Density Functional Theory E-Book

David S. Sholl

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 429

Veröffentlichungsjahr: 2011

Beschreibung

Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to students from a variety of backgrounds. The book therefore offers several features that have proven to be helpful in enabling students to master the subject, including: * Problem sets in each chapter that give readers the opportunity to test their knowledge by performing their own calculations * Worked examples that demonstrate how DFT calculations are used to solve real-world problems * Further readings listed in each chapter enabling readers to investigate specific topics in greater depth This text is written at a level suitable for individuals from a variety of scientific, mathematical, and engineering backgrounds. No previous experience working with DFT calculations is needed.

Leseprobe

Contents

PREFACE

1 WHAT IS DENSITY FUNCTIONAL THEORY?

1.1 HOW TO APPROACH THIS BOOK

1.2 EXAMPLES OF DFT IN ACTION

1.3 THE SCHRÖDINGER EQUATION

1.4 DENSITY FUNCTIONAL THEORY—FROM WAVE FUNCTIONS TO ELECTRON DENSITY

1.5 EXCHANGE–CORRELATION FUNCTIONAL

1.6 THE QUANTUM CHEMISTRY TOURIST

1.7 WHAT CAN DFT NOT DO?

1.8 DENSITY FUNCTIONAL THEORY IN OTHER FIELDS

1.9 HOW TO APPROACH THIS BOOK (REVISITED)

REFERENCES

FURTHER READING

2 DFT CALCULATIONS FOR SIMPLE SOLIDS

2.1 PERIODIC STRUCTURES, SUPERCELLS, AND LATTICE PARAMETERS

2.2 FACE-CENTERED CUBIC MATERIALS

2.3 HEXAGONAL CLOSE-PACKED MATERIALS

2.4 CRYSTAL STRUCTURE PREDICTION

2.5 PHASE TRANSFORMATIONS

EXERCISES

FURTHER READING

APPENDIX CALCULATION DETAILS

3 NUTS AND BOLTS OF DFT CALCULATIONS

3.1 RECIPROCAL SPACE AND k POINTS

3.2 ENERGY CUTOFFS

3.3 NUMERICAL OPTIMIZATION

3.4 DFT TOTAL ENERGIES—AN ITERATIVE OPTIMIZATION PROBLEM

3.5 GEOMETRY OPTIMIZATION

EXERCISES

REFERENCES

FURTHER READING

APPENDIX CALCULATION DETAILS

4 DFT CALCULATIONS FOR SURFACES OF SOLIDS

4.1 IMPORTANCE OF SURFACES

4.2 PERIODIC BOUNDARY CONDITIONS AND SLAB MODELS

4.3 CHOOSING k POINTS FOR SURFACE CALCULATIONS

4.4 CLASSIFICATION OF SURFACES BY MILLER INDICES

4.5 SURFACE RELAXATION

4.6 CALCULATION OF SURFACE ENERGIES

4.7 SYMMETRIC AND ASYMMETRIC SLAB MODELS

4.8 SURFACE RECONSTRUCTION

4.9 ADSORBATES ON SURFACES

4.10 EFFECTS OF SURFACE COVERAGE

EXERCISES

REFERENCES

FURTHER READING

APPENDIX CALCULATION DETAILS

5 DFT CALCULATIONS OF VIBRATIONAL FREQUENCIES

5.1 ISOLATED MOLECULES

5.2 VIBRATIONS OF A COLLECTION OF ATOMS

5.3 MOLECULES ON SURFACES

5.4 ZERO-POINT ENERGIES

5.5 PHONONS AND DELOCALIZED MODES

EXERCISES

REFERENCE

FURTHER READING

APPENDIX CALCULATION DETAILS

6 CALCULATING RATES OF CHEMICAL PROCESSES USING TRANSITION STATE THEORY

6.1 ONE-DIMENSIONAL EXAMPLE

6.2 MULTIDIMENSIONAL TRANSITION STATE THEORY

6.3 FINDING TRANSITION STATES

6.4 FINDING THE RIGHT TRANSITION STATES

6.5 CONNECTING INDIVIDUAL RATES TO OVERALL DYNAMICS

6.6 QUANTUM EFFECTS AND OTHER COMPLICATIONS

EXERCISES

REFERENCE

FURTHER READING

APPENDIX CALCULATION DETAILS

7 EQUILIBRIUM PHASE DIAGRAMS FROM AB INITIO THERMODYNAMICS

7.1 STABILITY OF BULK METAL OXIDES

7.2 STABILITY OF METAL AND METAL OXIDE SURFACES

7.3 MULTIPLE CHEMICAL POTENTIALS AND COUPLED CHEMICAL REACTIONS

EXERCISES

REFERENCES

FURTHER READING

APPENDIX CALCULATION DETAILS

8 ELECTRONIC STRUCTURE AND MAGNETIC PROPERTIES

8.1 ELECTRONIC DENSITY OF STATES

8.2 LOCAL DENSITY OF STATES AND ATOMIC CHARGES

8.3 MAGNETISM

EXERCISES

FURTHER READING

APPENDIX CALCULATION DETAILS

9 AB INITIO MOLECULAR DYNAMICS

9.1 CLASSICAL MOLECULAR DYNAMICS

9.2 AB INITIO MOLECULAR DYNAMICS

9.3 APPLICATIONS OF AB INITIO MOLECULAR DYNAMICS

EXERCISES

REFERENCE

FURTHER READING

APPENDIX CALCULATION DETAILS

10 ACCURACY AND METHODS BEYOND “STANDARD” CALCULATIONS

10.1 HOW ACCURATE ARE DFT CALCULATIONS?

10.2 CHOOSING A FUNCTIONAL

10.3 EXAMPLES OF PHYSICAL ACCURACY

10.4 DFT+X METHODS FOR IMPROVED TREATMENT OF ELECTRON CORRELATION

10.5 LARGER SYSTEM SIZES WITH LINEAR SCALING METHODS AND CLASSICAL FORCE FIELDS

