This book is a collection of problems that are intended to aid students in graduate and undergraduate courses in Classical and Quantum Physics. It is also intended to be a study aid for students that are preparing for the PhD qualifying exam. Many of the included problems are of a type that could be on a qualifying exam. Others are meant to elucidate important concepts. Unlike other compilations of problems, the detailed solutions are often accompanied by discussions that reach beyond the specific problem.The solution of the problem is only the beginning of the learning process--it is by manipulation of the solution and changing of the parameters that a great deal of insight can be gleaned. The authors refer to this technique as "massaging the problem," and it is an approach that the authors feel increases the pedagogical value of any problem.

This thesis provides a comprehensive description of methods used to compute the vibrational spectra of liquid systems by molecular dynamics simulations. The author systematically introduces theoretical basics and discusses the implications of approximating the atomic nuclei as classical particles. The strengths of the methodology are demonstrated through several different examples. Of particular interest are ionic liquids, since their properties are governed by strong and diverse intermolecular interactions in the liquid state. As a novel contribution to the field, the author presents an alternative route toward infrared and Raman intensities on the basis of a Voronoi tessellation of the electron density. This technique is superior to existing approaches regarding the computational resources needed. Moreover, this book presents an innovative approach to obtaining the magnetic moments and vibrational circular dichroism spectra of liquids, and demonstrates its excellent agreement with experimental reference data.

The series Structure and Bonding publishes critical reviews on topics of research concerned with chemical structure and bonding. The scope of the series spans the entire Periodic Table and addresses structure and bonding issues associated with all of the elements. It also focuses attention on new and developing areas of modern structural and theoretical chemistry such as nanostructures, molecular electronics, designed molecular solids, surfaces, metal clusters and supramolecular structures. Physical and spectroscopic techniques used to determine, examine and model structures fall within the purview of Structure and Bonding to the extent that the focus is on the scientific results obtained and not on specialist information concerning the techniques themselves. Issues associated with the development of bonding models and generalizations that illuminate the reactivity pathways and rates of chemical processes are also relevant. The individual volumes in the series are thematic. The goal of each volume is to give the reader, whether at a university or in industry, a comprehensive overview of an area where new insights are emerging that are of interest to a larger scientific audience. Thus each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years should be presented using selected examples to illustrate the principles discussed. A description of the physical basis of the experimental techniques that have been used to provide the primary data may also be appropriate, if it has not been covered in detail elsewhere. The coverage need not be exhaustive in data, but should rather be conceptual, concentrating on the new principles being developed that will allow the reader, who is not a specialist in the area covered, to understand the data presented. Discussion of possible future research directions in the area is welcomed. Review articles for the individual volumes are invited by the volume editors

This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.

Low-energy electrons are ubiquitous in nature and play an important role in natural phenomena as well as many potential and current industrial processes. Authored by 16 active researchers, this book describes the fundamental characteristics of low-energy electron-molecule interactions and their role in different fields of science and technology, including plasma processing, nanotechnology, and health care, as well as astro- and atmospheric physics and chemistry. The book is packed with illustrative examples, from both fundamental and application sides, features about 130 figures, and lists over 800 references. It may serve as an advanced graduate-level study course material where selected chapters can be used either individually or in combination as a basis to highlight and study specific aspects of low-energy electron-molecule interactions. It is also directed at researchers in the fields of plasma physics, nanotechnology, and radiation damage to biologically relevant material (such as in cancer therapy), especially those with an interest in high-energy-radiation-induced processes, from both an experimental and a theoretical point of view.

