Impressive advances have been made in the study of atomic structures, at both the experimental and theoretical levels. And yet, the scarcity of information on atomic energy levels is evident At the same time there exists a need for data, because of the developments in such diverse fields as astrophysics and plasma and laser research, all of them of fundamental importance as well as practical impact. This project of research in atomic structure, consisting of three components (formulation, computer program, and numerical results), constitutes a basic and comprehensive work with a variety of uses. In its most practical application, it will yield a rather accurate prediction of the energy levels of any atomic system, of use per se or in the interpretation and confirmation of experimental results. On the other hand, it will also be of use in the comparative study of the appropriateness of the various levels of approximation and as a point of reference.

This work is based on the observation that further major advances in geochemistry, particularly in understanding the rules that govern the ways in which elements come together to form minerals and rocks, will require the application of the theories of quantum mechanics. The book therefore outlines this theoretical background and discusses the models used to describe bonding in geochemical systems. It is the first book to describe and critically review the application of quantum mechanical theories to minerals and geochemical systems. The book consolidates valuable findings from chemistry and materials science as well as mineralogy and geochemistry, and the presentation has relevance to professionals in a wide range of disciplines. Experimental techniques are surveyed, but the emphasis is on applying theoretical tools to various groups of minerals: the oxides, silicates, carbonates, borates, and sulfides. Other topics dealt with in depth include structure, stereochemistry, bond strengths and stabilities of minerals, various physical properties, and the overall geochemical distribution of the elements.

Why is quantum theory so difficult to understand? In this book, written for modern undergraduate and postgraduate students of chemistry and physics, the author looks at the continuing debate about the meaning of quantum theory. The historical development of the theory is traced from the turn of the century through to the 1930s and the famous debate between Niels Bohr and Albert Einstein. The book examines in detail the arguments that quantum theory is incomplete, as made by Einstein, Boris Podolsky and Nathan Rosen. The development of Bell's theorem is also discussed, along with crucial experimental tests performed in the early 1980s. Alternative interpretations - pilot waves, quantum gravity, consciousness, and many worlds - are described in the closing chapter.

Supercomputer and Chemistry is the name of a series of seminars, which the Industrieanlagen-Betriebsgesellschaft (IABG), Ottobrunn near Munich, started in 1987. This third meeting stressed the fields of computational science, supercomputing and computer-aided chemistry. Moreover, ~he current situation in the supercomputer market as a whole, particularly in Germany, and the trends to be expected were discussed. The new generation of graphic workstations such as StARDENT have the power of minisupercomputers. Some performance results are pre- sented and comparisons with other machines are made. One of the most exciting prospects for improving the performance of computers is parallel processing. Especially, transputers seem to give unli- mited computing speed, in effect a Crayon your desk. We examine the technology of transputers and their usage in industrial and research projects. The user will have a formidable task in paral- lelizing software. The second part of the seminar addressed the usage of mainframes and supercomputers in the chemical industry. The interplay of ex- periments and computer-aided drug design was highlighted by spea- kers from Sandoz, Boehringer-Ingelheim and Merck. There is still one open question when using numerical methods, i.e. whether all the relevant and important conformations have been obtained. Cer- tainly the computational results have to be checked and verified against experimental results. Furthermore, the benefits, disadvantages and the reduction in costs and time in using supercomputers in pharmaceutical research were discussed.

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.

This volume features invited lectures presented in the workshop-cum-symposium on aspects of many-body effects in molecules and extended systems, Calcutta, February 1 - 10, 1988. The organizers invited leading experts to present recent developments of many-body methods as applied to molecules and condensed systems. The panorama portrayed is quite broad, but by no means exhaustive. The emphasis is undoubtedly on a "molecular point of view."

The present volume contains the text of the invited lectures presented at the Symposium on Many Body Methods in Quantum Chemistry, held on the campus of Tel Aviv University in August 1988. The Symposium was a satellite meeting of the Sixth International Congress on Quantum Chemistry held in Jerusalem. The development and application of many-body methods in Quantum chemistry have been on the rise for a number of years. This is therefore a good time for an interim report on the state of the field. It is hoped that such a report is hereby provided, though it may not be complete. The Symposium was held under the auspices of Tel Aviv University, Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry. Other sponsors were the Israeli Academy of Sciences and Humanities, and the Israeli Ministry of Science and Development. Many thanks go to all of them. Finally, I would like to thank all the speakers and participants for making the meeting the enjoyable and (I hope) profitable experience it was. Tel Aviv, Israel Uzi Kaldor TESTS AND APPLICATIONS OF COMPLETE MODEL SPACE QUASIDEGENERATE MANY-BODY PERTURBATION THEORY FOR MOLECULES Karl F. Freed The James Franck Institute and Department of Chemistry The University of Chicago, Chicago, DUnois 60637 U.S.A."

The work presented here is a result of an extended collaboration with a number of coworkers and guests. Particularly, I would like to thank Dr. P. Burkhard and Dr. W. Strub for their careful work performed for their Ph. D. thesis and Dr. M. Heming for his brilliant ideas and his dedication. Very fruitful and stimulating were collaborations with our guests, i. e. with G. A. Brinkman and P. W. F. Louwrier from NIKHEF-K in Amsterdam, B. C. Webster, M. J. Ramos and D. McKenna from the University of Glasgow, M. C. R. Symons, D. Geeson and C. J. Rhodes from the University of Leicester, S. F. J. Cox and C. A. Scott from the Rutherford Appleton Laboratory in Chilton, and R. De Renzi and M. Ricco from the University of Parma. Many invaluable discussions with friends and competitors in the field helped to address new viewpoints and to define new goals. I shall not forget my teacher and director of the radical chemistry group, Prof. H. Fischer, whom I wish to thank for his interest and active support and for the great liberty he allowed me for the planning and organization of the project. Last but not least, I thank my dear wife Hanny and our children Christian, Martin and Andrea who suffered, without complaint, daddy's absence for so many hours.

