Molecular chirality is one of the fundamental aspects of chemistry. Chirality properties of molecules have implications in a wide variety of subjects, ranging from the basic quantum mechanical properties of simple of a few atoms to molecular optical activity, asymmetric synthesis, systems and the folding pattern of proteins. Chirality, in both the geometrical and the topological sense, has also been the subject of investigations in various branches of mathematics. In particular, new developments in a branch of topology, called knot theory, as well as in various branches of discrete mathematics, have led to a novel perspective on the topological aspects of molecular chirality. Some of the mathematical advances have already found applications to the interpretation of new concepts in theoretical chemistry and mathematical chemistry, as well as to novel synthetic approaches leading to new molecules of exceptional structural properties. Some of the new developments in molecular chirality have been truly fundamental to the theoretical understanding and to the actual practice of many aspects of chemistry. The progress in this field has been very rapid, even accelerating in recent years, and a review appears more than justified. This book offers a selection of subjects covering some of the latest developments. Our primary aim is to clarify some of the basic concepts that are the most prone to misinterpretation and to provide brief introductions to some of those subjects that are expected to have further, important contributions to our understanding of molecular properties and chemical reactivity.

"Linear-Scaling Techniques in Computational Chemistry and Physics" summarizes recent progresses in linear-scaling techniques and their applications in chemistry and physics. In order to meet the needs of a broad community of chemists and physicists, the book focuses on recent advances that extended the scope of possible exploitations of the theory.

The first chapter provides an overview of the present state of the linear-scaling methodologies and their applications, outlining hot topics in this field, and pointing to expected developments in the near future. This general introduction is then followed by several review chapters written by experts who substantially contributed to recent developments in this field.

The purpose of this book is to review, in a systematic manner, recent developments in linear-scaling methods and their applications in computational chemistry and physics. Great emphasis is put on the theoretical aspects of linear-scaling methods.

This book serves as a handbook for theoreticians, who are involved in the development of new efficient computational methods as well as for scientists, who are using the tools of computational chemistry and physics in their research.

"Linear-Scaling Techniques in Computational Chemistry and Physics" summarizes recent progresses in linear-scaling techniques and their applications in chemistry and physics. In order to meet the needs of a broad community of chemists and physicists, the book focuses on recent advances that extended the scope of possible exploitations of the theory.

The first chapter provides an overview of the present state of the linear-scaling methodologies and their applications, outlining hot topics in this field, and pointing to expected developments in the near future. This general introduction is then followed by several review chapters written by experts who substantially contributed to recent developments in this field.

The purpose of this book is to review, in a systematic manner, recent developments in linear-scaling methods and their applications in computational chemistry and physics. Great emphasis is put on the theoretical aspects of linear-scaling methods.

This book serves as a handbook for theoreticians, who are involved in the development of new efficient computational methods as well as for scientists, who are using the tools of computational chemistry and physics in their research.

In recent years the fundamental concepts and applied methodologies of molecular similarity analysis have experienced a revolutionary development. Motivated by the increased degree of understanding of elementary molecular properties on the levels ranging from fundamental quantum chemistry to the complex interactions of biomolecules, and aided by the spectacular progress in computer technology and access to computer power, the area has opened up to many new ideas and new approaches. This book covers topics in quantum similarity approaches, electron density shape analysis methods, and it provides better theoretical understanding of molecular similarity. Additionally, quantitative shape analysis, especially activity relations (QShAR) and the prediction of the pharmacological or toxicological effects of molecules in the related context of quantum QSAR (QQSAR). This volume written by the experts in the various subfields of molecular similarity, provides a collection of the most recent ideas, advances, and methodologies. It is the hope of the Editors that by representing these topics within a single volume, the readers will find a balanced overview of the status of the field. We also hope that the book will serve as a tool for selecting and assessing the best approach for various new types of problems of molecular similarity that may arise and it will provide a set of easy references for further studies and applications.

