Localization-Delocalization Matrices and Electron Density-Weighted Adjacency Matrices: New Electronic Fingerprinting Tools for Medicinal Computational Chemistry

AIMLDM: A program to generate and analyze electron localization–delocalization matrices (LDMs)

“…There are several studies that report the use of LDMs in the empirical modeling to predict the properties of compounds in QSAR-type studies [4][5][6][7][8][9]. In what follows we just highlight two typical examples of how the concepts can be used in actual predictive modeling.…”

“…In what follows we just highlight two typical examples of how the concepts can be used in actual predictive modeling. The reader is referred to the primary literature for the details [4][5][6][7][8][9].…”

“…(5)) and that the sum of sums is N. The trace of the LDM equals N loc (Eq. (8)) while N deloc can be obtained by difference (Eq. (9)).…”

“…The theory also defines localization and delocalization indices (LIs and DIs) that count the number of electrons that, on average, are localized within an atomic basin or delocalized (shared) between a pair of basins in the molecule. Since QTAIM defines "self" (localization) and "shared" (delocalization) atomic populations one can cast these indices into a convenient matrix format that represents the complete fuzzy molecular graph [4][5][6][7][8][9][10].…”

The Localization–Delocalization Matrix and the Electron-Density-Weighted Connectivity Matrix of a Finite Graphene Nanoribbon Reconstructed from Kernel Fragments

“…Electronic fingerprinting using the quantum theory of atoms in molecules’ (QTAIM) − descriptors of bonding and of electron delocalization (sharing) has recently been shown to be useful in the prediction of a number of molecular properties. − The organized listing of bonding and of electron delocalization descriptors derived from QTAIM in matrix format allows for their analysis with the mathematical apparatus of chemical graph theory (CGT). − In CGT, matrix representatives of the molecular graph, whether hydrogen-suppressed or not, are manipulated mathematically to extract graph invariants that do not depend on atom numbering for use in predictive modeling of physicochemical properties. On the other hand, QTAIM defines local molecular descriptors of bonding such as the bond critical point (BCP) data between every pair of chemically bonded atoms, and nonlocal descriptors such as the delocalization (or electron sharing) index − that counts the number of electrons delocalized between every pair of atomic basins in a molecule (whether bonded or not) or the interatomic components of “interacting quantum atoms” energies. − …”