1. 1 STATEMENT OF THE PROBLEM Quantum chemistry judged not from the ever present possibility of unex pected developments but on the basis of the achievements in the last fifty years, is predominantly limited to attempts to solve for the energy and expectation values of wave functions representing, in the limit, an exact solution to the Schroedinger equation. Because of well-known dif ficulties in system with more than about 50 electrons, the adopted ap proximations are generally rather crude. As examples of quantum chemical approximations we mention the total or partial neglects of electron correlation, the neglect of relativistic effects, the use of subminimal basis sets, the still present neglect of inner-core electrons in semi-empirical methods, the acceptance of the Born-Oppenheimer approximations, and so on. In general, the larger the system, in terms of the number of electrons, the cruder the approxima tion. In a way, the present status of quantum chemistry might appear as nearly paradoxical. Indeed, for small systems, where very accurate ex periments are often available, and therefore, there is not a great need to obtain (from quantum chemistry) predictions of new data but rather, a theoretical interpretation of the existing data, we find increasi gly powerful and reliable quantum chemical methods and techniques."

Since the discovery of quantum mechanics, more than fifty years ago, the theory of chemical reactivity has taken the first steps of its development. The knowledge of the electronic structure and the properties of atoms and molecules is the basis for an un derstanding of their interactions in the elementary act of any chemical process. The increasing information in this field during the last decades has stimulated the elaboration of the methods for evaluating the potential energy of the reacting systems as well as the creation of new methods for calculation of reaction probabili ties (or cross sections) and rate constants. An exact solution to these fundamental problems of theoretical chemistry based on quan tum mechanics and statistical physics, however, is still impossible even for the simplest chemical reactions. Therefore, different ap proximations have to be used in order to simplify one or the other side of the problem. At present, the basic approach in the theory of chemical reactivity consists in separating the motions of electrons and nu clei by making use of the Born-Oppenheimer adiabatic approximation to obtain electronic energy as an effective potential for nuclear motion. If the potential energy surface is known, one can calculate, in principle, the reaction probability for any given initial state of the system. The reaction rate is then obtained as an average of the reaction probabilities over all possible initial states of the reacting artic1es. In the different stages of this calculational scheme additional approximations are usually introduced."

This highly informative and carefully presented book comprises select proceedings of Foundation for Molecular Modelling and Simulation (FOMMS 2018). The contents are written by invited speakers centered on the theme Innovation for Complex Systems. It showcases new developments and applications of computational quantum chemistry, statistical mechanics, molecular simulation and theory, and continuum and engineering process simulation. This volume will serve as a useful reference to researchers, academicians and practitioners alike.

Although the importance of steric fit for receptor-effector 1 interactions was recognized since Emil Fischer proposed his "lock and key" theory, the whole area of steric properties is still in a very 2-4 early stage of development. We have a fairly good idea about el- tronic and hydrophobic parameters, but it is not easy to describe ste- ric shapes of molecules without a large number of data. There are se- veral cases of good QSAR's developed for rather large series of mole- 5 cules without steric parameters - for example see papers by Hansch , 6 or Franke , but the state of steric parameters is nevertheless one of the most important drawbacks, especially concerning the ability of en- compassing, within a single QSAR, molecules of different shapes and stereoisomers. From today's steric parameters, one may mention the 7 Taft parameters E ' which gave good results in organic chemistry, the S 8 10 ra th er cum b ersome way 0 f measurIng * s h ape d'ff I ere h ces 0 f Amoore - and , 11 12 AllInger ,and the L, B -B parameters of Verloop 1 4 The work described here consists of two types of approaches to the steric fit problem. The first approach consists of developing new parameters to describe different characteristics of the molecular shape (i. e. , branching, bulkiness); this is done by means of topological in- dices.

