Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention.

This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

Using the spin-Hamiltonian formalism the magnetic parameters are introduced through the components of the Lambda-tensor involving only the matrix elements of the angular momentum operator. The energy levels for a variety of spins are generated and the modeling of the magnetization, the magnetic susceptibility and the heat capacity is done. Theoretical formulae necessary in performing the energy level calculations for a multi-term system are prepared with the help of the irreducible tensor operator approach. The goal of the programming lies in the fact that the entire relevant matrix elements (electron repulsion, crystal field, spin-orbit interaction, orbital-Zeeman, and spin-Zeeman operators) are evaluated in the basis set of free-atom terms. The modeling of the zero-field splitting is done at three levels of sophistication. The spin-Hamiltonian formalism offers simple formulae for the magnetic parameters by evaluating the matrix elements of the angular momentum operator in the basis set of the crystal-field terms. The magnetic functions for dn complexes are modeled for a wide range of the crystal-field strengths.

Transition metal catalysis belongs to the most important chemical research areas because a ubiquitous number of chemical reactions are catalyzed by transition metal compounds. Many efforts are being made by industry and academia to find new and more efficient catalysts for chemical processes. Transition metals play a prominent role in catalytic research because they have been proven to show an enormous diversity in lowering the activation barrier for chemical reactions. For many years, the search for new catalysts was carried out by trial and error, which was costly and time consuming. The understanding of the mechanism of the catalytic process is often not very advanced because it is difficult to study the elementary steps of the catalysis with experimental techniques. The development of modern quantum chemical methods for calculating possible intermediates and transition states was a breakthrough in gaining an understanding of the reaction pathways of transition metal catalyzed reactions. This volume, organized into eight chapters written by leading scientists in the field, illustrates the progress made during the last decade. The reader will obtain a deep insight into the present state of quantum chemical research in transition metal catalysis.

In Periodic Nanostructures, the authors demonstrate that structural periodicity in various nanostructures has been proven experimentally. The text covers the coalescence reactions, studied by electronic microscopy, and shows that the nanoworld is continuous, giving rise to zero- (fullerenes), one- (tubules), two-(graphite) and three-(diamond, spongy carbon) dimensional carbon allotropes.

The authors explore foam-like carbon structures, which relate to schwarzites, and which represent infinite periodic minimal surfaces of negative curvature. They show that these structures contain polygons (with dimensions larger than hexagons w.r.t. to graphite) that induce this negative curvature. The units of these structures appear as nanotube junctions (produced via an electron beam) that have wide potential molecular electronics applications. Self-assembled supramolecular structures (of various tessellation) and diamond architectures are also proposed. The authors propose that the periodicity of close repeat units of such structures is most evident not only in these formations but also present in all of the carbon allotropes. It is also shown that depending on the lattice tessellation, heteroatom type, and/or doping, metal nanostructures (nanotubes in particular) can display both metallic and semiconductor characteristics. Therefore, their properties can be manipulated by chemical functionalization. The authors therefore suggest that nanostructures have heralded a new generation of nanoscale biological, chemical, and physical devices.

The text also provides literature and data on the field of nanostructure periodicity and the authors own results on nanostructure building and energy calculations as well as topological characterization by means of counting polynomials of periodic nanostructures. The aromaticity of various coverings of graphitic structures is also discussed.

This book is aimed at scientists working in the field of nanoscience and nanotechnology, Ph.D. and MSc. degree students, and others interested in the amazing nanoarchitectures that could inspire the cities of the future."

The discussions and plans on all scienti?c, advisory, and political levels to realize an even larger "European Supercomputer" in Germany, where the hardware costs alone will be hundreds of millions Euro - much more than in the past - are getting closer to realization. As part of the strategy, the three national supercomputing centres HLRS (Stuttgart), NIC/JSC (Julic ] h) and LRZ (Munich) have formed the Gauss Centre for Supercomputing (GCS) as a new virtual organization enabled by an agreement between the Federal Ministry of Education and Research (BMBF) and the state ministries for research of Baden-Wurttem ] berg, Bayern, and Nordrhein-Westfalen. Already today, the GCS provides the most powerful high-performance computing - frastructure in Europe. Through GCS, HLRS participates in the European project PRACE (Partnership for Advances Computing in Europe) and - tends its reach to all European member countries. These activities aligns well with the activities of HLRS in the European HPC infrastructure project DEISA (Distributed European Infrastructure for Supercomputing Appli- tions) and in the European HPC support project HPC-Europa. Beyond that, HLRS and its partners in the GCS have agreed on a common strategy for the installation of the next generation of leading edge HPC hardware over the next ?ve years. The University of Stuttgart and the University of Karlsruhe have furth- more agreed to bundle their competences and resources."

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.

Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation.
The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material.
In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

The book offers new concepts and ideas that broaden reader 's perception of modern science.

