Density Functional Theory (eBook)

A Practical Introduction

David S. Sholl, Janice A. Steckel (Autoren)

eBook Download: EPUB

2022 | 2. Auflage
224 Seiten
Wiley (Verlag)
978-1-119-84088-6 (ISBN)

Infos

Density Functional Theory

A concise and rigorous introduction to the applications of DFT calculations

In the newly revised second edition of Density Functional Theory: A Practical Introduction, the authors deliver a concise and easy-to-follow introduction to the key concepts and practical applications of density functional theory (DFT) with an emphasis on plane-wave DFT. The authors draw on decades of experience in the field, offering students from a variety of backgrounds a balanced approach between accessibility and rigor, creating a text that is highly digestible in its entirety.

This new edition:

• Discusses in more detail the accuracy of DFT calculations and the choice of functionals
• Adds an overview of the wide range of available DFT codes
• Contains more examples on the use of DFT for high throughput materials calculations
• Puts more emphasis on computing phase diagrams and on open ensemble methods widely used in electrochemistry
• Is significantly extended to cover calculation beyond standard DFT, e.g., dispersion-corrected DFT, DFT+U, time-dependent DFT

Perfect for graduate students and postdoctoral candidates in physics and engineering, Density Functional Theory: A Practical Introduction will also earn a place in the libraries of researchers and practitioners in chemistry, materials science, and mechanical engineering.

David S. Sholl leads the Transformational Decarbonization Initiative at the Oak Ridge National Laboratory and is a Professor of Chemical & Biomolecular Engineering at the Georgia Institute of Technology.

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

Textauszug

1
What is Density Functional Theory?

1.1 How to Approach This Book

There are many fields within the physical sciences and engineering where the key to scientific and technological progress is understanding and controlling the properties of matter at the level of individual atoms and molecules. Density functional theory (DFT) is a phenomenally successful approach to finding approximate solutions to the fundamental equation that describes the quantum behavior of atoms and molecules, the Schrödinger equation, in settings of practical value. This approach has rapidly grown from being a specialized art practiced by a small number of physicists and chemists at the cutting edge of quantum mechanical theory to a tool that is used regularly by large numbers of researchers in chemistry, physics, materials science, engineering, geology, and other disciplines. A search of the Science Citation Index for papers published in 1986 with the words “Density Functional Theory” in the title or abstract yields less than 50 papers. Repeating this search for 1996, 2006, 2016, and 2021 gives more than 1,100, 5,600, 13,700, and 199,719 papers, respectively.

Our aim with this book is to provide just what the title says, an introduction to using DFT calculations in a practical context. We do not assume that you have done such calculations before or that you even understand what they are. We do assume that you want to find out what is possible with these methods, either so you can perform calculations yourself in a research setting or so you can interact knowledgeably with collaborators who use these methods.

An analogy related to cars may be useful here. Before you learned how to drive, it was presumably clear to you that you can accomplish many useful things with the aid of a car. For you to use a car, it is important to understand the basic concepts that control cars (you need to put fuel in the car regularly, you need to follow basic traffic laws, and so on) and spend time driving a car in a variety of road conditions. You do not, however, need to know every detail of how fuel injectors work, how to construct a radiator system that efficiently cools an engine, or any of the other myriad of details that are required if you were going to build a car. Many of these details may be important if you plan on undertaking some especially difficult car‐related project like, say, driving single‐handed across Antarctica, but you can make it across town to a friend’s house and back without understanding them.

With this book, we hope you can learn to “drive across town” when doing your own calculations with a DFT package or when interpreting other people’s calculations as they relate to physical questions of interest to you. If you are interested in “building a better car” by advancing the cutting edge of method development in this area, then we applaud your enthusiasm. You should continue reading this chapter to find at least one surefire project that could win you a Nobel Prize, then delve into the books listed in the “Further Reading” at the end of the chapter.

At the end of most chapters, we have given a series of exercises, most of which involve actually doing calculations illustrating the ideas described in the chapter. Your knowledge and ability will grow most rapidly by doing rather than by simply reading, so we strongly recommend doing as many of the exercises as you can in the time available to you.

1.2 Examples of DFT in Action

Before we even define what DFT is, it is useful to relate a few vignettes of how it has been used in several scientific fields. We have chosen four examples from quite different areas of science from the thousands of papers that have been published using these methods. These specific examples have been selected because they show how DFT calculations have been used to make important contributions to a diverse range of compelling scientific questions, generating information that would be essentially impossible to determine through experiments.

