Fuzzy Electron Density Fragments in Macromolecular Quantum Chemistry, Combinatorial Quantum Chemistry, Functional Group Analysis, and Shape-Activity Relations

CONSPECTUS: Just as complete molecules have no boundaries and have fuzzy electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such fuzzy electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for example, in medicinal drug design, and (g) tools for combinatorial quantum chemistry approaches using fuzzy fragment databanks and rapid construction of a large number of approximate electron densities for large sets of related molecules, relevant in theoretical molecular and nanostructure design.