It is an indisputable fact that computational physics form part of the essential landscape of physical science and physical education. When writing such a book, one is faced with numerous decisions, e. g. : Which topics should be included? What should be assumed about the readers' prior knowledge? How should balance be achieved between numerical theory and physical application? This book is not elementary. The reader should have a background in qu- tum physics and computing. On the other way the topics discussed are not addressed to the specialist. This work bridges hopefully the gap between - vanced students, graduates and researchers looking for computational ideas beyond their fence and the specialist working on a special topic. Many imp- tant topics and applications are not considered in this book. The selection is of course a personal one and by no way exhaustive and the material presented obviously reflects my own interest. What is Computational Physics? During the past two decades computational physics became the third fun- mental physical discipline. Like the 'traditional partners' experimental physics and theoretical physics, computational physics is not restricted to a special area, e. g. , atomic physics or solid state physics. Computational physics is a meth- ical ansatz useful in all subareas and not necessarily restricted to physics. Of course this methods are related to computational aspects, which means nume- cal and algebraic methods, but also the interpretation and visualization of huge amounts of data.

In this volume we have collected some of the contributions made to the Twelfth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-XII) in 2007. The workshop was held at Royal Holloway College, the most westerly campusof the University of London, and situated just a stone's throw from Windsor Great Park. The workshop, which ran from 30 August to 5 September, continued the series that was established by Roy McWeeny in April 1996 with a meeting held at San Miniato, near Pisa. The purpose of the QSCP workshops is to bring together, in an informal atmosphere and with the aim of fostering collaboration, those chemists and physicists who share a common ?eld of interest in the theory of the quantum many-body problem. Quantum mechanics provides a theoretical foundation for our understandingof the structure, propertiesanddynamicsof atoms, moleculesandthe solid state, in terms of their component particles: electrons and nuclei. The study of 'Quantum Systems in Chemistry and Physics' therefore underpins many of the emerging?elds in twenty-?rstcenturyscience andtechnology: nanostructure, smart materials, drug design - to name but a few. Members of the workshop were keen to discuss their research and engage in collaboration centred upon the development of fundamental and innovative theory which would lead to the exploration of new concepts. The proceedings of all of the workshops, which have been held annually since 1996, have been published both to disseminate the latest developments within the wider community and to stimulate further collaboration.

There is a unity to physics; it is a discipline which provides the most fundamental understanding of the dynamics of matter and energy. To understand anything about a physical system you have to interact with it and one of the best ways to learn something is to use electrons as probes. This book is the result of a meeting, which took place in Magdalene College Cambridge in December 2001. Atomic, nuclear, cluster, soHd state, chemical and even bio- physicists got together to consider scattering electrons to explore matter in all its forms. Theory and experiment were represented in about equal measure. It was meeting marked by the most lively of discussions and the free exchange of ideas. We all learnt a lot. The Editors are grateful to EPSRC through its Collaborative Computational Project program (CCP2), lOPP, the Division of Atomic, Molecular, Optical and Plasma Physics (DAMOPP) and the Atomic Molecular Interactions group (AMIG) of the Institute of Physics for financial support. The smooth running of the meeting was enormously facilitated by the efficiency and helpfulness of the staff of Magdalene College, for which we are extremely grateful. This meeting marked the end for one of us (CTW) of a ten-year period as a fellow of the College and he would like to take this opportunity to thank the fellows and staff for the privilege of working with them.

RF Probeheads 1. J. Link, Faellanden, Switzerland The Design of Resonator Probes with Homogeneous Radiofrequency Fields 2. M. Schnall, Philadelphia, PA/USA Probes Tuned to Multiple Frequencies for In-Vivo NMR RF Pulses 3. P.C.M. van Zijl, Rockville, MD/USA; C.T.W. Moonen, Bethesda, MD/USA Solvent Suppression Strategies for In Vivo Magnetic Resonance Spectroscopy 4. M. Garwood, K. Ugurbil, Minneapolis, MN/USA B1 Insensitive Adiabatic RF Pulses 5. P.G. Morris, Nottingham, UK Frequency Selective Excitation Using Phase-Compensated RF Pulses in One andTwo Dimensions 6. S. Mueller, Basel, Switzerland RF Pulses for MultipleFrequency Excitation: Theory and Application Spectrum Analysis 7. R. de Beer, D. van Ormondt, Delft, The Nethelands Analysis of NMR Data Using Time Domain Fitting Procedures 8. E.B. Cady, London, UK Determination of Absolute Concentrations of Metabolites from NMR Spectra

The aim of this highly original book is to survey a number of chemical compounds that some chemists, theoretical and experimental, find fascinating. This is the first book to feature compounds/classes of compounds of theoretical interest that have been studied theoretically but have defied synthesis. It is hoped that this collection of idiosyncratic molecules will appeal to chemists who find the study of chemical oddities interesting and, on occasion, even rewarding.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Stuttgart High Performance Computing Center in 2007. The reports cover all fields of computational science and engineering, with emphasis on industrially relevant applications. Presenting results for both vector-based and microprocessor-based systems, the book allows comparison between performance levels and usability of various architectures.