Until recently quantum chemical ab initio calculations were re stricted to atoms and very small molecules. As late as in 1960 Allen l and Karo stated : "Almost all of our ab initio experience derives from diatomic LCAO calculations *** N and we have found in the litera ture "approximately eighty calculations, three-fourths of which are for diatomic molecules *** There are approximately twenty ab initio calculations for molecules with more than two atoms, but there is a decided dividing line between the existing diatomic and polyatomic wave functions. Confidence in the satisfactory evaluation of the many -center two-electron integrals is very much less than for the diatom ic case". Among the noted twenty calculations, SiH was the largest 4 molecule treated. In most cases a minimal basis set was used and the many-center two-electron integrals were calculated in an approximate way. Under these circumstances the ab initio calculations could hard ly provide useful chemical information. It is therefore no wonder that the dominating role in the field of chemical applications was played by semiempirical and empirical methods. The situation changed essentially in the next decade. The problem of many-center integrals was solved, efficient and sophisticated computer programs were devel oped, basis sets suitable for a given type of problem were suggested, and, meanwhile, a considerable amount of results has been accumulated which serve as a valuable comparative material. The progress was of course inseparable from the development and availability of computers.

Traditionally, when one deals with crystals, the first property to be presented is the periodicity of the lattice, and all methods of study are based on this characteristic, which is considered essential. In fact, crystals differ from the molecules of finite size that are studied in chemistry, only in their extremely large number of particles. Furthermore, the existence of faces, which limit the spread of crystals in space, necessarily breaks the periodicity of the system. For these reasons it is natural to apply to crystals the concepts and methods that have been widely tested in the study of molecules. Pauling first emphasized this point 1 and used it to explain the electronic structure of crystals, thought to be infinite and perfect. The aim of this work is to show, with the help of a few examples, the possibilities offered by quantum chemistry for tackling the problems of crystal electronic structure, of crystallographic arrangements as well as their macroscopic shape, and of distortion effects caused by the presence of faces. The area related to the existence of energy bands (allowed or forbidden), gap, electric, magnetic or optical properties will not be touched upon.

Introduction 1 1. 2. Basic Concepts and Phenomenological Description 6 2.1. Separation of the Center-of-Mass Motion 8 2.2. Separation of Electronic and Nuclear Motions. Interaction Potentials (Potential-Energy Surfaces) 11 2.2.1. Heuristic Considerations 11 2.2.2. Born-Oppenheimer Separation. Adiabatic Approximation, 16 Present State of Potential-Energy-Burface 2.2.3. Calculations 23 2.3. Scattering Channels ~6 2.4. Classification of Elementary Processes. Microscopic Mechanism 27 D.ynamics of Atomic and Molecular Collisions: 3. Electronically Adiabatic Processes 32 Classical Approach 3.1. 33 Some Arguments for the Reliability of the Classical Approach 33 Atom-Atom Collisions. Elastic Scattering 34 Quasiclassical Treatment of Elementary Processes in Triatomic Systems: Inelastic and Reactive Scattering 44 IV Examples of Results of Trajectory Calculations 59 3.1.4. 64 Elements of Quantum-Mechanical Methods 3.2. Correspondence of Classical and Quantum 3.2.1. 64 Mechanical Theories Time-Dependent Scattering Theory 71 3.2.2. Stationary Scattering Theory 77 3.2.3. One-Dimensional Scattering 78 3.2.3.1 * Three-Dimensional Elastic Scattering 83 3.2.3.2. Rearrangement Scattering (Reactions) 85 3.2.3.3. Examples of Quantum-Mechanical Calculations 3.2.4.

One should distinguish between coordination numbers and hydration numbers. Following Bockris

The present text is a rational analysis of the concept of the chemical bond by means of the principles of wave mechanics. The discussion of the material has been arranged so as to render its main content comprehensible for readers who may not have had pre"ious training in quantum mechanics. The text comprises three major parts. It begins with an exposition of the fundamental ideas. In this section the principles are reviewed from which de Broglie developed his mechanics; this allows the book to be read by chemistry majors and freshmen alike. However, we believe that it may also be of interest to university-and college teachers who must include certain aspects of quantum chemistry into their courses while being insufficiently familiar with the subject. It may even be of interest to science teachers in secondary schools. Finally, having been a witness to the evolution of these notions for over a quarter of a century, we present certain concepts from a particular point of view which might prove attractive to chemists of all kinds, perhaps even quantum chemists. The second, more technical part summarizes the methods of constructing wave functions that describe the electrons in molecules. This section can only be fully appreciated by those readers who are familiar with some aspects of the algorithms used in quantum mechanics.

