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Local and Global Similarities of Molecules : Electron Density Theorems , Computational Aspects , and Applications

The local and global properties of molecular electron densities are interrelated by some of the fundamental theorems of molecular physics. These relations have significant consequences regarding the similarities between molecular properties and reactivities on various levels: in the comparisons of the roles of individual functional groups, and also on the level of spatial requirements and global shapes of molecules. The “Holographic Electron Density Theorem” [1] and the “Holographic Molecular Symmetry Theorem” [2] provide extensions of the celebrated Hohenberg-Kohn Theorem of density functional theory [3], and also provide new computational tools for assessing molecular similarity and other shape properties [4,5]. These new approaches, in combination with macromolecular quantum chemistry approaches [6,7] and various Electron Density Transform and Electron Density Averaging methods [8], represent a new computational chemistry toolbox. One of the aims of these methods is application for systematic, quantum chemistry approaches to QSAR in pharmaceutical drug discovery, toxicological risk assessment, and the study of olfactory activity of various molecular series. The holographic approach to electron density similarities also provides a basis for treating host-guest interactions, macromolecular bonding, and the problem of molecular recognition within a unified framework. The high selectivity of some molecular recognition processes is justified by a theoretical result concerning the uniqueness of molecular recognition that is a direct consequence of locality principles and the holographic electron density property.