This book presents a variety of techniques for tackling phenomena that are not amenable to the conventional approach based on the concept of probabilities. The methods described rely on the use of path integration, thermal Green functions, time-temperature propagators, Liouville operators, second quantization, and field correlators at finite density and temperature. Also exploring the statistical mechanics of unstable quantum systems, the book is intended as a supplementary or reference text for use in one-semester graduate courses on Quantum Mechanics, Thermodynamics, Electromagnetism, and Mathematical Methods in Physics.

Maximilian Scheurer presents a method for modeling excited states in atomistic, heterogeneous environments. The method utilizes the polarizable embedding (PE) model to mimic electrostatic and polarization interactions of a molecule with its environment. For high-level modeling of the molecule's excited states, the algebraic-diagrammatic construction scheme for the polarization propagator (ADC) is employed. The presented work outlines the theoretical foundations of PE and ADC and the combination of both methods, termed PE-ADC. The accuracy of PE-ADC is tested, and the charge-transfer (CT) excitation in the dodecin protein is studied. This book presents a comprehensive elaboration on the new PE-ADC method and a state-of-the-art application of PE-ADC to a photo-biochemical process.

Since the second half of the 20th century machine computations have played a critical role in science and engineering. Computer-based techniques have become especially important in molecular biology, since they often represent the only viable way to gain insights into the behavior of a biological system as a whole. The complexity of biological systems, which usually needs to be analyzed on different time- and size-scales and with different levels of accuracy, requires the application of different approaches, ranging from comparative analysis of sequences and structural databases, to the analysis of networks of interdependence between cell components and processes, through coarse-grained modeling to atomically detailed simulations, and finally to molecular quantum mechanics. This book provides a comprehensive overview of modern computer-based techniques for computing the structure, properties and dynamics of biomolecules and biomolecular processes. The twenty-two chapters, written by scientists from all over the world, address the theory and practice of computer simulation techniques in the study of biological phenomena. The chapters are grouped into four thematic sections dealing with the following topics: the methodology of molecular simulations; applications of molecular simulations; bioinformatics methods and use of experimental information in molecular simulations; and selected applications of molecular quantum mechanics. The book includes an introductory chapter written by Harold A. Scheraga, one of the true pioneers in simulation studies of biomacromolecules.

This book provides a comprehensive review of both traditional and cutting-edge methodologies that are currently used in computational toxicology and specifically features its application in regulatory decision making. The authors from various government agencies such as FDA, NCATS and NIEHS industry, and academic institutes share their real-world experience and discuss most current practices in computational toxicology and potential applications in regulatory science. Among the topics covered are molecular modeling and molecular dynamics simulations, machine learning methods for toxicity analysis, network-based approaches for the assessment of drug toxicity and toxicogenomic analyses. Offering a valuable reference guide to computational toxicology and potential applications in regulatory science, this book will appeal to chemists, toxicologists, drug discovery and development researchers as well as to regulatory scientists, government reviewers and graduate students interested in this field.

Special numerical techniques are already needed to deal with n x n matrices for large n. Tensor data are of size n x n x...x n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2010. The reports cover all fields of computational science and engineering, ranging from CFD to computational physics and chemistry to computer science, with a special emphasis on industrially relevant applications. Presenting results for both vector systems and microprocessor-based systems, the book makes it possible to compare the performance levels and usability of various architectures. As HLRS operates the largest NEC SX-8 vector system in the world, this book gives an excellent insight into the potential of vector systems, covering the main methods in high performance computing. Its outstanding results in achieving the highest performance for production codes are of particular interest for both scientists and engineers. The book includes a wealth of color illustrations and tables.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2012. The reports cover all fields of computational science and engineering ranging from CFD via computational physics and chemistry to computer science with a special emphasis on industrially relevant applications. Presenting results for both vector-systems and micro-processor based systems the book allows to compare performance levels and usability of various architectures. As HLRS operates not only a large cluster system but also one of the largest NEC vector systems in the world this book gives an excellent insight also into the potential of vector systems. The book covers the main methods in high performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for both the scientist and the engineer. The book comes with a wealth of coloured illustrations and tables of results.