Quantum Theory of Chemical Reactivity may be read without reference to the fact that it is actually the third of three volumes of a treatise on quantum chemistry, the science resulting from the implementation of mathematical laws in the realm of molecular populations. The first two volumes of the treatise, 'Fondement de la Chimie Tbeorique' and 'Structure Electrique des Molecules' were, like this third volume, originally published by Gauthier-Villars; Pergamon published the English translations of these two volumes. I am grateful to D. Reidel Publishing Company for translating the third volume of the treatise into English. Readers familiar with English rather than French now have access to the complete series. This treatise is a reflection of the courses I taught at the Sorbonne from 1950 until 1967 to students in their second cycle (3rd and 4th year) and third cycle (5th and 6th year) working towards a doctorate in this particular field. It is based on the reading of over a thousand articles, and is intended for students as well as for physical chemists, and chemists, research workers and engineers taking an interest in quantum chemistry for its own sake or for its application in industry, pharmacology and the life sciences. Reidel's initiative is particularly valuable because in my opinion Quantum Theory of Chemical Reactivity is the most important of the three volumes of the treatise. Doubtless for this reason only the third volume was published in Japanese by Baifukan, thanks to Professors Hayashi and Sohma.

This book provides an introduction to the classical, quantum and symmetry aspects of multipole theory, demonstrating the successes of the theory and also its unphysical aspects. It presents a transformation theory, which removes these unphysical properties. The book will be of interest to physics students wishing to advance their knowledge of multipole theory, and also a useful reference work for molecular and optical physicists, theoretical chemists working on multipole effects, solid state physicists studying the effects of electromagnetic fields on condensed matter, engineers and applied mathematicians with interests in anisotrpoic materials. An interesting recent development has been the increasing use of computer calculations in applications of multipole theory. The book should assist computational physicists and chemists wishing to work in this area to acquire the necessary background in multipole theory.

This is a companion volume to K. Kong Wan's textbook Quantum Mechanics: A Fundamental Approach, published in 2019 by Jenny Stanford Publishing. The book contains more than 240 exercises and problems listed at the end of most chapters. This essential manual presents full solutions to all the exercises and problems that are designed to help the reader master the material in the textbook. Mastery of the material in the book would contribute greatly to the understanding of the concepts and formalism of quantum mechanics.

This textbook provides a simple approach to understand the various complex aspects of stereochemistry. It deals with basic static stereochemistry and gives an overview of the different isomeric forms and nomenclatures. With simple writing style and many examples, this book covers the topics such as stereochemistry of hydrocarbons, alkenes, cycloalkenes, optically active compounds, trivalent carbon, fused, bridged and caged rings and related compounds. This textbook also covers the additional topics such as optical rotatory dispersion and circular dichroism, steroechemistry of elimination reactions, substitution reactions, rearrangement reactions and pericyclic reactions. The book includes pedagogical features like end-of-chapter problems and key concepts to help students in self-learning. The textbook is extremely useful for the senior undergraduate and postgraduate students pursuing course in chemistry, especially organic chemistry. Besides, this book will also be a useful reference book for professionals working in various chemical industries, biotechnology, bioscience and pharmacy.

This book covers recent advances of the fragment molecular orbital (FMO) method, consisting of 5 parts and a total of 30 chapters written by FMO experts. The FMO method is a promising way to calculate large-scale molecular systems such as proteins in a quantum mechanical framework. The highly efficient parallelism deserves being considered the principal advantage of FMO calculations. Additionally, the FMO method can be employed as an analysis tool by using the inter-fragment (pairwise) interaction energies, among others, and this feature has been utilized well in biophysical and pharmaceutical chemistry. In recent years, the methodological developments of FMO have been remarkable, and both reliability and applicability have been enhanced, in particular, for non-bio problems. The current trend of the parallel computing facility is of the many-core type, and adaptation to modern computer environments has been explored as well. In this book, a historical review of FMO and comparison to other methods are provided in Part I (two chapters) and major FMO programs (GAMESS-US, ABINIT-MP, PAICS and OpenFMO) are described in Part II (four chapters). dedicated to pharmaceutical activities (twelve chapters). A variety of new applications with methodological breakthroughs are introduced in Part IV (six chapters). Finally, computer and information science-oriented topics including massively parallel computation and machine learning are addressed in Part V (six chapters). Many color figures and illustrations are included. Readers can refer to this book in its entirety as a practical textbook of the FMO method or read only the chapters of greatest interest to them.