Computational Studies of RNA and DNA includes, in an integrated way, modern computational studies of nucleic acids, ranging from advanced electronic structure quantum chemical calculations through explicit solvent molecular dynamics (MD) simulations up to mesoscopic modelling, with the main focus given to the MD field. It gives an equal emphasis to the leading methods and applications while successes, as well as pitfalls of the computational techniques are discussed.

The systems and problems considered include:

- Basic principles of nucleic acid structure and structural databases
- Introduction to key molecular modelling tools and methods
- Application of atomistic simulations to a wide variety of DNA and RNA systems
- Accurate QM calculations of base pairing, stacking and cation binding
- Charge transfer, excited states and NMR parameters
- Calculating mechanical properties of nucleic acids
- Mesoscopic simulation of DNA, chromatin modelling

This book is ideally suited to academics and researchers in organic and computational chemistry, structural molecular biology and biophysics as well as biochemistry, and particularly those interested in the molecular modelling of nucleic acids.

Besides the state-of-the-art science, the book also provides extensive introductory information for non-specialists and students to enter and understand this field.

Les hypotheses, n'en deplaise a mon contradicteur, sont l'ame des progres de la science. Louis Pasteur The concept of chirality, established 100 years ago, plays an im- portant role in almost all domains and dimensions of our recent scientific view of life. Chiral properties can be found in fundamen- tal nuclear particles, in molecules, and in the macroscopic world of living nature (plants and animals) and inanimate nature (crystals). In particular, chirality, or more precisely chiral excess, is evident in human beings. For example, the expected symmetry of the hands turns out to be functionally non-existent. Consequently chirality occurs in the technical sphere, where screws are the best-known examples, since most of them are made for right-handed people. Chirality is not confined to static objects but influences processes such as chemical reactions. The occurrence of chiral objects on different dimensional scales has been treated in the past in mutually independent frameworks. There were, however, two remarkable events from which the conclu- sion can be drawn that the appearance of chirality in various fields has a common cause. On the one hand, physicists found evidence that the well-known biomolecular homochirality can be traced back to the chirality of weak bosons. At the same time, on the other hand, the so-called thalidomide tragedy occurred when thalido- mide molecules of a certain chirality, taken by pregnant women, caused deformed children.

The analysis of singular perturbed di?erential equations began early in the twentieth century, when approximate solutions were constructed from asy- totic expansions. (Preliminary attempts appear in the nineteenth century - see[vD94].)Thistechniquehas?ourishedsincethemid-1960sanditsprincipal ideas and methods are described in several textbooks; nevertheless, asy- totic expansions may be impossible to construct or may fail to simplify the given problem and then numerical approximations are often the only option. Thesystematicstudyofnumericalmethodsforsingularperturbationpr- lems started somewhat later - in the 1970s. From this time onwards the - search frontier has steadily expanded, but the exposition of new developments in the analysis of these numerical methods has not received its due attention. The ?rst textbook that concentrated on this analysis was [DMS80], which collected various results for ordinary di?erential equations. But after 1980 no further textbook appeared until 1996, when three books were published: Miller et al. [MOS96], which specializes in upwind ?nite di?erence methods on Shishkin meshes, Morton's book [Mor96], which is a general introduction to numerical methods for convection-di? usion problems with an emphasis on the cell-vertex ?nite volume method, and [RST96], the ?rst edition of the present book. Nevertheless many methods and techniques that are important today, especially for partial di?erential equations, were developed after 1996.

This series presents critical reviews of the present position and future trends in modern chemical research. It contains short and concise reports on chemistry, each written by the world renowned experts. This series remains valid and useful after 5 or 10 years.

More information as well as the electronic version of the whole content available at: springerlink.com.

This is a self-contained advanced review offering step by step derivation of the consistent theoretical picture of hybrid modeling methods and the thorough analysis of the concepts and current practical methods of hybrid modeling based on this theory. The book presents its material in a sequential way paying attention both to the physical soundness of the approximations used and to the mathematical rigor necessary for practical developing of the robust modeling code.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2006. The reports cover all fields of computational science and engineering ranging from CFD via computational physics and chemistry to computer science with a special emphasis on industrially relevant applications. The book comes with illustrations and tables.