The authors of this volume illustrate recent trends in the design and application of accurate force fields. 15 papers reflect the present questions including the strategies for (i) the inclusion of the polarization energy and (ii) an optimal parametrization of models. They highlight the directions to follow as new exciting fields of application emerge. Expert authors discuss the optimization and parametrization of new models, put in perspectives the actual importance of the polarization energy, as well as review or propose new models explicitly for incorporating polarization. They also present models that are applied to difficult systems or challenging fields of application. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format. This volume is of benefit in particular to those research groups and libraries that have chosen to have only electronic access to the journal. It also provides valuable content for all researchers in theoretical chemistry.

This concise book introduces and discusses the basic theory of conical intersections with applications in atomic, molecular and condensed matter physics. Conical intersections are linked to the energy of quantum systems. They can occur in any physical system characterized by both slow and fast degrees of freedom - such as e.g. the fast electrons and slow nuclei of a vibrating and rotating molecule - and are important when studying the evolution of quantum systems controlled by classical parameters. Furthermore, they play a relevant role for understanding the topological properties of condensed matter systems. Conical intersections are associated with many interesting features, such as a breakdown of the Born-Oppenheimer approximation and the appearance of nontrivial artificial gauge structures, similar to the Aharonov-Bohm effect. Some applications presented in this book include - Molecular Systems: some molecules in nonlinear nuclear configurations undergo Jahn-Teller distortions under which the molecule lower their symmetry if the electronic states belong to a degenerate irreducible representation of the molecular point group. - Solid State Physics: different types of Berry phases associated with conical intersections can be used to detect topologically nontrivial states of matter, such as topological insulators, Weyl semi-metals, as well as Majorana fermions in superconductors. - Cold Atoms: the motion of cold atoms in slowly varying inhomogeneous laser fields is governed by artificial gauge fields that arise when averaging over the fast internal degrees of freedom of the atoms. These gauge fields can be Abelian or non-Abelian, which opens up the possibility to create analogs to various relativistic effects at low speed.

Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.

This book sheds new light on the dynamical behaviour of electron spins in molecules containing two unpaired electrons (i.e. a radical pair). The quantum dynamics of these spins are made complicated by the interaction between the electrons and the many nuclear spins of the molecule; they are intractable using analytical techniques, and a naive numerical diagonalization is not remotely possible using current computational resources. Hence, this book presents a new method for obtaining the exact quantum-mechanical dynamics of radical pairs with a modest number of nuclear spins. Readers will learn how a calculation that would take 13 years using conventional wavepacket propagation can now be done in 1 day, and will also discover a new semiclassical method for approximating the dynamics in the presence of many nuclear spins. The new methods covered in this book are shown to provide significant insights into three topical and diverse areas: charge recombination in molecular wires (which can be used in artificially mimicking photosynthesis), magnetoelectroluminescence in organic light-emitting diodes, and avian magnetoreception (how birds sense the Earth's magnetic field in order to navigate).

This book reviews various aspects of molecular spectroscopy and its application in materials science, chemistry, physics, medicine, the arts and the earth sciences. Written by an international group of recognized experts, it examines how complementary applications of diverse spectroscopic methods can be used to study the structure and properties of different materials. The chapters cover the whole spectrum of topics related to theoretical and computational methods, as well as the practical application of spectroscopic techniques to study the structure and dynamics of molecular systems, solid-state crystalline and amorphous materials, surfaces and interfaces, and biological systems. As such, the book offers an invaluable resource for all researchers and postgraduate students interested in the latest developments in the theory, experimentation, measurement and application of various advanced spectroscopic methods for the study of materials.

What is quantum mechanics? Learn from the experts in the ALL-NEW LADYBIRD EXPERT SERIES A clear, simple and entertaining introduction to the weird, mind-bending world of the very, very small. Written by physicist and broadcaster Professor Jim Al-Khalili, Quantum Mechanics explores all the key players, breakthroughs, controversies and unanswered questions of the quantum world. You'll discover: - How the sun shines - Why light is both a wave and a particle - The certainty of the Uncertainty Principle - Schrodinger's Cat - Einstein's spooky action - How to build a quantum computer - Why quantum mechanics drives even its experts completely crazy 'Jim Al-Khalili has done an admirable job of condensing the ideas of quantum physics from Max Planck to the possibilities of quantum computers into brisk, straightforward English' THE TIMES Learn about other topics in the Ladybird Experts series including The Big Bang, Gravity, Climate Change and Evolution. Written by the leading lights and most outstanding communicators in their fields, the Ladybird Expert books provide clear, accessible and authoritative introductions to subjects drawn from science, history and culture. For an adult readership, the Ladybird Expert series is produced in the same iconic small format pioneered by the original Ladybirds. Each beautifully illustrated book features the first new illustrations produced in the original Ladybird style for nearly forty years.

