably, extracting the relevant information from their ab initio wave function. Typical problems of continuous quantum similarity measures are thereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para and meta substituted benzoic acids. On the basis of our definition of distances between molecules in BCP (Bond Critical Point) space, we are able to reproduce the experimental sequence of acidities determined by the well-known sigma constant of a set of substituted congeners. Moreover, our approach points out where the common reactive center of the molecules is. Due to these promising results we embark on a research program systematically addressing further issues outlined in this work. The generality and feasibility of our approach will enable predictions in medically related QSARs.