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."

The aim of these notes is to offer a modern picture of the pertur bative approach to the calculation of intermolecular forces. The point of view taken is that a perturbative series truncated at a low order can provide a valuable way for valuating interaction energies, especial ly if one limits oneself to the case of intermediate- and long-range distances between the interacting partners. Although the situation corresponding to short distances is essen tially left out from our presentation, the problems which are within the range of the theory form a vast and important class: a large var iety of phenomena of matter, in fact, depends on the existence of in teractions among atoms or molecules, which over a substantial range of distances should be classified as weak in comparison to the interactions occurring inside atoms or molecules. We are aware of the omission of some topics, which in principle could have been included in our review. For instance, a very scarce at tention has been paid to the analysis of problems involving interacting partners in degenerate states, which is of particular relevance in the case of interactions between excited atoms (only a rather quick presen tation of the formal apparatus of degenerate perturbation theory is in cluded in Chap. III). Interactions involving the simultaneous presence of more than two atoms (or mOlecules) have not been considered, with the consequent non-necessity of considering nonadditive effects which characterize the general N-body problem."

The aim of this chapter is to discuss in detail the Monte Carlo algorithms developed to compute the sequence distributions in polymers. Because stereoregular polymers constitute a unique form of copolymer, the stereosequence distributions in vinyl homopolymers and the sequence distributions in copolymers can be computed using the same algorithms. Also included is a brief review of probabilistic models (i. e. , Bernoulli trials and Markov chains) frequently used to compute the sequence distribtuion. The determination of sequence distributions is important for the under- standing of polymer physical properties, to compute the monomer reactivity para- meters and to discriminate among polymerization mechanisms. 2. 2. Short review of analytical models, Monte Carlo algorithms and computer programs. l A Bernoullian model was developed by Price. Within this model the probability of a given state of the system is independent of the previous state and does not condition the next state. The Bernoullian behaviour has been shown 24 to describe cls-trans distributions among 1, 4 additions in polybutadienes - , 5 the comonomer distribution in ethylene-vinyl acetate copolymer , and configura- 6 tional distributions in polystyrene , poly (vinyl chloride)7, poly (vinyl alcohol)7 Consider the binary copolymerization:;1,J=1,2 (1) where - MI* , I = 1,2, is an ionic or radical polymeric chain end, and M, J = 1,2, J is a monomer. Because the final state (i. e.

Analytical chemistry of the recent years is strongly influenced by automation. Data acquisition from analytica instruments - and some times also controlling of instruments - by a computer are principally solved since many years. Availability of microcomputers made these tasks also feasible from the economic point of view. Besides these basic applications of computers in chemical measurements scientists developed computer programs for solving more sophisticated problems for which some kind of "intelligence" is usually supposed to be necessary. Harm less numerical experiments on this topic led to passionate discussions about the theme "which jobs cannot be done by a computer but only by human brain ? . If this question is useful at all it should not be ans wered a priori. Application of computers in chemistry is a matter of utility, sometimes it is a social problem, but it is never a question of piety for the human brain. Automated instruments and the necessity to work on complex pro blems enhanced the development of automatic methods for the reduction and interpretation of large data sets. Numerous methods from mathematics, statistics, information theory, and computer science have been exten sively investigated for the elucidation of chemical information; a new discipline "chemometrics" has been established. Three different approaches have been used for computer-assisted interpretations of chemical data. 1. Heuristic methods try to formu late computer programs working in a similar way as a chemist would solve the problem. 2."

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."

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.

Stereochemistry is defined as the study of the three-dimensional structure of molecules. Stereochemical considerations are important in both isomerism and studies of the mechanisms of chemical reactions. Implicit in a mechanism is the stereochemistry of the reaction: in other words, the relative three-dimensional orientation of the reacting particles at any time in the reaction. Concentrating on organic chemistry, early chapters deal mainly with definitions of terms such as chirality, enantiomers, diastereoisomers and racemization, complete with suitable examples to illustrate key concepts. Use of a polarimeter and associated definitions are described, together with two different conventions D, L and R, S for specification of configuration. Chirality without a stereogenic centre, in molecules such as allenes for example, is also covered. The distinction between conformation and configuration is developed to include assignment of configurations to di-substituted cyclohexanes and to the decalins. The conventions E, Z and Re, Si are introduced for sp2 hybridized carbons as found in alkenes and carbonyl compounds. Diastereotopic groups are discussed. Aspects of stereochemistry are explored through consideration of addition reactions to alkenes and carbonyl groups, nucleophilic substitution, and reactions (and interactions) involved in the resolution of racemic mixtures. Additional material is available on the website at www.rsc.org/tct Ideal for the needs of undergraduate chemistry students, Tutorial Chemistry Texts is a major series consisting of short, single topic or modular texts concentrating on the fundamental areas of chemistry taught in undergraduate science courses. Each book provides a concise account of the basic principles underlying a given subject, embodying an independent-learning philosophy and including worked examples.

