"Mas has dicho, Sancho, de 10 que sabes (dixo Don Quixote), que hay algunos que se cansan en saber, y averiguar cosas que despues de sabidas, y averiguadas, no importa un ardite al entendimiento, ni a la memoria. " "You have said more than you know, Sancho," said Don Quixote, "for there are some who tire them selves out learning and proving things which, once learnt and proved, do not concern either 'the under standing 01' the memory a jot. " Cervantes, Don Quixote, Part II, Chapter LXXV, Of the great Adventure of Montesinos' Cave in the heart of La Mancha, which the valorous Don Quixote brought to a happy ending. This book explores a relationship between classical tessellations and three-manifolds. All of us are very familiar with the symmetrical ornamental motifs used in the decoration of walls and ceilings. Oriental palaces contain an abundance of these, and many examples taken from them will be found in the following pages. These are the so-called mosaics or symmetrical tessellations of the euclidean plane. Even though we can imagine or even create very many of them, in fact the rules governing them are quite restrictive, if our purpose is to understand the symmetric group of the tessellation, that is to say, the group consisting of the plane isometries which leave the tessel lation invariant."

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.

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.

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.

This book delivers a comprehensive account of the main features and possibilities of LCAO methods for the first principles calculations of electronic structure of periodic systems. The first part describes the basic theory underlying the LCAO methods applied to periodic systems and the use of wave-function-based, density-based (DFT) and hybrid hamiltonians. The second part deals with the applications of LCAO methods for calculations of bulk crystal properties.

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.

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.

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 study of energy landscapes holds the key to resolving some of the most important contemporary problems in chemical physics. Many groups are now attempting to understand the properties of clusters, glasses and proteins in terms of the underlying potential energy surface. The aim of this book is to define and unify the field of energy landscapes in a reasonably self-contained exposition. This is the first book to cover this active field. The book begins with an overview of each area in an attempt to make the subject matter accessible to workers in different disciplines. The basic theoretical groundwork for describing and exploring energy landscapes is then introduced followed by applications to clusters, biomolecules and glasses in the final chapters. Beautifully illustrated in full colour throughout, this book is aimed at graduate students and workers in the field.

This textbook covers the basics necessary for understanding the statistical theory of unimolecular reactions in its original and variational, phase-space and angular momentum-conserved incarnations. Because the emphasis is on "why" rather than "how to", there are many problems and answers to explore further. The book is targeted at graduate and advanced undergraduate students studying chemical dynamics, chemical kinetics and theoretical chemistry.

Concepts and Methods in Modern Theoretical Chemistry: Statistical Mechanics, the second book in a two-volume set, focuses on the dynamics of systems and phenomena. A new addition to the series Atoms, Molecules, and Clusters, this book offers chapters written by experts in their fields. It enables readers to learn how concepts from ab initio quantum chemistry and density functional theory (DFT) can be used to describe, understand, and predict chemical dynamics. This book covers a wide range of subjects, including discussions on the following topics: Time-dependent DFT Quantum fluid dynamics (QFD) Photodynamic control, nonlinear dynamics, and quantum hydrodynamics Molecules in a laser field, charge carrier mobility, and excitation energy transfer Mechanisms of chemical reactions Nucleation, quantum Brownian motion, and the third law of thermodynamics Transport properties of binary mixtures Although most of the chapters are written at a level that is accessible to a senior graduate student, experienced researchers will also find interesting new insights in these experts' perspectives. This book provides an invaluable resource toward understanding the whole gamut of atoms, molecules, and clusters.

This book consolidates and brings up to date the variational theory and methods currently used in many branches of theoretical physics and chemistry. The text surveys essential ideas and methods, concentrating on theory as used in applications rather than on fine points of rigorous mathematics. Essential concepts are developed in a common notation and from a uniform critical point of view. Examples of important applications are reviewed in sufficient detail to provide the reader with a critical understanding of context and methodology.

Valence bond theory is one of two commonly used methods in molecular quantum mechanics; the other is molecular orbital theory. This book focuses on the first of these methods: ab initio valence bond theory. The book is split into two parts. Part I gives simple examples of two-electron calculations and the necessary theory to extend these to larger systems. Part II gives a set of case studies of related molecule sets designed to show the nature of the valence bond description of molecular structure. The book is of primary interest to researchers and students working on electronic theory and computation in chemistry and chemical physics.

