Molecules as networks: A localization-delocalization matrices approach

Abstract

Inspired by chemical graph theory (CGT), a matrix representation of molecules and reaction paths is presented within the framework of Bader’s quantum theory of atoms in molecules (QTAIM). A molecule is viewed as a network of electron delocalization channels or highways (vertices) that connect every pair of atoms in the system and electron localization cul-de-sacs loops connecting any given atom to itself. The representation of a molecule as a fuzzy, complete, non-directed graph, captured mathematically as an electron localization-delocalization matrix (an LDM), is rich with coded physical and chemical information. An LDM contains information on the bond-path molecular graph, bond strengths, molecular geometry, atomic electron populations and atomic charges, newly proposed multidimensional atomic charges, atomic volumes, free valences, NMR proton-proton coupling constants, and molecular branching. LDMs can quantify molecular (di)similarity by matrix difference measures such as the Frobenius distance, possibly after diagonalization and/or size adjustments with ghost atoms, or by the use of principal component analysis (PCA). Because they condense information at an atomic resolution, LDMs can be used to construct predictive quantitative-structure-to-activity/property-relationship (QSAR/QSPR) models with a wide range of applications including, for example, thermochemical properties, stress-corrosion cracking inhibitors’ activity, mosquito repellency, ribotoxicity, pKa's, aromaticity of rings-in-molecules, etc. The LDM philosophy can be extended to other properties that associate to each atom a “self” term and a sum of “interaction” terms with every other atom in the system. Such properties include the Oviedo Group’s “interacting quantum atoms” (IQAs) atomic energy decomposition and the integrated Bader-Gatti source function. The potential uses and connections between these different matrix representations of a molecule are explored. The coarse graining of LDMs to possibly compare macromolecular structures is also briefly discussed.