Dieser Band enthAlt die BeitrAge des 2. Workshops "Comuter in der Chemie" (18. -20. November 1987). Das Meeting wurde von der Fachgruppe Chemie-Information der GDCH veranstaltet und enthAlt BeitrAge fA1/4r folgende Gebiete: - Kodierung und Verarbeitung struktureller Informationen - MolekA1/4lmodellierung - Design und Aufbau von Datenbanken - Spektrenbibliotheken und -interpretation mit Schwerpunkt NMR- und Massenspektrometrie - Datenerfassung in der Analytik - Elektronisches Publizieren - UmweltgefAhrlichkeit von Chemikalien - Struktur-Wirkungs-Beziehungen

The project that finally led to this book, was originally started with Dr. Jean-Paul Desclaux. It is a pleasure to thank hirn for a fruitful collaboration stretching over more than a decade. While accepting the responsibility for any remaining errors and omissions, I wish to acknowledge in particular the comments by Teijo Aberg, Viktor Flambaum, Burkhard Fricke, Franz Mark and Arne Rosen. The Bibliography was compiled using a Fortran program, written for the DEC 20 at the University of Turku by Matti Hotokka, and adap ted to the University of Helsinki Burroughs 7800 by Dage Sundholm. Harriet Bjornstrom did most of the typing and Kathe Ramsay cross checked the text against the Bibliography. Readers, interested in obtaining a Wordstar-readable, IBM PC compatible diskette file (about 520 kb on a two-sided diskette) of the Bibliography should contact the author Helsinki, 20 August, 1986 Pekka Pyykko CONTENTS 1. Introduction ................................................. 1 Table 1.1. Managraphs and ather general references ........... 2 2. One-particle problems ........................................ 5 2.1. Special relativity and the ald quantum theary ........... 5 2.2. On the Klein-Gardon equation ............................ 5 2.3. The Dirac equation ...................................... 6 Table 2.l. The Dirac equation: interpretative studies, symmetry properties and non-relativistic limits ............ 7 Table 2.2. The Dirac equation: further transformations ...... 13 Table 2.3. The Dirac equation: solutions for hydrogen-like systems. . ........................................ 1 6 Table 2.4. The Dirac equations: solutions for various n- coulomb fields. . ................................. 21 Table 2.5. Relativistic virial theorems ..................... 26 3. Quantum electrodynamical effects ............................ 27 Table 3.1."

The purpose of these notes is to give some simple tools and pictures to physicists and ' chemists working on the many-body problem. Abstract thinking and seeing have much in common - we say "I see" meaning "I understand" , for example. Most of us prefer to have a picture of an abstract object. The remarkable popularity of the Feynman diagrams, and other diagrammatic approaches to many-body problem derived thereof, may be partially due to this preference. Yet, paradoxically, the concept of a linear space, as fundamental to quantum physics as it is, has never been cast in a graphical form. We know that is a high-order contribution to a two-particle scattering process (this one invented by Cvitanovic(1984)) corresponding to a complicated matrix element. The lines in such diagrams are labeled by indices of single-particle states. When things get complicated at this level it should be good to take a global view from the perspective of the whole many-particle space. But how to visualize the space of all many-particle states ? Methods of such visualization or graphical representation of the ,spaces of interest to physicists and chemists are the main topic of this work.

The "Seventh International Symposium on the Photochemistry and Photo- physics of Coordination Compounds" was held in the charming Schlo~ Elmau lying in a hidden valley of the Bavarian Alps above Garmisch- Partenkirchen, Federal Republic of Germany, from March 29 to April 2, 1987. About ninety participants from seventeen countries including about thirty non-European scientists as far away as Japan and Australia came together for this symposium. Forty-five oral and twenty-five poster contributions were presented. These presentations and the opportunity for many formal and informal discussions stimulated an intense scienti- fic interaction between the participants. This meeting followed previous symposia held in Muhlheim 1974 (Koerner von Gustorf), Ferrara 1976 (Carassiti, Scandola), Koln 1978 (Wasgestian), Montreal 1980 (Serpone), Paris 1982 (Gianotti) and London 1984 (Harriman). The main fields covered by this 7th Symposium were photo-redox processes, organometallic photochemistry, and properties of metal centered excited states. Furthermore, special complexes such as 2+ [Ru(bpy)3] and related compounds as well as Cr(III)-complexes were discussed extensively. Moreover, a series of potential applications such as solar energy conversion and storage (e.g. water splitting) and photoresist technology were important subjects of this meeting. Thus, it was shown again that the rapidly expanding field of excited-state chemistry and physics of coordination compounds has become an important part of inorganic chemistry.

