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."

The lattice dynamics of molecular crystals has undergone an enor mous progress in these last twenty years or so. The experimental and theoretical advances have been realized by two different approaches. From one side molecular spectroscopists have been primarily interested in the vibrational properties of the molecules themselves subjected to the perturbing influence of the crystal environment. From the other side the lattice dynamical theory familiar in solid state physics for atomic lattices has been extended to molecular arrays. Although the overlap between the two approaches has been considerable the reference material is rather scattered in specialized papers. The purpose of this book is to partly fill this gap and to discuss the lattice dynamical theory of molecular crystals in a compact and specialized form. As such, the book is not intended exclusively for researchers and specialists in the field but also for graduate students entering an activity in solid state mo lecular spectroscopy."

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.

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.

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.

The focus of this excellent textbook is the topic of molecular reaction dynamics. The chapters are all written by internationally recognised researchers and, from the outset, the contributors are writing with the young scientist in mind. The easy to use, stand-alone, chapters make it of value to students, teachers, and researchers alike. Subjects covered range from the more traditional topics, such as potential energy surfaces, to more advanced and rapidly developing areas, such as femtochemistry and coherent control. The coverage of reaction dynamics is very broad, so many students studying chemical physics will find elements of this text interesting and useful. Tutorials in Molecular Reaction Dynamics includes extensive references to more advanced texts and research papers, and a series of 'Study Boxes' help readers grapple with the more difficult concepts. Each chapter is thoroughly cross-referenced, helping the reader to link concepts from different branches of the subject. Worked problems are included, and each chapter concludes with a selection of problems designed to test understanding of the subjects covered. Supplementary reading material, and worked solutions to the problems, are contained on a secure website.

This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mathematics of a relatively simple system, before moving on to more complicated systems. After describing polarization, the text goes on to describe spin systems, time evolution, continuous variable systems (particle in a box, harmonic oscillator, hydrogen atom, etc.), and perturbation theory. The book also includes chapters which describe material that is frequently absent from undergraduate texts: quantum measurement, entanglement, quantum field theory and quantum information. This material is connected not only to the laboratories described in the text, but also to other recent experiments. Other subjects covered that do not often make their way into undergraduate texts are coherence, complementarity, mixed states, the density operator and coherent states. Supplementary material includes further details about implementing the laboratories, including parts lists and software for running the experiments. Computer simulations of some of the experiments are available as well. A solutions manual for end-of-chapter problems is available to instructors.

Problem-solving is one of the most challenging aspects students encounter in general chemistry courses, leading to frustration and failure. Consequently, many students become less motivated to take additional chemistry courses after the first year. This book tackles this issue head on and provides innovative, intuitive, and systematic strategies to tackle any type of calculations encountered in chemistry. The material begins with the basic theories, equations, and concepts of the underlying chemistry, followed by worked examples with carefully explained step-by-step solutions to showcase the ways in which the problems can be presented. The second edition contains additional problems at the end of each chapter with varying degrees of difficulty, and many of the original examples have been revised.

Das Werk gibt eine in sich geschlossene einfuhrende Darstellung der Grundlagen und Methoden zur theoretischen Beschreibung molekularer Strukturen und Prozesse sowie ihrer Anwendung auf Probleme der Chemie. Neben den traditionellen Kerngebieten Quantenchemie und Reaktionsdynamik werden Verfahren zur Modellbildung, praktischen Berechnung bzw. Computersimulation komplexer molekularer Systeme behandelt. Der Umfang ist so gefasst, dass damit der Stoff nicht nur fur einen Basiskurs Theoretische Chemie im Rahmen der Chemieausbildung, sondern auch fur anschliessende vertiefende Studien zur Verfugung steht. Anschlussstellen fur den Einstieg in die aktuelle Forschung und fur den Einsatz theoretisch-chemischer Methoden in Nachbargebieten (Molekulspektroskopie, Biochemie u. a.) werden aufgezeigt.