Robert S. Mulliken, Nobel Laureate in chemistry, always had the intention to write a book about his field of research: molecular orbital theory. This is his scientific autobiography, edited posthumously by his former student Bernard J. Ransil and complemented with a memoir by Friedrich Hund, his scientific protagonist. Mulliken describes his career and gives an account of the contributions of his friends and colleagues at home and in Europe where he frequently travelled. And last but not least, he gives an accurate history of how the molecular orbital theory originated and how it evolved in an atmosphere of international exchange. The book is written in a particularly lively style, full of reminiscences and scientific facts, interwoven to produce an account of the Life of a Scientist.

The rivers run into the sea, yet the sea is not full Ecclesiastes What is quantum chemistry? The straightforward answer is that it is what quan tum chemists do. But it must be admitted, that in contrast to physicists and chemists, "quantum chemists" seem to be a rather ill-defined category of scientists. Quantum chemists are more or less physicists (basically theoreticians), more or less chemists, and by large, computationists. But first and foremost, we, quantum chemists, are conscious beings. We may safely guess that quantum chemistry was one of the first areas in the natural sciences to lie on the boundaries of many disciplines. We may certainly claim that quantum chemists were the first to use computers for really large scale calculations. The scope of the problems which quantum chemistry wishes to answer and which, by its unique nature, only quantum chemistry can only answer is growing daily. Retrospectively we may guess that many of those problems meet a daily need, or are say, technical in some sense. The rest are fundamental or conceptual. The daily life of most quantum chemists is usually filled with grasping the more or less technical problems. But it is at least as important to devote some time to the other kind of problems whose solution will open up new perspectives for both quantum chemistry itself and for the natural sciences in general.

This book is an extensive revision of the earlier 2nd Edition with the same title, of 1988. The book has been rewritten in, I hope, a much more did- tic manner. Subjects such as discretisations or methods for solving ordinary di?erential equations are prepared carefully in early chapters, and assumed in later chapters, so that there is clearer focus on the methods for partial di?erential equations. There are many new examples, and all programs are inFortran90/95, whichallows amuchclearerprogrammingstylethanearlier Fortran versions. In the years since the 2nd Edition, much has happened in electrochemical digital simulation. Problems that ten years ago seemed insurmountable have been solved, such as the thin reaction layer formed by very fast homogeneous reactions, or sets of coupled reactions. Two-dimensional simulations are now commonplace, and with the help of unequal intervals, conformal maps and sparse matrix methods, these too can be solved within a reasonable time. Techniques have been developed that make simulation much more e?cient, so that accurate results can be achieved in a short computing time. Stable higher-order methods have been adapted to the electrochemical context. The book is accompanied (on the webpage www.springerlink.com/ openurl.asp?genre=issue&issn=1616-6361&volume=666) by a number of - ample procedures and programs, all in Fortran 90/95. These have all been veri?edasfaraspossible.Whilesomeerrorsmightremain, theyarehopefully very few.

The first edition of this book was published in 1978 and a new Spanish e(, tition in 1989. When the first edition appeared, Professor A. Martin suggested that an English translation would meet with interest. Together with Professor A. S. Wightman, he tried to convince an American publisher to translate the book. Financial problems made this impossible. Later on, Professors E. H. Lieband W. Thirring proposed to entrust Springer-Verlag with the translation of our book, and Professor W. BeiglbOck accepted the plan. We are deeply grateful to all of them, since without their interest and enthusiasm this book would not have been translated. In the twelve years that have passed since the first edition was published, beautiful experiments confirming some of the basic principles of quantum me chanics have been carried out, and the theory has been enriched with new, im portant developments. Due reference to all of this has been paid in this English edition, which implies that modifications have been made to several parts of the book. Instances of these modifications are, on the one hand, the neutron interfer ometry experiments on wave-particle duality and the 27r rotation for fermions, and the crucial experiments of Aspect et al. with laser technology on Bell's inequalities, and, on the other hand, some recent results on level ordering in central potentials, new techniques in the analysis of anharmonic oscillators, and perturbative expansions for the Stark and Zeeman effects."

This phonon atlas presents a collection of phonon-dispersion and density-of states curves of more than a hundred insulating crystals. It grew out of an appendix to a handbook article on phonon spectra 2.1J from which it was fin ally separated mainly because this phonon atlas provides a rather self-con tained tool for every scientist who is working in the field of dynamical properties of solids. He often may find it' useful to have a handy documen tation of the experimental phonon dispersion curves which have been measured so far, together with information on calculated dispersion relations and densities of states. The book will be found to be incomplete by readers who are interested not only in phonon frequencies of a specific crystal but would also like to know about related properties such as elastic and dielectric constants. This is, at the present time, beyond the scope of this volume, but the authors would welcome all suggestions and criticism which could be considered for a forth coming edition. Furthermore, we would be pleased to provide interested readers with information about phonon spectra which came to our knowledge after completion of the manuscript. On the other hand, we will be most grateful for all information about phonon dispersion curves which is missing in our collection or new data for further editions."

