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The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.
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"Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. A Mathematical Introduction to Electronic Structure Theory begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree-Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn-Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy." [Publisher]
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Molecular structure. --- Electronic structure. --- Electronic structure --- Molecular structure
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Atomic physics --- Electronic structure --- Chemical bonds --- Solid state physics --- Chemical bonds. --- Electronic structure.
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Electronic structure --- Atoms --- Molecules --- Électrons --- Atomes. --- Molécules. --- Corrélation.
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CHEMICAL BONDS --- ELECTRONIC STRUCTURE --- SOLID STATE CHEMISTRY --- SOLID STATE PHYSICS
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Electronic structure. --- Materials. --- Phase transformations (statistical physics) --- Solid state physics
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Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.
Electronic structure. --- Geometric quantum phases. --- Quantum electronics. --- Electronics.
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This book compiles detailed results of electronic structure calculations for most possible cubic monohydrides, dihydrides and selected trihydrides related to superconductivity, comprising elements with atomic numbers up to 103. Beginning with an introduction to the theory and details of the computational methods implemented, this handbook presents a collection of chapters containing results for different classes of cubic hydrides, featuring tables of three-centre and two-centre tight-binding parameterizations, diagrams of energy bands, and densities of states with angular momentum decomposition. Equilibrium lattice parameters and bulk moduli are also included, along with the electron-ion matrix element (Hopfield-McMillan parameter), Stoner criterion for ferromagnetism and values of Fermi velocities and plasmon energies. Each chapter features a brief text explaining the results presented with comparison to experimental values when available. A selection of the implemented computer codes is reproduced for the reader’s own use. This handbook is an ideal complement to any standard electronic structure text for students and researchers in materials science, condensed matter physics, and quantum chemistry.
Quantum mechanics. Quantumfield theory --- quantumfysica --- Electronic structure. --- Hydrides.
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The study of the electronic structure of materials is at a momentous stage, with the emergence of computational methods and theoretical approaches. Many properties of materials can now be determined directly from the fundamental equations for the electrons, providing insights into critical problems in physics, chemistry, and materials science. This book provides a unified exposition of the basic theory and methods of electronic structure, together with instructive examples of practical computational methods and real-world applications. Appropriate for both graduate students and practising scientists, this book describes the approach most widely used today, density functional theory, with emphasis upon understanding the ideas, practical methods and limitations. Many references are provided to original papers, pertinent reviews, and widely available books. Included in each chapter is a short list of the most relevant references and a set of exercises that reveal salient points and challenge the reader.
Electronic structure --- Electronics and optics of solids --- Electronic structure. --- Structure électronique --- Structure, Electronic --- Atomic structure --- Energy-band theory of solids --- Monograph
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