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."

For more than 100 years the Beilstein Handbook has been publishing checked and evaluated data on organic compounds. It has become the major reference book for the chemical and physical properties of organic com pounds. The prediction of these physical properties was the subject of the Beilstein workshop. The ability to predict physical properties is for several reasons of great interest to the Beilstein Institute. It is of primary importance to be able to check the abstracted data for accuracy and to eliminate simple mistakes like typing errors. Presently all the work whether manuscript writing or evaluation of data is carried out manually. This is very time consuming, with the entry of Beilstein into electronic data gathering and publication, the opportunity for computerized consistency checking has become available. Contrary to belief, when one examines the Beilstein Handbook or Chemical Abstracts there is a dearth of chemical information. There are a great many compounds but few are well defined resulting in large gaps in the information available to the chemist. These information gaps could be filled by using algorithmic methods to estimate the properties of interest. An important question to answer is "What is the chemist's reaction to estimated data?" Will he accept it for use, within limits defined by the method, or will it be unacceptable and therefore detrimental for the data base. However if one could partly fill gaps in the data base the increase in the power of the search techniques would be marked."

Nuclear magnetic resonance spectroscopy, which has evolved only within the last 20 years, has become one of the very important tools in chemistry and physics. The literature on its theory and application has grown immensely and a comprehensive and adequate treatment ofall branches by one author, or even by several, becomes increasingly difficult. by experts workinginvarious This seriesis planned to present articles written fields of nuclear magnetic resonance spectroscopy, and will contain review articles as well as progress reports and original work. Its main aim, however, is to fill a gap, existing in literature, by publishing articles written by specialists, which take the reader from the introductory stage to the latest development in the field. The editors are grateful to the authors for the time and effort spent in writing the articles, and for their invaluable cooperation. The Editors Computer Assistance in the Analysis of High-Resolution NMR Spectra P. DIEHL and H. KELLERHALS Departmentof Physics, University ofBasle, Switzerland E. LUSTIG Food and Drug Administration, Washington, D.C., U.S.A.

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.

Chemistry is the science of substances (today we would say molecules) and their transformations. Central to this science is the complexity of shape and function of its typical representatives. There lies, no longer dependent on its vitalistic antecedents, the rich realm of molecular possibility called organic chemistry. In this century we have learned how to determine the three-dimensional structure of molecules. Now chemistry as whole, and organic chemistry in particular, is poised to move to the exploration of its dynamic dimension, the busy business of transformations or reactions. Oh, it has been done all along, for what else is synthesis? What I mean is that the theoretical framework accom panying organic chemistry, long and fruitfully laboring on a quantum chemical understanding of structure, is now making the first tentative motions toward building an organic theory of reactivity. The Minkin, Simkin, Minyaev book takes us in that direction. It incorporates the lessons of frontier orbital theory and of Hartree-Fock SCF calculations; what chemical physicists have learned about trajectory calculations of selected reactions, and a simplified treatment of all-important solvent effects. It is written by professional, accomplished organic chemists for other organic chemists; it is consistently even-toned in its presentation of contending approaches. And very much up to date. That this contemporary work should emerge from a regional university in a country in which science has been highly centralized and organic chemistry not very modern, invites reflection."

"Highly recommended for all academic library chemistry collections; biochemistry and medical collections may also want to consider." (Choice)
"Each entry is provided with a definition, a description of the effect, application, and literature citations...". the selection in this book is broad and useful." (J. of Am. Chem. Soc.)
"The book is not just a collection of definitions of acronyms, each entry contains a concise and informative explanation of the origins of the technique or method to which it refers... this book is a must for progression of any budding spectroscopist." (Analyst)

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.

Understanding molecular orbitals (MOs) is a prerequisite to appreciating many physical and chemical properties of matter. This extensively revised second edition of A Pictorial Approach to Molecular Bonding presents the author's innovative approach to MOs, generating them pictorially for a wide variety of molecular geometries. A major enhancement to the second edition is the PC- and Macintosh-compatible Nodegame software, which is coordinated with the text and aids in pictorially teaching molecular orbital theory using generator orbitals.

Predicting molecular structure and energy and explaining the nature of bonding are central goals in quantum chemistry. With this book, the editors assert that the density functional (DF) method satisfies these goals and has come into its own as an advanced method of computational chemistry. The wealth of applications presented in the book, ranging from solid state sys tems and polymers to organic and organo-metallic molecules, metallic clus ters, and biological complexes, prove that DF is becoming a widely used computational tool in chemistry. Progress in the methodology and its imple mentation documented by the contributions in this book demonstrate that DF calculations are both accurate and efficient. In fact, the results of DF calculations may pleasantly surprise many chem ists. Even the simplest approximation of DF, the local spin density method (LSD), yields molecular structures typical of ab initio correlated methods. The next level of theory, the nonlocal spin density method, predicts the energies of molecular processes within a few kcallmol or less. Like the Hartree-Fock (HF) and configuration interaction (CI) methods, the DF method is based only on fundamental physical constants. Therefore, it does not require semiempirical parameters and can be applied to any molecular system and to metallic phases. However, DF's greatest advantage is that it can be applied to much larger systems than those approachable by tradition al ab initio methods, especially when compared with correlated ab initio methods."

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.

In NMR, it is well-known that the chemical shift conveys structural informa tion, e. g. a carbonyl carbon will have a resonance frequency appreciably dif ferent from a methyl carbon, etc. The relation between structure and chemical shift is mostly established by empirical rules on the basis of prior experience. It is only quite recently that the advent of both comparatively cheap comput ing power and novel quantum chemistry approaches have provided feasible routes to calculate the chemical shift at the ab initio level for molecules of reasonable size. This raises the question whether application of these novel theoretical concepts offers a means of obtaining new structural information for the complex chain molecules one deals with in polymer science. Solid state 13C-NMR spectra of glassy amorphous polymers display broad, partially structured resonance regions that reflect the underlying disorder of the polymer chains. The chemical shift responds to the variation of the ge ometry of the chain, and the broad resonance regions can be explained by an inhomogeneous superposition of various chain geometries (and thus chem ical shifts). In this review, we present a novel approach to combine polymer chain statistical models, quantum chemistry and solid state NMR to pro vide quantitative information about the local chain geometry in amorphous polymers. The statistical model yields the relative occurrence of the various geometries, and quantum chemistry (together with a force field geometry op timization) establishes the link between geometry and chemical shift."

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 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.

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.

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. "

"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."

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.

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 is an excellent introduction to density functional theory for electrons. Largely written in review style, it will also serve as an excellent overview of recent developments.
Nonrelativistic and relativistic approaches are discussed and conventional ground-state as well as polarization density functional and time-dependent density functional formalisms are introduced. A careful discussion of the exchange-correlation functional and approximations is presented and a chapter is devoted to an analysis of hybrid wavefunction/density-functional approximations.

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.