Electronic Structure: Basic Theory and Practical Methods

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Richard M. MartinCambridge University PressEdition: 2, 8/27/2020EAN 9781108429900, ISBN10: 1108429904Hardcover, 788 pages, 24.1 x 17.1 x 3.8 cmLanguage: EnglishOriginally published in EnglishThe 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.PrefaceAcknowledgmentsNotationPart I. Overview and background topics1. Introduction2. Overview3. Theoretical background4. Periodic solids and electron bands5. Uniform electron gas and sp-bonded metalsPart II. Density functional theory6. Density functional theoryfoundations7. The Kohn–Sham auxiliary system8. Functionals for exchange and correlation I9. Functionals for exchange and correlation IIPart III. Important preliminaries on atoms10. Electronic structure of atoms11. PseudopotentialsPart IV. Determination of electronic structurethe basic methods12. Plane waves and gridsbasics13. Plane waves and real space methodsfull calculations14. Localized orbitalstight-binding15. Localized orbitalsfull calculations16. Augmented functionsAPW, KKR, MTO17. Augmented functionslinear methods18. Locality and linear scaling O(N) methodsPart V. From Electronic Structure to Properties of Matter19. Quantum molecular dynamics (QMD)20. Response functionsphonons, magnons, . . .21. Excitation spectra and optical properties22. Surfaces, interfaces, and lower dimensional systems23. Wannier functions24. Polarization, localization, and Berry phasesPart VI. Electronic Structure and Topology25. Topology of the electronic structure of a crystalintroduction26. Two band modelsBerry phase, winding and topology27. Topological insulators ITwo dimensions28. Topological insulators IIThree dimensionsPart VII. APPENDICESA. Functional equationsB. LSDA and GGA functionalsC. Adiabatic approximationD. Perturbation Theory, response functions and Green's functionsE. Dielectric functions and optical propertiesF. Coulomb interactions in extended systemsG. Stress from electronic structureH. Energy and stress densitiesI. Alternative force expressionsJ. Scattering and phase shiftsK. Useful relations and formulasL. Numerical methodsM. Iterative methods in electronic structureN. Two-center matrix elementsexpressions for arbitrary angular momentum lO. Dirac equation and spin-orbit interactionP. Berry phase, curvature and Chern numbersQ. Quantum Hall effect and edge conductivityR. Codes for electronic structure calculations for solidsReferencesIndex. Show more