This treatment of molecular and atomic physics is primarily meant as a textbook. It is intended for both chemists and physicists. *It can be read without much knowledge of quantum mechanics or mathematics, since all such details are explained-. It has developed through a series of lectures at the Royal Institute of Technology. The content is to about 50 % theoretical and to 50 % experimental. The reason why the authors, who are experimentalists, went into theory is the following. When we during the beginning of the 1970's measured photo electron spectra of organic molecules, it appeared to be impossible to understand them by use of available theoretical calculations. To handle hydrocarbons we ( together with C. Fridh ) constructed in 1972 a purely empirical procedure, SPINDO [1] which has proved to be useful, but the extension to molecules with hetero atoms appeared to be difficult. One of us ( L.A.) proposed then another purely ~~E!E!~~! EE2~~~~E~ ( Hydrogenic Atoms in Molecules, HAM/1, unpublished), in which the Fock matrix elements f5..y were parametrized using Slater's shielding concept. The self-repulsion was compensated by a term "-1". The ~~2~~_~ff2E~, HAM/2 [2] , started from the total energy E:. of the molecule. The atomic parts of L used the Slater shielding constants, and the bond parts of E. were taken from SPINDO. The Fock matrix elements Fpv were then obtained from E in a conventional way.

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.

I get by with a little help from my friends The Beatles: Sgt. Pepper This book should have been in Danish. Any decent person must be able to express himself in his mother's tongue, also when expounding scientific ideas and results. Had I stuck to this ideal, the book would have been read by very few people, and, indeed, appreciated by even fewer. Having it publ ished in English gives me a chance to fulfill one ambition: to be read and judged by the international scientific community. Another reason is that the majority of my professional friends are regrettably unread in Danish, just as I am in Hebrew, Finnish and even Italian. I want to deprive them of the most obvious excuse for not reading my opus. Like a man I admired, I will first of all thank my wife. In his autobiography, Meir Weisgal, then President of the Weizmann Insti tute of SCience, wrote about his wife: "In addition to her natural endowments - which are considerable - she was a more than competent part-tim secretary." He wrote on, and so shall I. The book has been edited by my wife. So if the reader finds the layout pleasant as, in actual fact, I myself do, Birgit is to be praised. If there are blemishes, I am to be blamed for not having caught them."

The present Volume of Lecture Notes in Chemistry fulfils one of the stated aims of the Series, that of disseminating results discussed and evaluated at recent scientific international conferences; in our case a Satellite Meeting of the well-known Conference Series on the Physics of Electronic and Atomic a:ollisions, the XIIIth ICPEAC, which took place in Castelgandolfo, near Rome, from 23 to 25 July 1983. Since the Satellite Meeting attracted a widely international and in- terdisciplina~y audience whose general consensus was one of warm appro- val for the scie'ntific level achieved during it, we hope that the pre- sent collection of essays will be met by similar success, thus warran- ting our having asked the participants to work still further for us. Before turning to their efforts, however, it is only just to thank the Italian National Research Council (Chemistry Committee and Physics Committee), the University of Rome, the C.N.R. Tnstitute H.A.I. of the Rome Research Area (Montelibretti) and the E.N.E.A. Organisation for their financial aid, which made the Castelgandolfo Meeting possible. We warmly acknowledge the professional expertise of the staff at Villa Montecucco and for their collaboration we are grateful to: Rita Abbasciano, Catherine Cajone, Lucilla Crescentini, .Roberta Fantoni, An- tonio Montani, Amedeo Palma, Rosario Platania, Maurizio Venanzi.

