Chemical applications of electron localization-delocalization matrices (LDMs) with an emphasis on predicting molecular properties

Abstract

A matrix is constructed where the vertices (atoms) are connected by edges (bonds) resulting in a square matrix that is symmetrical. The localization index (unshared electrons) occupies the long diagonal where the delocalization index (shared electrons between two di erent atoms divided by 2) represent the o -diagonal elements. Such a matrix is called a localization-delocalization matrix or LDM. These matrices have shown promise as a novel Quantitative Structure Activity Relationship (QSAR) method via the Frobenius Distance, a method to compare matrices of similar sizes that returns a Euclidean distance. Some notable results that will be expanded upon are that for a series of 14 para-substituted benzoic acids for pKa prediction (r2 = 0.986), and a series of 13 polycyclic benzenoid hydrocarbons (PBH) separated by inner and outer rings (r2= 0.97). A program (AIMLDM) was developed in Python 3.4.1 to construct these matrices and perform the required calculations.