Liquid crystals, polymers and polymer liquid crystals are soft condensed matter systems of major technological and scientific interest. An understanding of the macroscopic properties of these complex systems and of their many and interesting peculiarities at the molecular level can nowadays only be attained using computer simulations and statistical mechanical theories. Both in the Liquid Crystal and Polymer fields a considerable amount of simulation work has been done in the last few years with various classes of models at different special resolutions, ranging from atomistic to molecular and coarse-grained lattice models. Each of the two fields has developed its own set of tools and specialized procedures and the book aims to provide a state of the art review of the computer simulation studies of polymers and liquid crystals. This is of great importance in view of a potential cross-fertilization between these connected areas which is particularly apparent for a number of experimental systems like, e.g. polymer liquid crystals and anisotropic gels where the different fields necessarily merge. An effort has been made to assess the possibilities of a coherent description of the themes that have developed independently, and to compare and extend the theoretical and computational techniques put forward in the different areas.

This book offers an introduction to photochemistry for students with a minimal background in physical chemistry and molecular quantum mechanics. The focus is from a theoretical perspective and highlights excited state dynamics. The authors, experienced lecturers, describe the main concepts in photochemical and photophysical processes that are used as a basis to interpret classical steady-state experimental results (essentially product branching ratios and quantum yields) and the most advanced time-resolved techniques. A significant portion of the content is devoted to the computational techniques present in quantum chemistry and molecular dynamics.With its short summaries, questions and exercises, this book is aimed at graduate students, while its theoretical focus differentiates it from most introductory textbooks on photochemistry.

Polyoxometalates (POMs) form a large, distinctive class of molecular inorganic compounds of unrivaled electronic versatility and structural variation, with impacts ranging from chemistry, catalysis, and materials science to biology, and medicine. This book covers the basic principles governing the structure, bonding and reactivity of these metal-oxygen cluster anions and the major developments in their molecular science.

The book comprises three sections. The first covers areas ranging from topological principles via synthesis and stability to reactivity in solution. It also focuses on the physical methods currently used to extract information on the molecular and electronic structures as well as the physical properties of these clusters. The second part reviews different types of POMs, focusing on those systems that currently impact other areas of interest, such as supramolecular chemistry, nanochemistry and molecular magnetism. The third section is devoted to POM-based materials and their applications and prospects in catalysis and materials science.

There exists a wide variety of patterns in nature, from inert matter such as crystalline dendrites and flames, to filamentous fungi and neurones in the living world. Their structural evolution during growth can be theoretically modeled in order to predict the shape of their forms, their dimensions and their growth rate. New Visions on Growth and Form aims at answering such questions by employing different theoretical approaches and providing a critical appraisal.
The book is part of the wide field of non-equilibrium statistical physics, and explores different mechanisms such as transport, interfacial tension, and chemical reactions, which govern the growth of a material. It explains the fundamental equations relating different morphological quantities, as well as the relevant experimental control parameters. From the unifying concepts arising in the theoretical approach the author proposes a tentative description of cell morphogenesis as a further application of the theory.

An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: Essential theoretical techniques to describe the properties and dynamics of chemical systems Electronic Structure methods for stationary calculations Methods for electronic excited states from both a quantum chemical and time-dependent point of view A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

The aim of this volume is to offer a balanced overview of molecular Rydberg spectroscopy as it has developed over recent decades. Recent evolution has split Rydberg spectroscopy into two apparently distinct fields: the one concerns the low (n=3-5) Rydberg states, the other the very high (typically n>150) Rydberg states. The former is aimed at spectral levels where Rydberg, valence-shell, and intermediate-type states interact, with a variety of photochemical consequences. The latter considers states extremely close to the ionization limit, from whereionization is possible with a very slight amount of additional energy. Recently developed techniques make it possible to produce ions in well-defined electronic, vibrational and rotational states, including states resulting from spin-orbit or Jahn-Teller splitting. It is then possible to study the structure and reactions of such state-selected ions as well as those of the corresponding neutral molecules. These techniques amount to badly needed high resolution photoelectron spectroscopy.

