Molecular Informatics and Topology in Chemistry

Abstract

The information content of molecules is very rich, as manifested by the phenomenal versatility even medium size molecules are able to exhibit, depending on the circumstances and reaction partners. The actual medium for the storage and representation of this information is the molecular electron density. Some of the most essential features of the molecular electron density are represented by the molecular graph, implying that, ultimately, the Wiener index, the fundamental index of molecular graph theory, is connected to the molecular electron density. Naturally, the shape features of molecular electron densities, specifically, the fundamental topological features of these shapes are important information carriers. In recent years significant advances have been achieved in the computation of ab initio quality electron densities of large molecules, including proteins, as well as other macromolecular properties including approximate forces acting on individual nuclei. Consequently, the topological shape analysis methods of electron densities have become applicable to truly large molecular systems, and in this context, the study of relations between molecular fragments and complete molecules have acquired new significance. One related advance is the recent proof of the “Holographic Electron Density Theorem”, stating that any nonzero volume part of a molecular electron density in a non-degenerate electronic ground state contains the complete information about all properties of the entire, boundaryless molecule. This fundamental property of all molecules is in fact stronger than the property described by the celebrated Hohenberg-Kohn theorem (Walter Kohn, Nobel Prize, 1998), which states only that the electron density of the complete molecule determines all molecular properties. However, according to the Holographic Electron Density Theorem, much less than the complete molecular electron density is quite sufficient: in fact, any nonzero volume piece of the density cloud already contains all information about the molecule. Several applications of this holographic property will be reviewed, including applications to QShAR. In addition, a newly recognised fundamental aspect of molecular informatics, the holographic principle for latent molecular properties and some of its surprising consequences will be discussed.