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

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.

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 textbook facilitates students' ability to apply fundamental principles and concepts in classical thermodynamics to solve challenging problems relevant to industry and everyday life. It also introduces the reader to the fundamentals of statistical mechanics, including understanding how the microscopic properties of atoms and molecules, and their associated intermolecular interactions, can be accounted for to calculate various average properties of macroscopic systems. The author emphasizes application of the fundamental principles outlined above to the calculation of a variety of thermodynamic properties, to the estimation of conversion efficiencies for work production by heat interactions, and to the solution of practical thermodynamic problems related to the behavior of non-ideal pure fluids and fluid mixtures, including phase equilibria and chemical reaction equilibria. The book contains detailed solutions to many challenging sample problems in classical thermodynamics and statistical mechanics that will help the reader crystallize the material taught. Class-tested and perfected over 30 years of use by nine-time Best Teaching Award recipient Professor Daniel Blankschtein of the Department of Chemical Engineering at MIT, the book is ideal for students of Chemical and Mechanical Engineering, Chemistry, and Materials Science, who will benefit greatly from in-depth discussions and pedagogical explanations of key concepts. Distills critical concepts, methods, and applications from leading full-length textbooks, along with the author's own deep understanding of the material taught, into a concise yet rigorous graduate and advanced undergraduate text; Enriches the standard curriculum with succinct, problem-based learning strategies derived from the content of 50 lectures given over the years in the Department of Chemical Engineering at MIT; Reinforces concepts covered with detailed solutions to illuminating and challenging homework problems.

Scientists are increasingly finding themselves engaged in research problems that cross the traditional disciplinary lines of physics, chemistry, biology, materials science, and engineering. Because of its broad scope, statistical mechanics is an essential tool for students and more experienced researchers planning to become active in such an interdisciplinary research environment. Powerful computational methods that are based in statistical mechanics allow complex systems to be studied at an unprecedented level of detail. This book synthesizes the underlying theory of statistical mechanics with the computational techniques and algorithms used to solve real-world problems and provides readers with a solid foundation in topics that reflect the modern landscape of statistical mechanics. Topics covered include detailed reviews of classical and quantum mechanics, in-depth discussions of the equilibrium ensembles and the use of molecular dynamics and Monte Carlo to sample classical and quantum ensemble distributions, Feynman path integrals, classical and quantum linear-response theory, nonequilibrium molecular dynamics, the Langevin and generalized Langevin equations, critical phenomena, techniques for free energy calculations, machine learning models, and the use of these models in statistical mechanics applications. The book is structured such that the theoretical underpinnings of each topic are covered side by side with computational methods used for practical implementation of the theoretical concepts.

This book deals with a central topic at the interface of chemistry and physics-the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. The emphasis is on concepts and insights obtained via analytical theories rather than computational and numerical aspects. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics, the dynamics of uni- and bi-molecular elementary reactions are described. The book features a comprehensive presentation of transition-state theory which plays an important role in practice, and a detailed discussion of basic theories of reaction dynamics in condensed phases. Examples and end-of-chapter problems are included in order to illustrate the theory and its connection to chemical problems. The second edition includes updated descriptions of adiabatic and non-adiabatic electron-nuclear dynamics, an expanded discussion of classical two-body models of chemical reactions, including the Langevin model, additional material on quantum tunnelling and its implementation in Transition-State Theory, and a more thorough description of the Born and Onsager models for solvation.

Used in materials science, physical chemistry and physics, density functional methods provide a unifying description of electronic properties applicable to all materials while also giving specific information on the system under study. A large number of very different materials and systems (atoms, molecules, macromolecules, clusters, bulk solids, surfaces and interfaces) are presently being studied with methods based on density functional formalism. Density Functional Methods in Chemistry and Materials Science reports the results of this research. This book will be of particular interest to those research materials science from a theoretical standpoint. This work will demonstrate how the formalism has become a methodology leading to useful information on structural and electronic properties of a broad range of materials.