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

This series reflects the breadth of modern research in inorganic chemistry and fulfils the need for advanced texts. The series covers the whole range of inorganic and physical chemistry, solid state chemistry, coordination chemistry, main group chemistry and bioinorganic chemistry.

Understanding the nature of the chemical bond is the key to understanding all chemistry, be it inorganic, physical, organic or biochemistry. In the form of a question and answer tutorial the fundamental concepts of chemical bonding are explored. These range from the nature of the chemical bond, via the regular hexagonal structure of benzene and the meaning of the term ‘metallic bond’, to d-orbital involvement in hypervalent compounds and the structure of N₂O. Chemical Bonds: A Dialog provides

• a novel format in terms of a dialog between two scientists
• insights into many key questions concerning chemical bonds
• an orbital approach to quantum chemistry

Chemical Modeling equips the reader with the knowledge to understand the behaviour of solids, gases and liquids in terms of the basic properties of their atoms, molecules, and polymer chains. In particular the interactions between these fundamental building blocks and the intermolecular and intramolecular potentials are examined. Carefully structured, the book starts by the discussion of classical, quantum and statistical mechanics which then leads on to a discussion of modeling techniques applied to solids, gases and liquids. The subject is brought to life through many real life examples and practical illustrations. Features

• Classical mechanics and quantum mechanics are both introduced from a basic level
• Explains the relationships between microscopic and macroscopic quantities
• Gives an up-to-date treatment of a variety of chemical modeling techniques
• Avoids unnecessary mathematical rigour
• Carefully structured into ‘bite-sized’ chapters

Advances in Quantum Chemistry, Volume 77, presents surveys of current topics in this rapidly developing field, one that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology. It features detailed reviews written by leading international researchers, with this release focusing on topics such as Per-Olov Loewdin's Impact on a 'Lost Son', Electron impact ionization cross sections for inner L- and M-subshells of atomic targets at relativistic energies, Aromaticity Revisited, Electron-atom and electron-molecule resonances, Precise Born-Oppenheimer potentials of the excited states of H_2 using explicitly correlated exponential functions, and more.

Small systems are a very active area of research and development due to improved instrumentation that allows for spatial resolution in the range of sizes from one to 100 nm. In this size range, many physical and chemical properties change, which opens up new approaches to the study of substances and their practical application. This affects both traditional fields of knowledge and many other new fields including physics, chemistry, biology, etc. This book highlights new developments in statistical thermodynamics that answer the most important questions about the specifics of small systems - when one cannot apply equations or traditional thermodynamic models.

An authoritative, up-to-date volume covering all of the major spin-bearing intermediates of radical chemistry ... This essential sourcebook provides unified coverage of the main types of spin-bearing intermediates-free radicals, anion radicals, cation radicals, ion radical pairs, diradicals, and triplets. Integrating simple molecular orbital theory and electron spin resonance concepts throughout, the book develops basic material with minimal emphasis on mathematics. This straightforward presentation of up-to-date information enables readers to apply radical chemistry and electron transfer chemistry effectively to their own research. In addition to helpful references, an extensive bibliography, and nearly 300 illustrations, this book:
* Emphasizes electron transfer reactions, radical and ion radical clocks, and biological processes that involve spin-bearing intermediates
* Provides a clear view of close interrelationships between spin-bearing intermediates
* Integrates MO theory and ESR spectroscopy into chapters on each class of reactive intermediate
* Offers examples of many common organic reactions that have been found to proceed through the intermediates
* Features challenging chapter-end problem sets
Suitable for students and professionals in chemistry, biology, polymer science, and environmental science, this book is an indispensable guide to the rapid growth area of radical chemistry.