Density functional theory (DFT) is by now a well-established method for tackling the quantum mechanics of many-body systems. Originally applied to compute properties of atoms and simple molecules, DFT has quickly become a work horse for more complex applications in the chemical and materials sciences. The present set of lectures, spanning the whole range from basic principles to relativistic and time-dependent extensions of the theory, is the ideal introduction for graduate students or nonspecialist researchers wishing to familiarize themselves with both the basic and most advanced techniques in this field.

Applications of Supramolecular Chemistry introduces the use of non-covalent interactions and molecular recognition for many fields. Applications include the analysis of technically, medically, and environmentally important chemical compounds, their separation, purification and removal, and the design of new materials, including supramolecular electronics. The book also explores biological interactions and applications in the food and textile industries.

This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments.

so easy it seemed Once found, which yet unfound most would have thought Impossible. (John Milton, 1608 -1674) There are essentially two types of books on a scientific subject: in the first one several authors contribute their specialized approaches to parts of the field in question, which then are edited and compiled to yield a comprehensive and authoritative account. In the second type of book a single author tries to pre sent a view from an individual standpoint which might lead to a more balanced and homogeneous source of information. Both kinds have their merits and de ficiencies. I decided to write this book as a monolithic piece of work for several rea sons. Of course, there was the challenge of coping with the many problems of such an undertaking due to the fact that this field has grown tremendously during the last decades. In addition, being heavily involved in linear oligopyr role chemistry for nearly two decades, it seemed worthwile to prepare a more unifying approach. The request of several colleagues from abroad to give an account in English also triggered this endeavor since most of the work of my group has been published in German."

Per-Olov Lowdin's stature has been a symbol of the world of quantum theory during the past five decades, through his basic contributions to the development of the conceptual framework of Quantum Chemistry and introduction of the fundamental concepts; through a staggering number of regular summer schools, winter institutes, innumerable lectures at Uppsala, Gainesville and elsewhere, and Sanibel Symposia; by founding the International Journal of Quantum Chemistry and Advances in Quantum Chemistry; and through his vision of the possible and his optimism for the future, which has inspired generations of physicists, chemists, mathematicians, and biologists to devote their lives to molecular electronic theory and dynamics, solid state, and quantum biology.

Fundamental World of Quantum Chemistry Volumes I, II and III form a collection of papers dedicated to the memory of Per-Olov Lowdin. These volumes are of interest to a broad audience of quantum, theoretical, physical, biological, and computational chemists; atomic, molecular, and condensed matter physicists; biophysicists; mathematicians working in many-body theory; and historians and philosophers of natural science. The volumes will be accessible to all levels, from students, PhD students, and postdocs to their supervisors."

It is difficult to overestimate the impact that density functional theory has had on computational quantum chemistry over the last two decades. Indeed, this period has seen it grow from little more than a theoreticalcuriosity to become a central tool in the computational chemist s armoury. Arguably no area of ch- istry has benefited more from the meteoric rise in density functional theory than inorganic chemistry. the ability to obtainreliable results in feasible ti- scales on systems containing heavy elements such as the d and f transition - tals has led to an enormous growth in computational inorganic chemistry. The inorganic chemical literature reflects this growth; it is almost impossible to open a modern inorganic chemistry journal without finding several papers devoted exclusively or in part to density functional theory calculations. The real imp- tance of the rise in density functional theory in inorganic chemistry is undou- edly the much closer synergy between theory and experiment than was p- viously posible. In these volumes, world-leading researchers describe recent developments in the density functional theory and its applications in modern inorganic and b- inorganic chemistry. These articles address key issues key issues in both sol- state and molecular inorganic chemistry, such as spectroscopy, mechanisms, catalysis, bonding and magnetism. The articles in volume I are more focussed on advances in density functional methodogy, while those in Volume II deal more with applications, although this is by no means a rigid distinction.

Comprehensive theoretical and experimental analysis of UV-radiation and low energy electron induced phenomena in nucleic acid bases (NABs) and base assemblies are presented in this book. NABs are highly photostable; the absorbed energy is dissipated in the form of ultrafast nonradiative decay. This book highlights the possible mechanisms of these phenomena which is important for all living species and discusses technical challenges in exploration of these processes.

This book provides a hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrodinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements. The book also contains numerical methods for solving the Schrodinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations. "