10.6 CONCLUSION

REFERENCES

FURTHER READING

INDEX

Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.Prepared in part with support by the National Energy Technology Laboratory

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Library of Congress Cataloging-in-Publication Data:

Sholl, David S.Density functional theory: a practical introduction/David S. Sholl and Jan Steckel.p. cm.Includes index.ISBN 978-0-470-37317-0 (cloth)1. Density functionals. 2. Mathematical physics. 3. Quantum chemistry. I. Steckel, Jan.II. Title.QC20.7.D43S55 2009530.14′4—dc222008038603

PREFACE

The application of density functional theory (DFT) calculations is rapidly becoming a “standard tool” for diverse materials modeling problems in physics, chemistry, materials science, and multiple branches of engineering. Although a number of highly detailed books and articles on the theoretical foundations of DFT are available, it remains difficult for a newcomer to these methods to rapidly learn the tools that allow him or her to actually perform calculations that are now routine in the fields listed above. This book aims to fill this gap by guiding the reader through the applications of DFT that might be considered the core of continually growing scientific literature based on these methods. Each chapter includes a series of exercises to give readers experience with calculations of their own.

We have aimed to find a balance between brevity and detail that makes it possible for readers to realistically plan to read the entire text. This balance inevitably means certain technical details are explored in a limited way. Our choices have been strongly influenced by our interactions over multiple years with graduate students and postdocs in chemical engineering, physics, chemistry, materials science, and mechanical engineering at Carnegie Mellon University and the Georgia Institute of Technology. A list of Further Reading is provided in each chapter to define appropriate entry points to more detailed treatments of the area. These reading lists should be viewed as identifying highlights in the literature, not as an effort to rigorously cite all relevant work from the thousands of studies that exist on these topics.

One important choice we made to limit the scope of the book was to focus solely on one DFT method suitable for solids and spatially extended materials, namely plane-wave DFT. Although many of the foundations of plane-wave DFT are also relevant to complementary approaches used in the chemistry community for isolated molecules, there are enough differences in the applications of these two groups of methods that including both approaches would only have been possible by significantly expanding the scope of the book. Moreover, several resources already exist that give a practical “handson”

introduction to computational chemistry calculations for molecules.

Our use of DFT calculations in our own research and our writing of this book has benefited greatly from interactions with numerous colleagues over an extended period. We especially want to acknowledge J. Karl Johnson (University of Pittsburgh), Aravind Asthagiri (University of Florida), Dan Sorescu (National Energy Technology Laboratory), Cathy Stampfl (University of Sydney), John Kitchin (Carnegie Mellon University), and Duane Johnson (University of Illinois). We thank Jeong-Woo Han for his help with a number of the figures. Bill Schneider (University of Notre Dame), Ken Jordan (University of Pittsburgh), and Taku Watanabe (Georgia Institute of Technology) gave detailed and helpful feedback on draft versions. Any errors or inaccuracies in the text are, of course, our responsibility alone.

DSS dedicates this book to his father and father-in-law, whose love of science and curiosity about the world are an inspiration. JAS dedicates this book to her husband, son, and daughter.

DAVID SHOLL

Georgia Institute of Technology,Atlanta, GA, USA

JAN STECKEL

National Energy Technology Laboratory,Pittsburgh, PA, USA