1.2.1 Ammonia Synthesis by Heterogeneous Catalysis

Our first example involves an industrial process of immense importance: the catalytic synthesis of ammonia (NH3). Ammonia is a central component of fertilizers for agriculture, and more than 100 million tons of ammonia are produced commercially each year. By some estimates, more than 1% of all energy used in the world is consumed in the production of ammonia. The core reaction in ammonia production is very simple:

To get this reaction to proceed, it is performed at high temperatures (> 400 °C) and high pressures (> 100 atm) in the presence of metals such as Fe or Ru that act as catalysts. Although these metal catalysts were identified by Haber and others over 100 years ago, much is still not known about the mechanisms of the reactions that occur on the surfaces of these catalysts. This incomplete understanding is partly because of the structural complexity of practical catalysts. To make metal catalysts with high surface areas, tiny particles of the active metal are dispersed throughout highly porous materials. This was a widespread application of nanotechnology long before that name was applied to materials to make them sound scientifically exciting! To understand the reactivity of a metal nanoparticle, it is useful to characterize the surface atoms in terms of their local coordination, since differences in this coordination can create differences in chemical reactivity; surface atoms can be classified into “types” based on their local coordination. The surfaces of nanoparticles typically include atoms of various types (based on coordination), so that overall surface reactivity is a complicated function of the shape of the nanoparticle and the reactivity of each type of atom.

This discussion raises a fundamental question: can a direct connection be made between the shape and size of a metal nanoparticle and its activity as a catalyst for ammonia synthesis? If detailed answers to this question can be found, they can potentially lead to the synthesis of improved catalysts. One of the most detailed answers to this question to date has come from the DFT calculations of Honkala and coworkers [1], who studied nanoparticles of Ru. Using DFT calculations, they showed that the net chemical reaction above proceeds via at least 12 distinct steps on a metal catalyst and that the rates of these steps depend strongly on the local coordination of the metal atoms involved. One of the most important reactions is the breaking of the N2 bond on the catalyst surface. On regions of the catalyst surface similar to the surfaces of bulk Ru (more specifically, atomically flat regions), a great deal of energy is required for this bond‐breaking reaction, implying that the reaction rate is extremely slow. Near Ru atoms that form a common kind of surface step edge on the catalyst, however, a much smaller amount of energy is needed for this reaction. Honkala and coworkers used additional DFT calculations to predict the relative stability of many different local coordinations of surface atoms in Ru nanoparticles in a way that allowed them to predict the detailed shape of the nanoparticles as a function of particle size. This prediction makes a precise connection between the diameter of a Ru nanoparticle and the number of highly desirable reactive sites for breaking N2 bonds on the nanoparticle. The size of about 1000 nanoparticles was analyzed by transmission electron microscopy to get a particle size distribution. Finally, these calculations were used to develop an overall model that describes how the individual reaction rates for the many different kinds of metal atoms on the nanoparticle’s surfaces couple together to define the overall reaction rate under realistic reaction conditions. At no stage in this process was any experimental data used to fit or adjust the model (beyond the size distribution of the nanoparticles), so the final result was a truly predictive description of the reaction rate of a complex catalyst. After all this work was done, Honkala et al. compared their predictions to experimental measurements made with Ru nanoparticle catalysts under reaction conditions similar to industrial conditions. Their predictions were in stunning quantitative agreement with the experimental outcome.

1.2.2 Embrittlement of Metals by Trace Impurities

It is highly likely that as you read these words, you are within a meter of several copper wires, since copper is the dominant metal used for carrying electricity between components of electronic devices of all kinds. Aside from its low cost, one of the attractions of copper in practical applications is that it is a soft, ductile metal. Common pieces of copper (and other metals) are almost invariably polycrystalline, meaning that they are made up of many tiny domains called grains that are each well‐oriented single crystals. Two neighboring grains have the same crystal structure and symmetry, but their orientation in space is not identical. As a result, the places where grains touch have a considerably more complicated structure than the crystal structure of the pure metal. These regions, which are present in all polycrystalline materials, are called grain boundaries.

It has been known for over 100 years that adding tiny amounts of certain impurities to copper can change the metal from being ductile to a material that will fracture in a brittle way (that is, without plastic deformation before the fracture). This occurs, for example, when bismuth (Bi) is...

Produkt-Details

• Erscheint lt. Verlag: 15.12.2022
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Schlagworte: Chemie • Chemistry • Computational Chemistry & Molecular Modeling • Computational Chemistry u. Molecular Modeling • Festkörperphysik • Materials Science • Materialwissenschaften • Materialwissenschaften / Theorie, Modellierung u. Simulation • Physics • Physik • Solid state physics • Theory, Modeling & Simulation
• ISBN-10: 1-119-84088-0 / 1119840880
• ISBN-13: 978-1-119-84088-6 / 9781119840886