# Density Functional Theory: A Practical Introduction

ISBN: 978-0-470-37317-0
252 pages
April 2009

## Description

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.

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Chapter 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 Wavefunctions to Electron Density.

1.5 The Exchange-Correlation Functional.

1.6 The Quantum Chemistry Tourist.

1.7 What Can’t DFT Do?.

1.8 Density Functional Theory in Other Fields.

1.9 How To Approach This Book (Revisited).

Chapter 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.

Chapter 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.

Chapter 4: DFT Calculations for Surfaces of Solids.

4.1 Why Surfaces Are Important.

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.

Chapter 5: DFT Calculations of Vibrational Frequencies.

5.1 Isolated Molecules.

5.2 Vibrations of Collections of Atoms.

5.3 Molecules on Surfaces.

5.4 Zero Point Energies.

5.5 Phonons and Delocalized Modes.

Chapter 6: Calculating Rates of Chemical Processes Using Transition State Theory.

6.1 A One-Dimensional Example.

6.2 Multi-dimensional Transition State Theory.

6.3 Finding Transition States.

6.4 Finding the Right Transition State.

6.5 Connecting Individual Rates to Overall Dynamics.

6.6 Quantum Effects and Other Complications.

Chapter 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 Potentials.

Chapter 8: Electronic Structure and Magnetic Properties.

8.1 Electronic Density of States.

8.2 Local DOS and Atomic Charges.

8.3 Magnetism.

Chapter 9: Ab Initio Molecular Dynamics.

9.1 Classical Molecular Dynamics.

9.2 Ab Initio Molecular Dynamics.

9.3 Applications of Ab Initio Molecular Dynamics.

Chapter 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 Correlations.

10.5 Large System Sizes With Linear Scaling Methods and Classical Forcefields.

10.6 Conclusion.

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## Author Information

David S. Sholl is a Professor of Chemical & Biomolecular Engineering at the Georgia Institute of Technology, where he holds the Michael Tennenbaum Family Chair and is a GRA Eminent Scholar in Energy Sustainability.

Janice A. Steckel is a Physical Scientist at the U.S. Department of Energy, National Energy Technology Laboratory in Pittsburgh, Pennsylvania.

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