This brief introduces readers to an alternative thermochemical reference system that makes it possible to use the heats of formation of organic compounds to deduce the energies that depend entirely on their structures, and which provides calculated values for most of the characteristic structures appearing in organic molecules. These structure-dependent energies are provided e.g. for selected compounds of normal and cyclic alkanes, open chain and cyclic olefins (including conjugated polyenes), alkynes, aromatic hydrocarbons and their substituted derivatives. The oxygen, sulfur and nitrogen derivatives of the above-mentioned compounds are also represented with calculated structure-dependent energies including alcohols, ethers, aldehydes and ketones, carboxylic acids, thiols, sulfides, amines, amides, heterocyclic compounds and others. Most organic reactions can be interpreted as the disappearance of certain structures and formation of others. If the structure-dependent energies are known, it can be shown how the disappearing and the newly formed structures contribute to the heat of reactions and to the driving forces. As experienced by the author, who pioneered the concept, structure dependent energies can help teachers to make organic chemistry more accessible for their students. Accordingly, the brief offers a valuable resource for all those who teach organic chemistry at universities, and for those who are learning it.

This book introduces basic concepts of mathematical physics to chemists. Many textbooks and monographs of mathematical physics may appear daunting to them. Unlike other, related books, however, this one contains a practical selection of material, particularly for graduate and undergraduate students majoring in chemistry. The book first describes quantum mechanics and electromagnetism, with the relation between the two being emphasized. Although quantum mechanics covers a broad field in modern physics, the author focuses on a hydrogen(like) atom and a harmonic oscillator with regard to the operator method. This approach helps chemists understand the basic concepts of quantum mechanics aided by their intuitive understanding without abstract argument, as chemists tend to think of natural phenomena and other factors intuitively rather than only logically. The study of light propagation, reflection, and transmission in dielectric media is of fundamental importance. This book explains these processes on the basis of Maxwell equations. The latter half of the volume deals with mathematical physics in terms of vectors and their transformation in a vector space. Finally, as an example of chemical applications, quantum chemical treatment of methane is introduced, including a basic but essential explanation of Green functions and group theory. Methodology developed by the author will also prove to be useful to physicists.

On-surface synthesis is appearing as an extremely promising strategy to create organic nanoarchitectures with atomic precision. Molecular building blocks holding adequate functional groups are dosed onto surfaces that support or even drive their covalent linkage. The surface confinement and the frequent lack of solvents (most commonly being performed under vacuum conditions) create a completely new scenario fully complementary to conventional chemistry. In a pedagogical way and based on the most recent developments, this volume presents our current understanding in the field, addressing fundamental reaction mechanisms, synthetic strategies to influence the reactions according to our needs, as well as the ultimate growth and characterization of functional materials. Verging on chemistry, physics and materials science, the book is aimed at students and researchers interested in nanochemistry, surface science, supramolecular materials and molecular devices. Chapters "Mechanistic insights into surface-supported chemical reactions", "Reactivity on and of Graphene Layers: Scanning Probe Microscopy Reviels" and "Bottom-up fabrication of atomically precise graphene nanoribbons" of this book are available open access under a CC BY 4.0 license at link.springer.com

This book describes the latest developments in the new research discipline of X-ray nanochemistry, which uses nanomaterials to enhance the effectiveness of X-ray irradiation. Nanomaterials now can be synthesized in such a way as to meet the demand for complex functions that enhance the X-ray effect. Innovative methods of delivering the X-rays, which can interact with those nanomaterials much more strongly than energetic electrons and gamma rays, also create new opportunities to enhance the X-ray effect. As a result, new concepts are conceived and new developments are made in the last decade, which are discussed and summarized in this book. This book will help define the discipline and encourage more students and scientists to work in this discipline. These efforts will eventually lead to formation of a full set of physical, chemical and materials principles for this new research field.