In this new edition of the book that was called "the most beautiful chemistry book ever written," Peter Atkins reveals the molecules responsible for the experiences of our everyday life in fabrics, drugs, plastics, explosives, detergents, fragrances, tastes, and sex. Atkins gives a non-technical account of a range of aspects of the world around us, revealing unexpected connections and insight into how it can be understood in terms of the atoms and molecules from which it is built. This new edition has dozens of new molecules, new graphic presentations, and a more accessible account of the molecules themselves. Peter Atkins is SmithKline Beecham Fellow and Tutor in Physical Chemistry at Oxford University. Atkins' research includes the fields of theoretical chemistry, particularly magnetic resonance and the electromagnetic properties of molecules. He spends virtually all his time writing books, which range from bestselling college textbooks to books on science for general audiences, including Galileo's Finger (Oxford, 2003); The Periodic Kingdom (Basic Books, 1997); The Second Law (W.H. Freeman, 1995); and Atoms, Electrons, and Change (W.H. Freeman, 1991). Previous Edition Paperback (W.H. Freeman, 1995) 0-7167-2928-8

This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.

Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrodinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativistic approaches are routinely implemented and applied in standard quantum chemical software packages. As it is essential for chemists and physicists to understand relativistic effects in molecules, the first edition of "Relativistic Quantum Chemistry - The fundamental Theory of Molecular Science" had set out to provide a concise, comprehensive, and complete presentation of this theory. This second edition expands on some of the latest developments in this fascinating field. The text retains its clear and consistent style, allowing for a readily accessible overview of the complex topic. It is also self-contained, building on the fundamental equations and providing the mathematical background necessary. While some parts of the text have been restructured for the sake of clarity a significant amount of new content has also been added. This includes, for example, an in-depth discussion of the Brown-Ravenhall disease, of spin in current-density functional theory, and of exact two-component methods and its local variants. A strength of the first edition of this textbook was its list of almost 1000 references to the original research literature, which has made it a valuable reference also for experts in the field. In the second edition, more than 100 additional key references have been added - most of them considering the recent developments in the field. Thus, the book is a must-have for everyone entering the field, as well as for experienced researchers searching for a consistent review.

At the heart of coordination chemistry lies the coordinate bond, in its simplest sense arising from donation of a pair of electrons from a donor atom to an empty orbital on a central metalloid or metal. Metals overwhelmingly exist as their cations, but these are rarely met 'naked' - they are clothed in an array of other atoms, molecules or ions that involve coordinate covalent bonds (hence the name coordination compounds). These metal ion complexes are ubiquitous in nature, and are central to an array of natural and synthetic reactions.

Written in a highly readable, descriptive and accessible style "Introduction to Coordination Chemistry" describes properties of coordination compounds such as colour, magnetism and reactivity as well as the logic in their assembly and nomenclature. It is illustrated with many examples of the importance of coordination chemistry in real life, and includes extensive references and a bibliography.

"Introduction to Coordination Chemistry" is a comprehensive and insightful discussion of one of the primary fields of study in Inorganic Chemistry for both undergraduate and non-specialist readers.

This book provides a vivid account of the early history of molecular simulation, a new frontier for our understanding of matter that was opened when the demands of theoretical physicists were met by the availability of the modern computers. Since their inception, electronic computers have enormously increased their performance, thus making possible the unprecedented technological revolution that characterizes our present times. This obvious technological advancement has brought with it a silent scientific revolution in the practice of theoretical physics. In particular, in the physics of matter it has opened up a direct route from the microscopic physical laws to observable phenomena. One can now study the time evolution of systems composed of millions of molecules, and simulate the behaviour of macroscopic materials and actually predict their properties. Molecular simulation has provided a new theoretical and conceptual tool that physicists could only dream of when the foundations of statistical mechanics were laid. Molecular simulation has undergone impressive development, both in the size of the scientific community involved and in the range and scope of its applications. It has become the ubiquitous workhorse for investigating the nature of complex condensed matter systems in physics, chemistry, materials and the life sciences. Yet these developments remain largely unknown outside the inner circles of practitioners, and they have so far never been described for a wider public. The main objective of this book is therefore to offer a reasonably comprehensive reconstruction of the early history of molecular simulation addressed to an audience of both scientists and interested non-scientists, describing the scientific and personal trajectories of the main protagonists and discussing the deep conceptual innovations that their work produced.

This book presents a number of studies on the molecular dynamics of cement-based materials. It introduces a practical molecular model of cement-hydrate, delineates the relationship between molecular structure and nanoscale properties, reveals the transport mechanism of cement-hydrate, and provides useful methods for material design. Based on the molecular model presented here, the book subsequently sheds light on nanotechnology applications in the design of construction and building materials. As such, it offers a valuable asset for researchers, scientists, and engineers in the field of construction and building materials.