The electron density of a non-degenerate ground state system determines essentially all physical properties of the system. This statement of the Hohenberg-Kohn theorem of Density Functional Theory plays an exceptionally important role among all the fundamental relations of Molecular Physics. In particular, the electron density distribution and the dynamic properties of this density determine both the local and global reactivities of molecules. High resolution experimental electron densities are increasingly becoming available for more and more molecules, including macromolecules such as proteins. Furthermore, many of the early difficulties with the determination of electron densities in the vicinity of light nuclei have been overcome. These electron densities provide detailed information that gives important insight into the fundamentals of molecular structure and a better understanding of chemical reactions. The results of electron density analysis are used in a variety of applied fields, such as pharmaceutical drug discovery and biotechnology. If the functional form of a molecular electron density is known, then various molecular properties affecting reactivity can be determined by quantum chemical computational techniques or alternative approximate methods.

In recent years the fundamental concepts and applied methodologies of molecular similarity analysis have experienced a revolutionary development. Motivated by the increased degree of understanding of elementary molecular properties on the levels ranging from fundamental quantum chemistry to the complex interactions of biomolecules, and aided by the spectacular progress in computer technology and access to computer power, the area has opened up to many new ideas and new approaches. This book covers topics in quantum similarity approaches, electron density shape analysis methods, and it provides better theoretical understanding of molecular similarity. Additionally, quantitative shape analysis, especially activity relations (QShAR) and the prediction of the pharmacological or toxicological effects of molecules in the related context of quantum QSAR (QQSAR). This volume written by the experts in the various subfields of molecular similarity, provides a collection of the most recent ideas, advances, and methodologies. It is the hope of the Editors that by representing these topics within a single volume, the readers will find a balanced overview of the status of the field. We also hope that the book will serve as a tool for selecting and assessing the best approach for various new types of problems of molecular similarity that may arise and it will provide a set of easy references for further studies and applications.

The electron density of a nondegenerate ground state system determines essentially all physical properties of the system. This statement of the Hohenberg-Kohn theorem of Density Functional Theory plays an exceptionally important role among all the fundamental relations of molecular physics. Electron densities provide detailed information that gives important insight into the fundamentals of molecular structure and a better understanding of chemical reactions. If the functional form of a molecular electron density is known, then various molecular properties affecting reactivity can be determined by quantum chemical computational techniques or alternative approximate methods. This book contains a selection of chapters based on papers given at the 12th conference of the Commission of Charge, Spin and Momentum Density of the International Union for Crystallography, held in Waskiesiu, Prince Albert National Park, Canada, on July 27 - August 1, 1997. The choice of topics represents some of the latest advances in the field of electron, spin, and momentum densities and the analysis of these densities with respect to their roles in determining chemical reactivity. This book provides an exciting collection of accounts of the latest advances, and also provides further motivation for new research to address some of the challenging, unsolved problems of the fascinating interrelations between electron, spin, and momentum densities, and the complex subject of chemical reactivity.

Molecular chirality is one of the fundamental aspects of chemistry. Chirality properties of molecules have implications in a wide variety of subjects, ranging from the basic quantum mechanical properties of simple of a few atoms to molecular optical activity, asymmetric synthesis, systems and the folding pattern of proteins. Chirality, in both the geometrical and the topological sense, has also been the subject of investigations in various branches of mathematics. In particular, new developments in a branch of topology, called knot theory, as well as in various branches of discrete mathematics, have led to a novel perspective on the topological aspects of molecular chirality. Some of the mathematical advances have already found applications to the interpretation of new concepts in theoretical chemistry and mathematical chemistry, as well as to novel synthetic approaches leading to new molecules of exceptional structural properties. Some of the new developments in molecular chirality have been truly fundamental to the theoretical understanding and to the actual practice of many aspects of chemistry. The progress in this field has been very rapid, even accelerating in recent years, and a review appears more than justified. This book offers a selection of subjects covering some of the latest developments. Our primary aim is to clarify some of the basic concepts that are the most prone to misinterpretation and to provide brief introductions to some of those subjects that are expected to have further, important contributions to our understanding of molecular properties and chemical reactivity.