This book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are:

The development of computational methods that support human health and environmental risk assessment of engineered nanomaterials (ENMs) has attracted great interest because the application of these methods enables us to fill existing experimental data gaps. However, considering the high degree of complexity and multifunctionality of ENMs, computational methods originally developed for regular chemicals cannot always be applied explicitly in nanotoxicology. This book discusses the current state of the art and future needs in the development of computational modeling techniques for nanotoxicology. It focuses on (i) computational chemistry (quantum mechanics, semi-empirical methods, density functional theory, molecular mechanics, molecular dynamics), (ii) nanochemoinformatic methods (quantitative structure-activity relationship modeling, grouping, read-across), and (iii) nanobioinformatic methods (genomics, transcriptomics, proteomics, metabolomics). It reviews methods of calculating molecular descriptors sufficient to characterize the structure of nanoparticles, specifies recent trends in the validation of computational methods, and discusses ways to cope with the uncertainty of predictions. In addition, it highlights the status quo and further challenges in the application of computational methods in regulation (e.g., REACH, OECD) and in industry for product development and optimization and the future directions for increasing acceptance of computational modeling for nanotoxicology.

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.

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.

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.

Modern experimental and computational techniques are capable of determining bond lengths and angles with precisions of a few thousandths of an angstrom and a few tenths of a degree. Such precisions are meaningful only if they are coupled with rigorous error analysis and careful evaluation of the physical meaning of the parameters. This book demonstrates the meaning and applicability of accurate structures and their variations following a rigorous exposure of the demands and caveats in their determination. It establishes guidelines for accuracy requirements in answering broadly varying questions in current chemical research. The 21 chapters by internationally recognized authors discuss the following topics: potential energy surfaces; microwave, infrared, and liquid crystal NMR spectroscopies; gas phase electron diffraction; X-ray and neutron crystallography; electron density studies; ab initio molecular orbital methods and molecular mechanics calculations; the use of structural databases; applications to organic inorganic and organometallic chemistry; studies of reaction pathways; effects of substitution and crystal environment on molecular structure.

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.

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.

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."