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## Pettifor D.G. Bonding and Structure of Molecules and Solids

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Start by pressing the button below! Bonding and Structure of Molecules and Solids D. Pettifor, All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press.

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David G. Solid state physics. Electronic structure. Chemical bonds. Composite materials-Bonding. The difference in energy between competing structure types is very small, often being a mere hundredth or thousandth of the total cohesive energy. Simple valence bond arguments, for example, can rationalize the well-known 8-N rule for the structures of sp-valent elements by assuming that single covalent bonds are formed between neighbouring atoms, thereby completing the stable octet shell of electrons about each atom.

But how do we account for the many exceptions to the 8-N rule such as group IV carbon and lead being most stable in the non-fourfold coordinated graphitic and cubic close-packed structure types respectively? The common assertion that the graphitic structure is stabilized by the formation of Sp2 hybrids on the carbon atoms is far too simplistic as the carbon atoms could equally well have formed Sp3 hybrids to stabilize the diamond structure instead.

In practice, the most stable structure is determined by a delicate balance between opposing terms in the total binding energy. The fundamental equation of quantum mechanics, the Schrodinger equation, can be solved exactly for the hydrogen atom. Its solution for the hydrogen molecule and for all other systems is a many-body problem.

The wave function is now no longer dependent on the coordinates of a single electron but on the coordinates of all. Unfortunately, the traditional Hartree-Fock approximation to solving the many-body Schrodinger equation was found to be insufficiently accurate for reliable structural predictions to be made for bulk materials, especially metals.

A breakthrough occurred, however, in the mids when Pierre Hohenberg, Walter Kohn, and Liu Sham proved that the total ground state energy of a many-electron system is a functional of the density.

This seemingly simple result, by focusing on the electron density rather than the many-body wave function, allowed them to derive an effective one-electron Schrodinger equation which could be solved within the so-called local density approximation.

Extensive computations during the past two decades have demonstrated the accuracy of local density functional theory in predicting the structural properties of a wide range of ionic, covalent, and metallic systems. This success of density functional theory allows the whole question of bonding and structure to be formulated within an effective one-electron framework that is so beloved by chemists in their molecular orbital description of molecules and by physicists in their band theory description of solids.

In this book I have tried to follow Einstein's dictum by simplifying the one-electron problem to the barest vi Preface essentials necessary for understanding observed trends in bonding and structure. In particular, the chemically intuitive tight binding approximation is shown to provide a unified treatment of the covalent bond in small molecules and extended solids, whereas the physically intuitive nearly free electron approximation is found to give a natural description of the metallic bond in sp-valent metals.

Emphasis is placed on recent theoretical developments that link structural stability to local topology or connectivity of the lattice through the moments of the electronic density of states. This moments approach creates a powerful bridge between the physicists' view of the global electronic structure in reciprocal space and the chemists' view of local bonding in real space. We will see that it leads to a fundamental understanding of the structural trends within the periodic table for the elements and within the AB structure map for binary compounds, experimental trends that are presented and discussed in the first chapter.

I assume, therefore, that the reader is familiar with concepts such as the covalent bond, hybrid orbitals, and electronegativity. However, in order to understand the structural trends. Both the quantification of old concepts and the development of new concepts requires the reader to take the plunge and to be swept along by the intemallogic and predictive power of the simple models presented in this book.

Most of the illustrative examples in the text require no more mathematical ability than the solution of a quadratic equation. By working through these examples readers will gain insight and experience that allows the newly learned concepts to become part of their everyday intuition and vocabulary. This intuition may be further honed by problems at the end of the book. The plunge required for understanding the elegant second-order perturbative treatment of the structure of sp-valent metals is deeper and more bracing than that needed for solving a 2 x 2 secular equation, so that Chapter 6 could be omitted on a first reading of the book.

This book is the product of many people's input and ideas. The importance of my past and present research students and postdocs is reflected in the credits to many figure captions. I should, however, like to mention in particular Nguyen Manh Due and Paul Lim who helped with a number of the illustrations.

I should also like to acknowledge the very helpful comments of Sir Alan Cottrell, Volker Heine, and John Jefferson on the first draft of this book which had been magnificently typed by Beatrice May from a nearly illegible original text.

And finally my wannest thanks to C. Liu who was amongst the first to appreciate the beauty and usefulness of the phenomenological structure maps, Masato Aoki who kept faith with the bond order potentials, Adrian Sutton who shares the dream of modelling materials across all the length scales, and Di Gold who provided love and support during the summer of '94 when this book was written. Oxford June D. Contents Note on the choice of units 1. Experimental trends in bonding and structure 1.

