Superatoms. An Introduction

113 Pages·2023·12.983 MB·English

by  Nicola Gaston

Superatoms
Superatoms are a growing topic of interest in nanoscience, bringing the physics of electronic
structure together with the chemistry of atomically precise clusters. They offer the prospect
of materials design based on the targeted tunability of nanoscale building blocks, creating
electronic materials that can be used as everything from catalysts to computing hardware.
This book is designed to be an introduction to the field, covering the history of the concept and
related theoretical models from cluster physics. It provides an overview of modern theoretical
techniques and presents a survey of recent literature, with particular emphasis on the utilisa-
tion of these nanoscale building blocks.
It explores the jellium model, shell structure in nuclear physics, and the relationship of these
to the solution of the Schrödinger equation for the atom. The subsequent extension into den-
sity functional theory enables multiple examples of recent literature studies to be used to
demonstrate the key concepts.
This book is an ideal introduction for students looking to build bridges between cluster and
condensed matter physics and the chemistry of superatoms, in particular at a graduate level.
Superatoms

An Introduction
Nicola Gaston
First edition published 2023
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ISBN: 978-0-367-76874-4 (hbk)
ISBN: 978-1-032-41722-6 (pbk)
ISBN: 978-1-003-35943-2 (ebk)
DOI: 10.1201/b23295
Typeset in CMR10
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
Contents
Preface ix
Chapter1(cid:4)What Makes an Atom? 1
1.1 SUPERATOMS 1
1.2 THE SCHRO¨DINGER EQUATION 3
1.2.1 The Many-Body Problem in Quantum Mechanics 3
1.2.2 Free Electrons in Three Dimensions 4
1.3 ATOMS 5
1.3.1 The Hydrogen Atom 6
1.3.2 The Helium Atom 8
1.3.3 Generalised Many-Electron Atoms 8
1.4 THE LIMITS OF THE PERIODIC TABLE 9
BIBLIOGRAPHY 12
Chapter2(cid:4)Electronic Shell Structure 13
2.1 METAL CLUSTERS 13
2.2 EXPERIMENTAL EVIDENCE OF MAGIC NUMBERS 14
2.3 THE EFFECTIVE POTENTIAL 16
2.3.1 Isotropic Potentials 16
2.3.2 Anharmonic and Aspherical Potentials 17
BIBLIOGRAPHY 18
Chapter3(cid:4)From the Jellium Model to Density Functional
Theory 19
3.1 THE JELLIUM MODEL 19
3.2 NUMERICAL CALCULATIONS 20
3.2.1 The Variational Principle 21
v
vi (cid:4) Contents
3.3 THE PSEUDOPOTENTIAL MODEL 21
3.4 ELECTRONICSTRUCTURECALCULATIONSFORMETAL
CLUSTERS 22
3.4.1 The Influence of Lattice Structure 22
3.4.2 The Behaviour of Different Metals 25
3.5 DENSITY FUNCTIONAL THEORY 25
3.5.1 The Hohenberg-Kohn Theorems 27
3.5.2 The Kohn-Sham Equations 29
BIBLIOGRAPHY 32
Chapter4(cid:4)From Density Functional Theory to Properties 33
4.1 ANALYSIS TECHNIQUES FOR ELECTRONIC
STRUCTURE OF SUPERATOMS 33
4.1.1 The Density of States 34
4.1.2 Spherical Harmonic Projection 36
4.2 THE PHYSICS OF THE EXCHANGE-CORRELATION
FUNCTIONAL 36
4.3 FAMILIES OF FUNCTIONALS 39
4.4 BEYOND THE INDEPENDENT PARTICLE
APPROXIMATION 40
BIBLIOGRAPHY 43
Chapter5(cid:4)Real Metal Clusters 45
5.1 MONOVALENT METALS 45
5.2 DIVALENT METALS 47
5.3 TRIVALENT METALS 49
5.3.1 Trivalent Metals with s2p1 Configurations 49
5.3.2 Trivalent Metals with s2d1 Configurations 52
5.4 TRANSITION METALS 55
BIBLIOGRAPHY 57
Chapter6(cid:4)Non-metal Superatoms 59
6.1 SUPERHALOGENS 59
6.2 SUPERALKALIS 61
Contents (cid:4) vii
BIBLIOGRAPHY 63
Chapter7(cid:4)Ligand Protected Metal Clusters 65
7.1 GOLD THIOLATE CLUSTERS 66
7.2 PHOSPHINE PROTECTED GOLD CLUSTERS 69
7.3 LIGAND PROTECTED ALUMINIUM AND GALLIUM
CLUSTERS 70
7.3.1 The Role of the Ligand Shell 72
BIBLIOGRAPHY 76
Chapter8(cid:4)Beyond Simple Superatoms 79
8.1 TUNABLE SUPERATOMS 80
8.1.1 Magnetic Dopants 82
8.2 OPEN SHELL MAGNETIC SUPERATOMS 82
8.3 SUPERATOMIC MOLECULES 85
BIBLIOGRAPHY 87
Chapter9(cid:4)Superatomic Assemblies 89
9.1 EXPERIMENTAL EVIDENCE OF SUPERATOMIC
ASSEMBLIES 89
9.2 THE BAND STRUCTURE OF SOLIDS 92
9.2.1 Crystal Structures 92
9.2.2 The Brillouin Zone 93
9.3 THE BAND STRUCTURE OF SUPERATOMIC
ASSEMBLIES 95
9.4 ELECTRONIC PROPERTIES OF CLUSTER
ASSEMBLIES 96
9.4.1 Boltzmann Theory: Application to Superatomic
Solids 97
9.5 SUPERATOMIC CHARACTER IN THE SOLID STATE 98
9.6 SUMMARY 100
BIBLIOGRAPHY 101
Index 103

Preface
This book is based on a course of lectures initially delivered as part of the
condensed matter programme in the Department of Physics at the University
of Auckland. The goal is to provide an understanding of an emergent field of
researchinclusterphysics:thatoftheconceptof‘superatoms’,andtheutility
of this concept for predicting and manipulating the electronic structure and
stability of materials.
The content aims to provide a survey of the last decade or so of research
onsuperatoms,incombinationwiththeexisting,textbookconceptsofcluster
physics, encompassing both theory and experiment. In surveying the litera-
ture, priority has been given to presenting current knowledge in a consistent
and systematic way rather than to providing an exhaustive list of relevant
publications. In particular, it needs to be recognised that work on the topic
spansbothphysicsandchemistry,andaconsistentlanguagefordiscussingthe
concepts is needed: I hope this small volume provides a useful introduction in
this sense.
Thanks are due to a number of colleagues who have worked with me on
this subject over the last years: in particular, I would like to thank Dmitri
Schebarchov,JamesT.A.Gilmour,DoreenMollenhauer,JuliaSchacht,Lukas
Hammerschmidt, Juliet Nelson, and Celina Sikorska.
FIGURE 1: Image credit Shutterstock; adapted from image ID: 297886754
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