Scientists are increasingly finding themselves engaged in research problems that cross the traditional disciplinary lines of physics, chemistry, biology, materials science, and engineering. Because of its broad scope, statistical mechanics is an essential tool for students and more experienced researchers planning to become active in such an interdisciplinary research environment. Powerful computational methods that are based in statistical mechanics allow complex systems to be studied at an unprecedented level of detail. This book synthesizes the underlying theory of statistical mechanics with the computational techniques and algorithms used to solve real-world problems and provides readers with a solid foundation in topics that reflect the modern landscape of statistical mechanics. Topics covered include detailed reviews of classical and quantum mechanics, in-depth discussions of the equilibrium ensembles and the use of molecular dynamics and Monte Carlo to sample classical and quantum ensemble distributions, Feynman path integrals, classical and quantum linear-response theory, nonequilibrium molecular dynamics, the Langevin and generalized Langevin equations, critical phenomena, techniques for free energy calculations, machine learning models, and the use of these models in statistical mechanics applications. The book is structured such that the theoretical underpinnings of each topic are covered side by side with computational methods used for practical implementation of the theoretical concepts.

This brief explains in detail fundamental concepts in acoustic cavitation and bubble dynamics, and describes derivations of the fundamental equations of bubble dynamics in order to support those readers just beginning research in this field. Further, it provides an in-depth understanding of the physical basis of the phenomena. With regard to sonochemistry, the brief presents the results of numerical simulations of chemical reactions inside a bubble under ultrasound, especially for a single-bubble system and including unsolved problems. Written so as to be accessible both with and without prior knowledge of fundamental fluid dynamics, the brief offers a valuable resource for students and researchers alike, especially those who are unfamiliar with this field. A grasp of fundamental undergraduate mathematics such as partial derivative and fundamental integration is advantageous; however, even without any background in mathematics, readers can skip the equations and still understand the fundamental physics of the phenomena using the book's wealth of illustrations and figures. As such, it is also suitable as an introduction to the field.

Metallic quantum clusters belonging to intermediate size regime between two and few hundred of atoms, represent unique building blocks of new materials. Nonlinear optical (NLO) characteristics of liganded silver and gold quantum clusters reveal remarkable features which can be tuned by size, structure and composition. The two-photon absorption cross sections of liganded noble metal quantum clusters are several orders of magnitude larger than that of commercially-available dyes. Therefore, the fundamental photophysical understanding of those two-photon processes in liganded clusters with few metal atoms deserve special attention, in particularly in context of finding the mechanisms responsible for these properties. A broad range of state-of-the-art experimental methods to determine nonlinear optical properties (i.e. two-photon absorption, two-photon excited fluorescence and second harmonic generation) of quantum clusters are presented. The experimental setup and underlying physical concepts are described. Furthermore, the theoretical models and corresponding approaches are used allowing to explain the experimental observations and simultaneously offering the possibility to deduce the key factors necessary to design new classes of nanoclusters with large NLO properties. Additionally, selected studied cases of liganded silver and gold quantum clusters with focus on their NLO properties will be presented as promising candidates for applications in imaging techniques such as fluorescence microscopy or Second-Harmonic Generation microscopy.

It is gratifying to launch the third edition of our book. Its coming to life testi?es about the task it has ful?lled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the ?rst and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from ch- istry as well as from other ?elds to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pl- sure in addition to learning experience. In our ?rst Preface we paid tribute to two books in particular from which we learned a great deal; they have in?uenced signi?cantly our approach to the subject matter of our book. They are Weyl's classic, Symmetry, and Shubnikov and Koptsik's Symmetry in Science and Art. The structure of our book has not changed. Following the Int- duction (Chapter 1), Chapter 2 presents the simplest symmetries using chemical and non-chemical examples. Molecular geometry is discussed in Chapter 3. The next four chapters present gro- theoretical methods (Chapter 4) and, based on them, discussions of molecular vibrations (Chapter 5), electronic structures (Chapter 6), and chemical reactions (Chapter 7). For the last two chapters we return to a qualitative treatment and introduce space-group sym- tries (Chapter 8), concluding with crystal structures (Chapter 9). For the third edition we have further revised and streamlined our text and renewed the illustrative material.

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.