Introduction 1. Structures of the elements 1. Lattice types: the Pearson notation 1. Local coordination polyhedra: the Jensen notation 1. Bonding and structural trends within the elements 1. Bonding and structural trends within AB compounds 1.

Structural trends within molecules References 2. Quantum mechanical concepts 2. Introd uction 2. Wave-particle duality 2. Heisenberg's uncertainty principle 2.

The Schrodinger equation 2. The free-electron gas 2. The free atoms 2. Quantum mechanical structural predictions References 3. Bonding of molecules 3. Introduction 3. Bond formation in s-valent dimers 3. Electronegativity scales 3. Dissociation of the hydrogen dimer 3. Bond formation in sp-valent dimers 3. Hybrid orbitals References 4.

Structure of molecules 4. Introduction 4. Structural stability: an illustrative example 4. The structural energy difference theorem xi , 1 1 5 6 10 12 17 19 20 20 20 26 29 31 35 45 49 50 50 50 57 60 66 68 74 76 77 77 77 81 viii Contents 4.

The structure of s-valent molecules 4. Origin of structural trends: a moments theorem 4. The bond order 4. Linear versus bent triatomic molecules References 5.

Bonding of sp-valent metals 5. Introduction 5. Jellium: from small molecules to the bulk 5. General principles of band theory 5. The nearly free electron approximation 5.

Pseudopotentials 5. The nature of the metallic bond in sp-valent metals 5. Embedded atom potentials References 6. Structure of sp-valent metals 6. Introduction 6. Screening: the Thomas-Fermi approximation 6. Screening: linear response theory 6. The reciprocal lattice representation 6. The real-space representation 6. Structural trends 6. Hume-Rothery electron phases References 85 91 96 7. Bonding of transition metals and semiconductors 7.

Introduction 7. The tight binding approximation 7. The nature of the metallic bond in transition metals 7. The rectangular d band model of cohesion 7.

## Bonding and Structure of Molecules and Solids

As a global organisation, we, like many others, recognize the significant threat posed by the coronavirus. During this time, we have made some of our learning resources freely accessible. Our distribution centres are open and orders can be placed online. Do be advised that shipments may be delayed due to extra safety precautions implemented at our centres and delays with local shipping carriers. This book explains the observed trends in the bonding and structure of molecules and solids within the framework of simple but predictive models that are based on the modern real-space approach to the electronic structure. Emphasis is placed throughout on recent theoretical developments that link structural stability to the local topology or connectivity of the lattice through the moments of the electronic density of states.

Pettifor, D. G. (David G.), Bonding and structure of molecules and solids / D.G. Pettifor,. 1. Solid state physics. 2. Electronic structure. 3. Molecules. 4.

## Articles citing this article

He was also a fellow of St Edmund Hall, Oxford. He was the author of a book entitled bonding and structure of molecules and solids "Oxford University press". He created "structure maps" which determine which crystal structure an alloy will form. He was a world authority on materials modelling and helped established the Oxford materials modelling laboratory.

### Bonding and Structure of Molecules and Solids

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below! Bonding and Structure of Molecules and Solids D.

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below! Bonding and Structure of Molecules and Solids D.

We obtain parameters for nonorthogonal and orthogonal tight-binding TB models from two-atomic molecules for all combinations of elements of period 1 to 6 and group 3 to 18 of the periodic table. The TB bond parameters for homoatomic and heteroatomic dimers show clear chemical trends. In particular, using our parameters we compare to the rectangular d -band model, the reduced s p TB model, as well as canonical TB models for s p - and d -valent systems, which have long been used to gain qualitative insight into the interatomic bond. The transferability of our dimer-based TB bond parameters to bulk systems is discussed exemplarily for the bulk ground-state structures of Mo and Si. Our dimer-based TB bond parameters provide a well-defined and promising starting point for developing refined TB parametrizations and for making the insight of TB available for guiding materials design across the periodic table. Jan Jenke 1 , Alvin N.

#### Atomistic modelling of materials with bond-order potentials

Pettifor D. Gschneidner K. Handbook on the Physics and Chemistry of Rare Earths. Clarendon Press. This book explains the observed trends in the bonding and structure of molecules and solids within the models of the electronic structure. Emphasis is placed throughout on recent theoretical developments that link structural stability to the local topology or connectivity of the lattice through the moments of the electronic density of states.

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He was also a fellow of St Edmund Hall, Oxford. He was the author of a book entitled bonding and structure of molecules and solids "Oxford University press". He created "structure maps" which determine which crystal structure an alloy will form. He was a world authority on materials modelling and helped established the Oxford materials modelling laboratory.

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