Density functional theory and quantum similarity

Quantum molecular similarity (QMS), for which the first measures were introduced by Carbo in the early 1980s, has been shown to be an important concept when comparing properties and reactivity of different, albeit mostly related, molecules. In this article we investigate how various subfields of Density Functional Theory (DFT) contribute in their own way to the evaluation and the understanding of QMS, reflecting the combined interest of our group in both domains in recent years. The contribution of computational DFT is easy to pinpoint, as DFT can now be used in the evaluation of electron densities of ever-increasing quality. When establishing a link between the fundamental(s) of DFT and QMS the role of the shape function turns out to be predominant and an extension of Mezey's Holographic Electron Density Theorem for rho(r) to the shape function sigma(r) is presented. On this basis, similarity in shape is the fundamental issue to be looked at, both globally and locally. As an application, global and local similarity measures were evaluated using the Hirshfeld partitioning technique for the two enantiomers of CHFClBr, giving numerical evidence for the Holographic Electron Density Theorem. As an application of conceptual DFT, similarity indices constructed via DFT based local reactivity descriptors (e.g., local softness) are used to probe the similarity of reactivity of a series of peptide isosteres. The use of the autocorrelation function for condensed indices turns out to be a valuable technique to circumvent the orientation-translation dependence of similarity indices. (C) 2004 Wiley Periodicals, Inc.