Stereochemistry is the part of chemistry that relates observable prop erties of chemical compounds to the structure of their molecules, i. e. the relative spatial arrangement of their constituent atoms. In classical stereochemistry, the spatial arrangements relevant for interpreting and predicting a given chemical property are customarily described by geometric features/ symmetries in some suitably chosen rigid model of the molecule The solution of stereochemical problems involving single molecular species is the danain of the geometry based approaches, such as the methods of classical stereochemistry, molecular mechanics and quantum chemistry. The molecules of a pure chemical compound form generally an ensemble of molecular individuals that differ in geometry and energy. Thus it is generally impossible to represent a chemical compund adequately by the geo metry of a rigid molecular model. In modern stereochemistry it is often necessary to analyze molecular relation within ensembles and families of stereoisomers and permutation isomers, including molecules whose geometric features are changing with time. Accordingly, there is definitely a need for new types of ideas, concepts, theories and techniques that are usable beyond the scope of customary methodology. This is why the present text was written."

The bond diagrammatic representation of molecules is the foundation of MOVB theory. To a certain extent, this kind of representation is analogous to the one on which "resonance theory" is based and this fact can be projected by a comparison of the various ways in which MOVB theory depicts a species made up of three core and two ligand MO's which define two subsystems containing a total of six electrons and the ways in which "resonance theory" (i. e. , qualitative VB theory) depicts a six-electron-six-AO species such as the pi system of CH =CH-CH=CH-CH=O. The 2 different pictorial representations are shown in Scheme 1 so that the analogies are made evident. First of all, the total MOVB diagrammatic representation of the 6/5 species is obtained by a linear combination of three complete bond diagrams, as in Al, which describe the optimal linear combination of!l! MOVB Configuration Wavefunctions (CW's). By the same token, a total VB diagrammatic representation of the 6/6 species can be obtained by writing a "dot structure", as in Bl, and taking this to mean the optimal linear combination of all VB CW's. Next, we can approxi mate the MOVB wavefunction of the 6/5 species by one complete (or detailed) bond dia gram" (A2). No simple VB representation analogy can be given in this case. Alterna tively, we can approximate the MOVB wavefunction by a linear combination of compact bond diagrams, as in A3, in the way described before.

Complex systems that bridge the traditional disciplines of physics, chemistry, biology, and materials science can be studied at an unprecedented level of detail using increasingly sophisticated theoretical methodology and high-speed computers. The aim of this book is to prepare burgeoning users and developers to become active participants in this exciting and rapidly advancing research area by uniting for the first time, in one monograph, the basic concepts of equilibrium and time-dependent statistical mechanics with the modern techniques used to solve the complex problems that arise in real-world applications. The book contains a detailed review of classical and quantum mechanics, in-depth discussions of the most commonly used ensembles simultaneously with modern computational techniques such as molecular dynamics and Monte Carlo, and important topics including free-energy calculations, linear-response theory, harmonic baths and the generalized Langevin equation, critical phenomena, and advanced conformational sampling methods. Burgeoning users and developers are thus provided firm grounding to become active participants in this exciting and rapidly advancing research area, while experienced practitioners will find the book to be a useful reference tool for the field.

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.

Das Buch enthalt Abschnitte uber Matrizengleichungen und -funktionen, eine computergerechte Darstellung und Losung der Bewegungsgleichungen von linearen ungedampften Schwingungssystemen mit endlich vielen Freiheitsgraden, sowie eine Einfuhrung in die Naherungsmethoden von Rayleigh und Ritz. Das fur Theorie und Praxis gleichermassen bedeutsame Eigenwertproblem wird anders als in der Literatur sonst ublich dem Leser von einem allgemeineren Standpunkt aus nahegebracht, wodurch die Darstellung an Verstandlichkeit wie an Anwendungsbreite gewinnt. Beibehalten wurde die in der Tradition von Rudolf Zurmuhl bewahrte Ausfuhrlichkeit. Das Buch ist sowohl fur Studierende als auch fur Physiker und Ingenieure in der Praxis geschrieben."

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."

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.

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.

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