Internationally established experts present the inspiring new science of complexity, which discovers new general laws covering wide range of science areas.

The book offers a broader view on complexity based on the expertise of the related areas of chemistry, biochemistry, biology, ecology, and physics.

Contains methodologies for assessing the complexity of systems that can be directly applied to proteomics and genomics, and network analysis in biology, medicine, and ecology.

Heterogeneous catalysis is a fascinating and complex subject of utmost importance in the present day. Its immense technological and economical importance and the inherent complexity of the catalytic phenomena have stimulated theoretical and experimental studies by a broad spectrum of scientists, including chemists, physicists, chemical engineers, and material scientists. Computational and theoretical techniques are now having a major impact in this field. This book aims to illustrate and discuss the subject of heterogeneous catalysis and to show the current capabilities of the theoretical and computational methods for studying the various steps (diffusion, adsorption, chemical reaction) of heterogeneous catalytic process involving zeolites, metal oxides, and transition metal surfaces. The book covers: the use of techniques of computational chemistry to simulate zeolites, metallic and bimetallic surfaces, and oxide-supported metals; the impact of simulation methods on the understanding of the diffusion and adsorption of molecules and cations within the pores of zeolites, and also on the adsorption of molecules on metal and metal-oxide surfaces; and the applications of quantum-mechanical methods to the study of the reaction mechanism and pathways of the adsorbed molecules. This book is recommended primarily to scientists and graduate students conducting research in the fields of heterogeneous catalysis and surface science. It will also be valuable to advanced undergraduate students wishing to become acquainted with the latest developments in these exciting fields of research, and to experimentalists seeking theoretical support for interpreting their results.

Non-Linear Optical Properties of Matter: From Molecules to Condensed Phases attempts to draw together both theory and application in this field. As such it will be of interest to both experimentalists and theoreticians alike. Divided into two parts, Part 1 is concerned with the theory and computing of non-linear optical (NLO) properties while Part 2 reviews the latest developments in experimentation.

Part 1: Surveys the current advances in the computation of the NLO properties of molecules, crystalline solids and nano-particles. It examines the methods employed to compute the properties of both microscopic and macroscopic forms of matter.

Part 2: Covers the recent advances on the NLO properties of organometallic compounds, rotaxanes, glasses, Langmuir-Blodget films, gold and silver nano-particles etc. Strategies to develop novel NLO materials are also discussed along with the Hyper-Rayleigh scattering technique.

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.

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."

"Multi-scale Quantum Models for Biocatalysis" explores various molecular modelling techniques and their applications in providing an understanding of the detailed mechanisms at play during biocatalysis in enzyme and ribozyme systems. These areas are reviewed by an international team of experts in theoretical, computational chemistry, and biophysics.

This book presents detailed reviews concerning the development of various techniques, including ab initio molecular dynamics, density functional theory, combined QM/MM methods, solvation models, force field methods, and free-energy estimation techniques, as well as successful applications of multi-scale methods in the biocatalysis systems including several protein enzymes and ribozymes.

This book is an excellent source of information for research professionals involved in computational chemistry and physics, material science, nanotechnology, rational drug design and molecular biology and for students exposed to these research areas.

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.

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.

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 covers the results obtained in the Tera op Workbench project during a four years period from 2004 to 2008. The Tera op Workbench project is a colla- ration betweenthe High PerformanceComputingCenter Stuttgart (HLRS) and NEC Deutschland GmbH (NEC-HPCE) to support users to achieve their research goals using high performance computing. The Tera op Workbench supports users of the HLRS systems to enable and - cilitate leading edge scienti c research. This is achieved by optimizing their codes and improving the process work ow which results from the integration of diff- ent modules into a "hybrid vector system." The assessment and demonstration of industrial relevance is another goal of the cooperation. The Tera op Workbench project consists of numerous individual codes, grouped together by application area and developed and maintained by researchers or c- mercial organizations. Within the project, several of the codes have shown the ab- ity to reach beyond the TFlop/s threshold of sustained performance. This created the possibility for new science and a deeper understanding of the underlying physics. The papers in this book demonstrate the value of the project for different scienti c areas.

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.

The gap between introductory level textbooks and highly specialized monographs is filled by this modern textbook. It provides in one comprehensive volume the in-depth theoretical background for molecular modeling and detailed descriptions of the applications in chemistry and related fields like drug design, molecular sciences, biomedical, polymer and materials engineering. Special chapters on basic mathematics and the use of respective software tools are included. Numerous numerical examples, exercises and explanatory illustrations as well as a web site with application tools (http://www.amrita.edu/cen/ccmm) support the students and lecturers.

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 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.

From the reviews: " ...] an excellent reference book. I have no doubt it will become a much-thumbed resource for students and researchers in mineralogy and crystallography." Geological Magazine

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.