| Description |
1 online resource (xv, 286 pages) : illustrations |
| Series |
Oxford series on materials modelling ; 1 |
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Oxford series on materials modelling ; 1.
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| Contents |
Cover -- CONTENTS -- I: THE FRAMEWORK -- 1 Essential Quantum Mechanics -- 1.1 The Time-independent Schrödinger Equation -- 1.2 Wave-mechanics of Non-interacting Fermions -- 1.3 Basis Vectors and Representations -- 1.4 Periodic Boundary Conditions -- 1.5 Local Orbitals and Spherical Harmonics -- 1.6 The Variational Principle and the Schrödinger Equation -- 1.7 The Density Matrix and the Charge Density -- 1.8 The Density of States -- 1.9 Jellium -- 1.10 The Matrix Eigenvalue Problem -- 1.11 Pseudopotentials -- 2 Essential Density Functional Theory -- 2.1 What is a Functional? |
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2.2 Functional Derivatives -- 2.3 The Thomas-Fermi Model -- 2.4 The Kohn-Sham Equations -- 3 Exploiting the Variational Principle -- 3.1 The Hellmann-Feynman Theorem -- 3.2 Perturbation Theory with the Density -- 3.3 The Second-order HKS Functional -- 3.4 The Harris-Foulkes Functional and its Generalizations -- 4 Linear response theory -- 4.1 Definition of the Response Function Xe(r, r') -- 4.2 Relationship to HKS Density Functional -- 4.3 The Non-interacting Response Function -- 4.4 The Dielectric Function -- 4.5 The Error in the Harris-Foulkes Functional |
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4.6 Linear Response and the Green Function -- 4.7 Linear Response in Jellium -- 4.8 Electron-Electron Interactions in the Jellium Response -- 4.9 The Long Wavelength Limit of Response Functions in Jellium -- 4.10 Linear Response in a Perfect Crystal -- 4.11 Non-local Potentials -- II: MODELLING ATOMS WITHIN SOLIDS -- 5 Testing an interatomic force model -- 5.1 The Cohesive Energy and Crystal Structures -- 5.2 The Structural Energy Difference Theorem -- 5.3 Elastic Constants -- 5.4 Phonons -- 5.5 Point Defects -- 6 Pairwise Potentials in Simple Metals -- 6.1 Introduction |
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6.2 The Energy in Terms of Pseudopotentials -- 6.3 Periodic Boundary Conditions -- 6.4 The Effective Pairwise Interaction -- 6.5 Example: The Ashcroft Empty-core Potential -- 6.6 Asymptotic Forms of the Pair Potential -- 6.7 The Pseudoatom Picture -- 7 Tight Binding -- 7.1 Introduction -- 7.2 Non-self-consistent Tight Binding -- 7.3 Slater-Koster Parameters -- 7.4 The Repulsive Energy -- 7.5 The Tight-Binding Bond Model -- 7.6 Hellmann-Feynman Forces -- 7.7 Self-consistent Tight-Binding -- 7.8 Moments of the Density of States -- 7.9 The Recursion Method -- 7.10 Second-moment Models |
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7.11 Fourth-moment Models -- 7.12 Bond-order Potentials -- 8 Hybrid Schemes -- 8.1 Generalized Pseudopotential Theory -- 8.2 Effective Medium Theory -- 9 Ionic models -- 9.1 Introduction -- 9.2 The Rigid Ion Model Derived -- 9.3 Beyond the Rigid Ion Model -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Y |
| Summary |
There is a continuing growth of interest in the computer simulation of materials at the atomic scale, using a variety of academic and commercial computer programs. Such programs work with very diverse models of the inter-atomic forces. This book explains how such models are constructed and their scientific basis |
| Bibliography |
Includes bibliographical references (pages 275-281) and index |
| Notes |
Print version record |
| Subject |
Condensed matter -- Computer simulation
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Atomic structure -- Computer simulation
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Density functionals.
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Condensed matter -- Computer simulation
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Density functionals
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Human Anatomy & Physiology.
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Health & Biological Sciences.
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Animal Biochemistry.
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| Form |
Electronic book
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| Author |
Oxford University Press
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| ISBN |
9780191545290 |
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0191545295 |
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0198509774 |
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9780198509776 |
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