This book presents a collection of invited research and review contributions on recent advances in (mainly) theoretical condensed matter physics, theoretical chemistry, and theoretical physics. The volume celebrates the 90th birthday of N.H. March (Emeritus Professor, Oxford University, UK), a prominent figure in all of these fields. Given the broad range of interests in the research activity of Professor March, who collaborated with a number of eminent scientists in physics and chemistry, the volume embraces quite diverse topics in physics and chemistry, at various dimensions and energy scales. One thread connecting all these topics is correlation in aggregated states of matter, ranging from nuclear physics to molecules, clusters, disordered condensed phases such as the liquid state, and solid state physics, and the various phase transitions, both structural and electronic, occurring therein. A final chapter leaps to an even larger scale of matter aggregation, namely the universe and gravitation. A further no less important common thread is methodological, with the application of theoretical physics and chemistry, particularly density functional theory and statistical field theory, to both nuclear and condensed matter.

London dispersion interactions are responsible for numerous phenomena in physics, chemistry and biology. Recent years have seen the development of new, physically well-founded models, and dispersion-corrected density functional theory (DFT) is now a hot topic of research. This book is an overview of current understanding of the physical origin and modelling of London dispersion forces manifested at an atomic level. It covers a wide range of system, from small intermolecular complexes, to organic molecules and crystalline solids, through to biological macromolecules and nanostructures. In presenting a broad overview of the of the physical foundations of dispersion forces, the book provides theoretical, physical and synthetic chemists, as well as solid-state physicists, with a systematic understanding of the origins and consequences of these ubiquitous interactions. The presentation is designed to be accessible to anyone with intermediate undergraduate mathematics, physics and chemistry.

This book describes fundamental theory and recent advances of sum frequency generation (SFG) spectroscopy. SFG spectroscopy is widely used as a powerful tool of surface characterization, although theoretical interpretation of the obtained spectra has been a major bottleneck for most users. Recent advances in SFG theory have brought about a breakthrough in the analysis methods beyond conventional empirical ones, and molecular dynamics (MD) simulation of SFG spectroscopy allows for simultaneous understanding of observed spectra and interface structure in unprecedented detail. This book explains these recently understood theoretical aspects of SFG spectroscopy by the major developer of the theory. The theoretical topics are treated at basic levels for undergraduate students and are described in relation to computational chemistry, such as molecular modeling and MD simulation, toward close collaboration of SFG spectroscopy and computational chemistry in the near future.

This thesis focuses on the nanomanufacturing of graphene-a newly discovered, two-dimensional material with extraordinary properties-in order to realize its numerous potential applications. Combining experimental implementation with theoretical modelling, it investigates three classes of graphene nanostructure fabrication using particle beam irradiation: (i) doping of graphene using low energy nitrogen irradiation; (ii) joining of graphene sheets with laser and C, N, and Ar ion beam irradiation; and (iii) fabrication of graphene nanopores by means of focused ion beam and electron beam irradiation. The feasibility of the nanomanufacture of graphene using particle beam irradiation is demonstrated by various experimental methods, and the mechanisms involved under different types of beam irradiation are revealed using theoretical calculations. Further, the book analyzes the mechanical and electrical properties of the fabricated graphene nanostructures by means of atomic simulations to predict the application potentials of the proposed methods. The findings help promote the implementation of graphene-structure applications in industry.

This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible.

This textbook extends from the basics of femtosecond physics all the way to some of the latest developments in the field. In this updated edition, the chapter on laser-driven atoms is augmented by the discussion of two-electron atoms interacting with strong and short laser pulses, as well as by a review of ATI rings and low energy structures in photo-electron spectra. In the chapter on laser-driven molecules a discussion of 2D infrared spectroscopy is incorporated. Theoretical investigations of atoms and molecules interacting with pulsed lasers up to atomic field strengths on the order of 10^16 W/cm(2) are leading to an understanding of many challenging experimental discoveries. The presentation starts with a brief introduction to pulsed laser physics. The basis for the non-perturbative treatment of laser-matter interaction in the book is the time-dependent Schroedinger equation. Its analytical as well as numerical solution are laid out in some detail. The light field is treated classically and different possible gauges for the field-matter interaction are discussed. Physical phenomena, ranging from paradigmatic Rabi-oscillations in two-level systems to the ionization of atoms, the generation of high-order harmonics, the ionization and dissociation of molecules, as well as the control of chemical reactions are presented and discussed on a fundamental level. In this way, the theoretical background for state of the art experiments with strong and short laser pulses is given. The new text is augmented by several additional exercises and now contains a total of forty-eight problems, whose worked-out solutions are given in the last chapter. In addition, some detailed calculations are performed in the appendices. Furthermore, each chapter ends with references to more specialized literature.