"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.

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.

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.

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.

Characteristic of Schwabl 's work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. New material has been added to this third edition.

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.

This fresh and original text on quantum mechanics focuses on: the development of numerical methods for obtaining specific results; the presentation of group theory and the systematic use of operators; the introduction of the functional integral and its applications in approximation; the discussion of distant correlations and experimental measurements. Numerous exercises with hints and solutions, examples and applications, and a guide to key references help the student to work with the text.

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.

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."

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.

Electronic-structure calculations of the properties of specific materials have become increasingly important over the last 30 years. Although several books on the subject have been published, it is rare to find one that covers in detail both the traditional quantum chemistry and the solid-state physics methods of electronic-structure calculations. This title bridges that gap, focusing equally on both types of method, including density-functional and Hartree—Fock-based approaches. The book is aimed at final-year undergraduate and postgraduate students of both chemistry and of physics. It describes in detail the fundamentals behind the various methods that are used in calculating electronic properties of materials, and that to some extent are commercially available. It should also be of interest to professional scientists working in related theoretical or experimental fields.

The concept of a chemical bond evolved from a variety of experimental observations. It became useful to understand, at times even predict, the molecular structure, reactivity and mechanism of chemical reactions. Every aspect of the concept of bonding received a quantitative interpretation from the advent of quantum mechanics and its application to chemistry.In Lectures on Chemical Bonding and Quantum Chemistry the reader will find a comprehensive discourse on the basic interpretation of the chemical bond as well as current understanding in terms of a 'dancing' molecule that not only travels, rotates and pulsates around an equilibrium molecular structure, but also interacts and collides with other molecules, thereby transferring linear and angular momentum characteristics and adjusting total energies. One will also find a thorough survey of quantum mechanical methodologies for calculation of molecular characteristics in specific states and their changes under spectroscopic transitions, tunneling, electron and proton transfer phenomena, and so on. Guides to more advanced levels of theory are also provided.

Volume II/26 supplements the previous compilations II/l, II/9 and II/17 of the magnetic properties of free radicals. Due to the still rapid growth of the field and the inclusion of new subjects the volume is divided into subvolumes which will appear in fast succession. Together with the earlier publications volume II/26 offers an up-to-date and comprehensive survey and collection of structures and data on the important chemical intermediates.

This is a Standard Reference Book with selected and easily retrievable data from the fields of physics and chemistry collected by international scientists. Volume II/28 is a supplemented and revised edition of the preceding volumes II/7, II/15, II/21, II/23 and II/25, containing up to date information on the geometric parameters (internuclear distances, bond angles, dihedral angles of internal rotation etc.) of free inorganic and organic polyatomic molecules.

Volume II/28 is a supplemented and revised edition of the preceding volumes II/7, II/15, II/21, II/23 and II/25, containing up to date information on the geometric parameters (internuclear distances, bond angles, dihedral angles of internal rotation etc.) of free inorganic and organic polyatomic molecules. The data has been critically evaluated and compiled.

This volume features up-to-date information on the geometric parameters of free inorganic and organic polyatomic molecules. Coverage takes into account all experimental methods for the determination of quantitative structural data of free molecules. The data obtained by these methods have been critically evaluated and compiled. They are presented separately for each molecule, together with a computer-drawn schematic figure of the structure.

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.

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.

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.