In this book the behavior of electrons in a crystal is described in terms of the one-electron model. Clearly, such a system would be best approached by a many-body formalism but because of mathe­ matical complexities only a very few real problems can be solved in this way. In the one-electron model, each electron is considered separately as moving in the averaged field of the nuclei and all the other electrons. The resulting picture is simpler conceptually, much more tractable mathematically and, at the same time, is quite comprehensive, which makes the one-electron model the most popu­ lar approach currently in use in solid state physics.In presenting the material, we have tried to show the logic the theory followed as it was developed and, to some extent at least, to show the “scaffolding” used to build it. Whether or not we have succeeded is for the reader to judge.The concept of pseudopotential, as we believe the reader will become convinced, is a direct consequence of quantum-mechanical scattering theory and we hope therefore that the book will be of interest not only for solid state specialists but also for a reader in­ volved in other “quantum” activities.The book should be read more than once, though some places can perhaps be skipped over. Some of the topics were chosen be­ cause they arc likely to be important in the future development of the one-electron model (these topics include scattering outside iso- energetic surfaces, the concept of effective medium, and higher- order perturbation corrections). Some problems are left, unobtrusive­ ly, for the reader to solve. For example, will a self-consistent cal­ culation yield wider or narrower energy bands than those resulting from the non-self-consistent treatment? To answer this question, the reader will have to master the material in Chapter 3. Our hope is that in the course of the book the reader will himself pose problems like this and we foresee the satisfaction he (or she) will take in solv­ ing them.We hope that this book will be helpful for both theorists and ex­ perimentalists.ContentsPreface 7Introduction 11Chapter 1. Principles of the one-electron theoryPart 1 Theoretical principles of the pseudopotential methodChapter 2. Scattering theory for “solid-state people”2.1. Mathematical formalism 232.2. Scattering on an isolated potential 312.3. Pseudism and scattering 462.4. Bound states, pseudopotentials and the convergence of series 54 2.5. Scattering theory and potential form factors 61Chapter 3. Theory of potential3.1. Potential seen by an atomic electron 693.2. Dielectric screening 833.3. The self-consistency of pseudopotential and additive screening 99 3.4. Muffin-tin potential 1073.5. Average value of the screened potential 124Chapter 4. Theory of pseudopotential form factors4.1. Nonlocality, the energy dependence of form factors and per­turbation theory 1324.2. The OPW formfactor 1444.3. Phase-shift form factors 1574.4. Effective medium and pseudopotential form factors 173Chapter 5. Pseudism and the secular equations of band theory5.1. The Green’s function (or KKR) method 181 5.2. Pseudopotential secular equations 196Part 2 The use of pseudopotential theory for crystal-structure calculationsChapter 6. Formalism of crystal-structure energy calculations6.1. Basic assumptions 2056.2. Band structure energy of pure metals and binary alloys 205 6.3. Electrostatic energy 2236.4. The total internal energy of an alloy: second-order pertur­bation theory and the locality approximation 2276.5. Higher-order perturbation analysis 232 6.6. OPW nonlocal alloy theory 236Chapter 7. Pseudopotential theory of alloys. Structure stabili­ty application7.1. Phase boundaries in terms of pseudopotential theory 2417.2. Ordered phases, their structures, and existence conditions 245 7.3. Short-range order problems 2567.4. Crystal structure stability in the OPW approach 261Chapter 8. Pseudopotential theory and imperfections in crystals8.1. Introductory remarks 2678.2. Crystal lattice vibrations 267 8.3. Static imperfections 279Chapter 9. Principles of pseudopotential calculations of the properties of metals9.1. Genera 2879.2. Calculation of the atomic properties of crystalline metals and alloys 2879.3. Transport properties of noncrystalline metals and alloys 297References 317 Index 331