Book Review: “Electron Localization‐Delocalization Matrices” by Chérif F. Matta, Paul W. Ayers, and Ronald Cook

In interest of full disclosure this writer indicates a professional relationship with the authors of the book. This notwithstanding, effort has been made to provide a fair and balanced review. In “Electron Localization-Delocalization Matrices,” Chérif F. Matta, Paul W. Ayers, and Ronald Cook present an exploration of the concepts and applications of electron localization-delocalization matrices (LDMs) in computational and theoretical chemistry. Published as part of the Lecture Notes in Chemistry series (No. 112), this book attempts to contribute to countless ways (which are not reviewed in the book) of bridging the gap between quantum theory and practical applications, presenting a framework that connects quantum chemical calculations with Chemical Graph Theory (CGT) to solve practical problems. (See Figure 1 for the book cover). The book reports on a matrix description of molecules that summarizes the electron distribution with atomic resolution in terms of the electron density and electron pair density obtained from quantum chemical calculations. The authors succeeded to predict molecular properties and activities using LDMs in modeling chemical bonding and molecular reactivity as well as offering insight into important physical phenomena like corrosion inhibition and enzyme-substrate interactions. The book guides the reader progressively through the principles of electron localization and delocalization, starting with a theoretical grounding and moving toward practical applications. Early chapters review the fundamental physics underlying electron (de)localization, while later chapters delve into computational aspects, matrix manipulation, and case studies. This logical flow makes the book accessible to both advanced students and seasoned researchers, though a foundational understanding of quantum chemistry and computational methods is assumed. The authors borrow some of the concepts from CGT [1-4] and apply and/or extend them to matrices formed using the electron localization and delocalization indices [5] computed using Bader's quantum theory of atoms in molecules (QTAIM) [6, 7] to extract useful chemical information. The work summarizes several papers by the authors (e.g., [8-11]) over the past decade which started with a 2014 article by Matta in this journal [12] where these matrices were defined with examples of their utility. four scientists [they] admire and whose oeuvre has laid the foundations for the work presented in this monograph. The four scientists to whom the book is dedicated, in that order, are: Richard F. W. Bader (the principal developer of QTAIM and the PhD advisor of the first author of the book Prof. Chérif F. Matta), Robert G. Parr (a most influential quantum chemist with numerous contributions to the field and the PhD advisor of the second author of the book Prof. Paul W. Ayers), Todd A. Keith (a former PhD student of Bader as well and the developer of a leading QTAIM software AIMAll/AIMStudio), and Ismat Sumar (a former undergraduate student of Ayers and a former joint M.Sc. student of both Matta and Ayers, and who programmed AIMDELOC, the first software implementing the LDM analysis). give us insight not numbers [14]. give us insight and numbers [14]. The preface and the first introductory chapter of the book set its tone in describing electron localization and delocalization indices collectively as a molecular descriptor to predict the properties of heterogeneous sets of compounds. Chapter 1 underscores the centrality of extracting matrix invariants from any matricial molecular representation to provide descriptors that are independent of the arbitrary atom numbering scheme. Chapter 2 reviews the physics of electron localization and delocalization described using the electron pair density. Chapter 3 introduced Bader's theory of atoms in molecule which provides a partitioning of the physical space into non-overlapping mono-nuclear regions termed atomic basins. Once atomic basins are defined in this manner, the exchange-correlation density can then be integrated over one and the same atomic basin to yield a count of localized electrons or over two basins to give a count of the electrons shared between them. The independence of this description for any particular orbital description is emphasized (also in Chapter 1). Chapter 2 also touches upon controversial topics such as the absence of bond paths where they would be expected on the basis of the proximity of two nuclei (e.g., with a distance criterion such as the sum of van der Waals radii) and the debate about the hydrogenhydrogen bonding [15, 16]. The book covers the integration of LDMs with statistical methods such as principal component analysis (PCA) to extract invariant molecular descriptors that can be applied to a range of chemical problems. This approach is introduced in Chapter 6 along with a review of the basics of PCA. For instance, in Chapter 7—the first one of three chapters of highly applied nature, the authors explore the use of LDMs to model and predict the efficiency of corrosion inhibitors, highlighting how LDM analysis surpasses traditional methods in predictive power. It is also shown how the PCA can be applied to LDMs of corrosion inhibitors to discover the actual active species that affect the inhibition of corrosion. Biochemical applications include examples where LDM PCA is used to predict mosquito repellency in Chapter 8 followed by the prediction of enzyme-substrate interactions in Chapter 9. In particular, Chapter 9 proposes an LDM approach to predict the behavior of acetylcholine esterase inhibitors, a class of molecules involved in treating Alzheimer's disease. Chapter 10, which is mixed methodological and applied in its coverage, extends the LDM analysis to large systems and explains two approaches to achieve this computational soft-scaling: One is termed the kernel energy method (KEM), which uses closed shell fragments capped with hydrogens as necessary to saturate dangling bonds and the other is assembling LDMs from open shell fragments. The book then closes with a forward look emphasizing that the applications of LDMs is a fast evolving field and that the work is in no way claimed to be complete at this point. The book is reasonably balanced between technical depth and readability. The text is probably accessible to upper-level undergraduate students and may be of interest to researchers in physical chemistry, molecular modeling, and related fields. It is peppered with case studies emphasizing the flexibility of LDMs showing how they can be adapted to different fields. The book also provides some insight into the software implementation of the LDM analysis approach including a brief description of the AIMDELOC program (Chapter 5). Electron Localization-Delocalization Matrices is a valuable addition to the theoretical chemistry library. Matta, Ayers, and Cook offer a guide to applying LDMs, providing both theoretical foundations and practical applications. This book offers a new methodology to enhance the applicability of quantum chemical calculations to fields such as corrosion science, drug design, and enzyme catalysis. In summary, Electron Localization-Delocalization Matrices is a reference for those interested in the intersection of quantum theory, computational chemistry, and CGT. Gratitude is expressed for the suggestions made by four anonymous reviewers that helped improve this book review considerably. L.M. is supported financially by Hunter College, CUNY and the ONR Visiting Professor Program at NRL. There is no data sharing associated with this paper.