These two volumes collect thirty-eight selected papers from the scientific contributions presented at the Fourth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-IV), held in Marly-le-Roi (France) in April 22-27, 1999. A total of one hundred and fifteen scientists attended the workshop, 99 from Europe and 16 from the rest of the world. They discussed the state of the art, new trends, and future evolution of the methods and applications. The workshop was held in the old town of Marly-le-Roi, which lies to the West of Paris between the historic centres of Saint-Germain-en-Laye and Versailles. Participants were housed at the National Youth Institute, where over sixty lectures were given by l- ding members of the scientific community; in addition, over sixty posters were presented in two very animated sessions. We are grateful to the oral speakers and to the poster p- senters for making the workshop such an stimulating experience. The social programme was also memorable - and not just for the closing banquet, which was held at the French Senate House. We are sure that participants will long remember their visit to the 'Musee des Antiquites Nationales' created by Napoleon III at the birthplace of Louis XIV, this museum boasts one of the world finest collections of archeological artifacts. The Marly-le-Roi workshop followed the format established at the three previous meetings, organized by Prof."

This book is meant to provide a window on the rapidly growing body of theoretical studies of condensed phase chemistry. A brief perusal of physical chemistry journals in the early to mid 1980's will find a large number of theor- ical papers devoted to 3-body gas phase chemical reaction dynamics. The recent history of theoretical chemistry has seen an explosion of progress in the devel- ment of methods to study similar properties of systems with Avogadro's number of particles. While the physical properties of condensed phase systems have long been principle targets of statistical mechanics, microscopic dynamic theories that start from detailed interaction potentials and build to first principles predictions of properties are now maturing at an extraordinary rate. The techniques in use range from classical studies of new Generalized Langevin Equations, semicl- sical studies for non-adiabatic chemical reactions in condensed phase, mixed quantum classical studies of biological systems, to fully quantum studies of m- els of condensed phase environments. These techniques have become sufficiently sophisticated, that theoretical prediction of behavior in actual condensed phase environments is now possible. and in some cases, theory is driving development in experiment. The authors and chapters in this book have been chosen to represent a wide variety in the current approaches to the theoretical chemistry of condensed phase systems. I have attempted a number of groupings of the chapters, but the - versity of the work always seems to frustrate entirely consistent grouping.

For the first time in the history of chemical sciences, theoretical predictions have achieved the level of reliability that allows them to - val experimental measurements in accuracy on a routine basis. Only a decade ago, such a statement would be valid only with severe qualifi- tions as high-level quantum-chemical calculations were feasible only for molecules composed of a few atoms. Improvements in both hardware performance and the level of sophistication of electronic structure me- ods have contributed equally to this impressive progress that has taken place only recently. The contemporary chemist interested in predicting thermochemical properties such as the standard enthalpy of formation has at his disposal a wide selection of theoretical approaches, differing in the range of app- cability, computational cost, and the expected accuracy. Ranging from high-level treatments of electron correlation used in conjunction with extrapolative schemes to semiempirical methods, these approaches have well-known advantages and shortcomings that determine their usefulness in studies of particular types of chemical species. The growing number of published computational schemes and their variants, testing sets, and performance statistics often makes it difficult for a scientist not well versed in the language of quantum theory to identify the method most adequate for his research needs.

These two volumes collect thirty-eight selected papers from the scientific contributions presented at the Fourth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-IV), held in Marly-le-Roi (France) in April 22-27, 1999, A total ofone hundred and fifteen scientists attended the workshop, 99 from Europe and 16 from the rest ofthe world. They discussed the state of the art, new trends, and future evolution of the methods and applications. The workshop was held in the old town of Marly-le-Roi, which lies to the West of Paris between the historic centres of Saint-Germain-en-Laye and Versailles. Participants were housed at the National Youth Institute, where over sixty lectures were given by l- ding members ofthe scientific community; in addition, over sixty posters were presented in two very animated sessions. We are grateful to the oral speakers and to the poster p- senters for making the workshop such an stimulating experience. The social programme was also memorable - and notjust for the closing banquet, which was held at the French Senate House. We are sure that participants will long remember their visit to the 'Musee des Antiquites Nationales': created by Napoleon III at the birthplace ofLouis XIV, this museum boasts one ofthe world finest collections ofarcheological artifacts. The Marly-le-Roi workshop followed the format established at the three previous meetings, organized by Prof.

This book describes mixed classical and quantum theories of dynamical processes with a particular emphasis on molecular Collisions. Purely quantum or purely classical approaches are inadequate for many systems.

Starting from a clear, concise introduction, the powerful finite element and boundary element methods of engineering are developed for application to quantum mechanics. The reader is led through illustrative examples displaying the strengths of these methods using applications to fundamental quantum mechanical problems and to the design/simulation of quantum nanoscale devices.