In this new edition of the book that was called "the most beautiful chemistry book ever written," Peter Atkins reveals the molecules responsible for the experiences of our everyday life in fabrics, drugs, plastics, explosives, detergents, fragrances, tastes, and sex. Atkins gives a non-technical account of a range of aspects of the world around us, revealing unexpected connections and insight into how it can be understood in terms of the atoms and molecules from which it is built. This new edition has dozens of new molecules, new graphic presentations, and a more accessible account of the molecules themselves. Peter Atkins is SmithKline Beecham Fellow and Tutor in Physical Chemistry at Oxford University. Atkins' research includes the fields of theoretical chemistry, particularly magnetic resonance and the electromagnetic properties of molecules. He spends virtually all his time writing books, which range from bestselling college textbooks to books on science for general audiences, including Galileo's Finger (Oxford, 2003); The Periodic Kingdom (Basic Books, 1997); The Second Law (W.H. Freeman, 1995); and Atoms, Electrons, and Change (W.H. Freeman, 1991). Previous Edition Paperback (W.H. Freeman, 1995) 0-7167-2928-8

The articles in this volume summarize the research results obtained in the former SFB 359 "Reactive Flow, Diffusion and Transport" which has been supported by the DFG over the period 1993-2004. The main subjects are physical-chemical processes sharing the difficulty of interacting diffusion, transport and reaction which cannot be considered separately. The modeling and simulation within this book is accompanied by experiments.

A concise textbook bridging quantum theory and spectroscopy! Designed as a practical text, Quantum Mechanical Foundations of Molecular Spectroscopy covers the quantum mechanical fundamentals of molecular spectroscopy from the view of a professional spectroscopist, rather than a theoretician. Written by a noted expert on the topic, the book puts the emphasis on the relationship between spectroscopy and quantum mechanics, and provides the background information and derivations of the subjects needed to understand spectroscopy including: stationary energy states, transitions between these states, selection rules, and symmetry. The phenomenal growth of all forms of spectroscopy over the past eight decades has contributed enormously to our understanding of molecular structure and properties. Today spectroscopy covers a broad field including the modern magnetic resonance techniques, non-linear, laser and fiber-based spectroscopy, surface and surface-enhanced spectroscopy, pico- and femtosecond time resolved spectroscopy, and many more. This up-to-date resource discusses several forms of spectroscopy that are used in many fields of science, such as fluorescence, surface spectroscopies, linear and non-linear Raman spectroscopy and spin spectroscopy. This important text: Contains the physics and mathematics needed to understand spectroscopy Explores spectroscopic methods the are widely used in chemistry, biophysics, biology, and materials science Offers a text written by an experienced lecturer and practitioner of spectroscopic methods Includes detailed explanations and worked examples Written for chemistry, biochemistry, material sciences, and physics students, Quantum Mechanical Foundations of Molecular Spectroscopy provides an accessible text for understanding molecular spectroscopy.

The series Topics in Current Chemistry presents critical reviews of the present and future trends in modern chemical research. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field.

This thesis examines various aspects of excess excitation energy dissipation via dynamic changes in molecular structure, vibrational modes and solvation. The computational work is carefully described and the results are compared to experimental data obtained using femtosecond spectroscopy and x-ray scattering. The level of agreement between theory and experiment is impressive and provides both a convincing validation of the method and significant new insights into the chemical dynamics and molecular determinants of the experimental data. Hence, the method presented in the thesis has the potential to become a very important contribution to the rapidly growing field of femtosecond x-ray science, a trend reflected in the several free-electron x-ray lasers (XFELs) currently being built around the world. Light-induced chemical processes are accompanied by molecular motion of electrons and nuclei on the femtosecond time scale. Uncovering these dynamics is central to our understanding of the chemical reaction on a fundamental level. Asmus O. Dohn has implemented a highly efficient QM/MM Direct Dynamics method for predicting the solvation dynamics of transition metal complexes in solution.

In this Festschrift dedicated to the 85th birthday of Professor Guosen Yan, selected researchers in theoretical chemistry present research highlights on major developments in the field. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format, as well as a special electronic edition. This volume provides valuable content for all researchers in theoretical chemistry, and will especially benefit those research groups and libraries with limited access to the journal.