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

One of the most interesting fields of mathematically oriented chemical research is the so-called computer-assisted organic synthesis design. These lecture notes elaborate the mathematical model of organic chemistry, which offers formal concepts for unambiguous description of computer algorithms for organic synthesis design including retrosynthesis and reaction mechanisms. All definitions and theorems are supplemented by many illustrative examples. The model is closely related to the course of thinking of organic chemists. These notes will be useful for all theoretically oriented organic chemists who are interested in mathematical modelling of organic chemistry and computer-assisted organic synthesis design.

From December 1985 through March 1986 the text of this book formed the basis of an in-hours course taught by the author at Harry Diamond Laborato ries. Considerable assistance in revising and organizing the first draft was given by John Bruno. The original draft of these notes was based on a collection of lectures delivered at the Universidade Federal de Pernambuco, Recife, Brazil, between 2 November 1981 and 2 December 1981. The visit to Recife was a response to an invi tation of Professor Gilberto F. de Sa of the Physics Department. In the preparation of these notes I made many requests of my coworkers for earlier resul ts and recollections of our early work. Among those consul ted were Donald Wortman, Nick Karayianis, and Richard Leavitt. Further, a number of .suggestions from my Brazilian colleagues helped make the lectures more clear. Particular among these were Professor Oscar Malta and Professor Alfredo A. da Gama both of whom I wish to thank for their help. Encouragement and assistance with funding for much of this work came from Leon Esterowitz of the Naval Research Laboratory and Rudolph Buser and Albert Pinto of the center for Night Vision and Electro-Optics."

There is no doubt about the importance of hydration in many areas of every day life, technology, biology, medicine, science etc. During the last years many investigations have been carried out upon problems of hydration and a large amount of experimental and theoretical data has been obtained by the application of different methods. One effi cient possibility to stimulate progress in scientific problems is to come together and discuss existing results and ideas. This was the aim of the 35th Bunsenkolloquium and a subsequent seminar held in Marburg, FRG from April 2 -4, 1987 with respect to the "Interaction of Water in Ionic and Nonionic Hydrates." The meeting was attended by more than one hundred participants from 25 countries. It will be seen from the content of the chapters in this book, which comprises the introductory papers and more or less extended abstracts of research seminars, that it was possible not only to stress the advantages and disadvantages of each method, but also to show how information gained by one method can complement the results of another one in order to increase our overall understanding of hydration pheno mena. The papers are divided into sections concerning the hydration of: ions, nonionic substances, biological and macromolecular substances, surfactants as well as a section containing methods, models and theo ries, which may stimulate investigations on hydrations."

More and more possible applications of organometallic compounds in organic synthesis have been uncovered and a growing number of scientists are attracted to this area of research. This book presents an state-of-the-art account of the successful application of main- and transition metal mediated syntheses. It will stimulate new ideas and initiate further research in all areas of this fascinating chemistry.

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.

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.

In the 1980's sonochemistry was considered to be a rather restricted branch of chemistry involving the ways in which ultrasound could improve synthetic procedures, predominantly in heterogeneous systems and particularly for organometallic reactions. Within a few years the subject began to expand into other disciplines including food technology, environmental protection and the extraction of natural materials. Scientific interest grew and led to the formation of the European Society of Sonochemistry in 1990 and the launch of a new journal Ultrasonics Sonochemistry in 1994. The subject continues to develop as an exciting and multi-disciplinary science with the participation of not only chemists but also physicists, engineers and biologists. The resulting cross-fertilisation of ideas has led to the rapid growth of interdisciplinary research and provided an ideal way for young researchers to expand their knowledge and appreciation of the ways in which different sciences can interact. It expands scientific knowledge through an opening of the closed doors that sometimes restrict the more specialist sciences. The journey of exploration in sonochemistry and its expansion into new fields of science and engineering is recounted in "Sonochemistry Evolution and Expansion" written by two pioneers in the field. It is unlike other texts about sonochemistry in that it follows the chronological developments in several very different applications of sonochemistry through the research experiences of the two authors Tim Mason and Mircea Vinatoru. Designed for chemists and chemical engineers Written by two experts and practitioners in the subject Volume 1 covers the historical background and evolution of sonochemistry Volume 2 explains the wider applications and expansion of the subject VOLUME 2 Applications and Developments Volume 2 contains six chapters which detail the developments of sonochemistry in fields which continue to attract considerable research and development interest from academia and industry. The topics range from the important developments in chemical synthesis through food technology and materials processing to therapeutic ultrasound. The authors have made contributions to all of these and so the content is written in a way which should be understandable to readers whose expertise may not necessarily be in the individual topic. Each of the applications and developments described help to illustrate not only the diverse nature of sonochemistry but also the unifying theme of the effects of acoustic cavitation on a wide range of procedures.

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.

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."

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 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.

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.

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."

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.