This book presents an in-depth study into the utility of σ-bond metathesis in Group 2 mediated reactivity. A comprehensive introduction defines the state of the art in both Group 2 mediated catalysis and dehydrocoupling. Structural investigations giving rise to a range of mixed s-block metal hydrides including a remarkable dodecabimetallic decahydride are then described. Subsequent extensive mechanistic work focussing on both silicon-nitrogen and boron-nitrogen dehydrocoupling gives insights into both congeneric effects down Group 2 and ligand effects centring upon magnesium. These studies show the striking effects of these factors, as well as the electronic nature of the hydridic coupling partner.  Finally, the unprecedented introduction of single-electron transfer steps into Group 2 catalytic manifolds is described. The use of the stable radical TEMPO to induce single-electron transfer to substituents bound to Group 2 centres coupled with σ-bond metathesis allows a novel hydrogen release from silanes.

In this Festschrift dedicated to the 60th birthday of Gregory S. Ezra, selected researchers in theoretical chemistry present research highlights on major developments in the field. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format, as well as a special electronic edition. This volume provides valuable content for all researchers in theoretical chemistry and will especially benefit those research groups and libraries with limited access to the journal.

Computational methods, and in particular quantum chemistry, have taken the lead in our growing understanding of noncovalent forces, as well as in their categorization. This volume describes the current state of the art in terms of what we now know, and the current questions requiring answers in the future. Topics range from very strong (ionic) to very weak (CH-- ) interactions. In the intermediate regime, forces to be considered are H-bonds, particularly CH--O and OH--metal, halogen, chalcogen, pnicogen and tetrel bonds, aromatic stacking, dihydrogen bonds, and those involving radicals. Applications include drug development and predictions of crystal structure.

Single Molecular Machines and Motors brings together different approaches and strategies to design, synthesize and study single molecular machines and motors in a multidisciplinary way. Written by leading international experts, this book summarizes the advances in the field through a number of disciplines. Some contributions describe molecular chemistry such as organic, aromatics, and coordination chemistry while others address theoretical chemistry in a predictive way or through post-experimental modelling. Experimental physics with extensive use of scanning probe microscopy (STM and AFM) is discussed for examining one single molecule. This book is aimed at those who are interested in the rapidly growing field of molecular machines and motors acting and studied at the single-molecule scale. The goal of the authors and editors is to provide the reader with an up-to-date summary while also offering future perspectives on the field.

This book deals with the theoretical and computational simulation of monoperiodic nanostructures for different classes of inorganic substances. These simulations are related to their synthesis and experimental studies. A theoretical formalism is developed to describe 1D nanostructures with symmetric shapes and morphologies. Three types of models are considered for this aim: (i) nanotubes (rolled from 2D nanolayers and described within the formalism of line symmetry groups); (ii) nanoribbons (obtained from 2D nanolayers by their cutting along the chosen direction of translation); (iii) nanowires (obtained from 3D lattice by its sectioning along the crystalline planes parallel to the chosen direction of translation). Quantum chemistry ab-initio methods applied for LCAO calculations on electronic and vibrational properties of 1D nanostructures are thoroughly described. Understanding of theoretical aspects presented here enlarges the possibilities for synthesis of monoperiodic nanostructures with predictable morphology and better interpretation of their properties.

This multi-author contributed volume gives a comprehensive overview of recent progress in various vibrational spectroscopic techniques and chemometric methods and their applications in chemistry, biology and medicine. In order to meet the needs of readers, the book focuses on recent advances in technical development and potential exploitations of the theory, as well as the new applications of vibrational methods to problems of recent general interest that were difficult or even impossible to achieve in the not so distant past. Integrating vibrational spectroscopy and computational approaches serves as a handbook for people performing vibrational spectroscopy followed by chemometric analysis hence both experimental methods as well as procedures of recommended analysis are described. This volume is written for individuals who develop new methodologies and extend these applications to new realms of chemical and medicinal interest.

In this Festschrift celebrating the career of Thom H. Dunning, Jr., selected researchers in theoretical chemistry present research highlights on major developments in the field. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format, as well as a special electronic edition. This volume provides valuable content for all researchers in theoretical chemistry and will especially benefit those research groups and libraries with limited access to the journal.

This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.