Theoretical Modeling of Inorganic Nanostructures: Symmetry and ab-initio Calculations of Nanolayers, Nanotubes and Nanowires

678 Pages·2015·35.36 MB·English

by  R.A. Evarestov (auth.)

NanoScience and Technology
R.A. Evarestov
Theoretical
Modeling
of Inorganic
Nanostructures
Symmetry and ab-initio Calculations of
Nanolayers, Nanotubes and Nanowires
NanoScience and Technology
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R.A. Evarestov
Theoretical Modeling
of Inorganic Nanostructures
Symmetry and ab-initio Calculations of
Nanolayers, Nanotubes and Nanowires
123
R.A. Evarestov
Department of Chemistry
St.Petersburg StateUniversity
St.Petersburg
Russia
ISSN 1434-4904 ISSN 2197-7127 (electronic)
ISBN 978-3-662-44580-8 ISBN 978-3-662-44581-5 (eBook)
DOI 10.1007/978-3-662-44581-5
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This book is dedicated to my teacher
and friend
Professor Marija I. Petrashen
Preface
The present book is dedicated to the theoretical modeling of nanostructures being
the second one published on this topic in Springer Series Nanoscience and
Technology.
ThefirstbookofthiskindNanostructures:TheoryandModelingwaspublished
in2004[1].TheauthorsofthebookProf.C.DelerueandProf.M.Lannoowrotein
theprefacethatitisanintroductiontothetheoryofnanostructuresprovidingbasic
concepts for the physics of nano-objects and reviewing the theoretical methods
ofthenanostructuremodeling.The authorshavetriedtomake thebookaccessible
to inexperienced readers, and it only requires basic knowledge in quantum
mechanics and solid state physics.
Since 2004, the science of nanostructures has had an explosive gross [2]. The
carbon nanotubes have remained to be widely investigated, including not only
electronics and sensor technology, but also nanocatalysis and nanobiotechnology.
The varied developments in carbon nanotubes are covered in book [2], citing over
2,000 references.
However,thenanostructuresofavarietyofinorganicmaterialshavesincebeen
synthesized, their properties and applications have been investigated. In the book
[2], the numbers of references cited are 500 and 900, respectively, in the case of
inorganic nanotubes and nanowires.
An essential information about the structure and properties of inorganic nano-
objectshasbeenobtainedduetothetheoreticalmodelingandabinitiocalculations
ofthenanostructureelectronicproperties.Theuseofthesymmetryofone-periodic
models of nanotubes and nanowires allows their calculations to be extended to the
systems, consisting of 300–400 atoms.
The description of the symmetry and first principles treatment of the inorganic
nanotubes based on BN, TiO , and SrTiO has been given by me recently in the
2 3
chapter13ofthebook[3].Thisbookwaspublishedin2012asthesecond(enlarged)
edition of my former book [4] in Springer Series in Solid State sciences, vol. 153.
Since its online publication on January 18, 2013, there has been a total of 5,167
downloadsformybookoritschaptersonSpringerLink.Thisbookwasoneofthetop
25%mostdownloadedeBooksintherelevantSpringereBookCollectionin2013.
vii
viii Preface
Iamsurethatnowitistimetocoverthemainresultsoftheabinitiocalculations
made on the different inorganic nanostructures, describing in more detail their
symmetry properties and overviewing the basic theoretical methods used, and the
results obtained. This is the motivation of my book writing.
This book is divided in two parts.
PartI(Theory)ofthebookisintendedfortheexperiencedresearcherswhofind
in Chap. 2 the detailed description of the symmetry of the one-periodic (1D)
nanotubes and nanowires. The basis of the modern ab initio methods of the
nanostructure calculations is given in Chap. 3.
However, the book is also useful for the experimentalists who can omit the
details of the ab initio methods description and read in Part II (Applications) the
results of the theoretical modeling and ab initio calculations for the concrete
inorganic nanostructures. To make such a work more convenient, I distributed the
material in Part II over separate chapters in such a way that each chapter is dedi-
cated to the concrete class of the inorganic nanostructures (boron compounds,
tetravalent semiconductors, nitrides, oxides, sulfides).
Chaps.4–6inPartIIincludematerialswrittenbyProf.Yu.Zhukovskii(Institute
of Solid State Physics, University of Latvia) and I am grateful to him for allowing
metousethesematerialsinmybook.Hepublishedanumberoforiginalpaperson
the ab initio treatment of inorganic nanostructures.
I am grateful to all my colleagues who took part in our joint nanostructure
research(Prof. Yu.Zhukovskii, Dr.A.Panin, Dr. A.Bandura, Prof.D.Migas,Dr.
S.Piskunov,D.Kuruch,M.Losev)orsentmefreshresultsoftheirresearch(Prof.
M. Damnjanovic, Prof. P. Deak, Prof. R. Tenne, Dr. B. Aradi).
I would like to express my thanks to the members of the Quantum Chemistry
DepartmentofSt.PetersburgStateUniversity,Dr.A.PaninandDr.A.Bandura,for
their help in preparing this book. I am especially indebted to Dr. C. Ascheron and
Mrs. A. Duhm of Springer-Verlag for the cooperation in the preparation of this
book.
St. Petersburg R.A. Evarestov
References
1. C.J.Delerue,M.Lannoo,Nanostructures:TheoryandModeling(Springer,Berlin,Heidelberg,
2004)
2. C.N.R. Rao, A. Govindaraj, Nanotubes and Nanowires, 2nd edn. RSC Nanoscience and
Nanotechnology,vol.18(RoyalSocietyofChemistry,Cambridge,2011)
3. R.A. Evarestov, Quantum Chemistry of Solids. LCAO Treatment of Crystals and Nanostruc-
tures,2ndedn.SpringerSeriesinSolidStateSciences,vol.153(Springer,Berlin,Heidelberg,
NewYork,2012)
4. R.A. Evarestov, Quantum Chemistry of Solids. The LCAO First Principles Treatment of
Crystals.SpringerSeriesinSolidStateSciences,vol.153(Springer,Berlin,2007)
Contents
Part I Theory
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The Symmetry Groups in Three-Dimensional Space . . . . . . . . . . . 9
2.1 Classification of the Symmetry Groups. . . . . . . . . . . . . . . . . . . 10
2.2 Space (Triperiodic) Symmetry Groups of Bulk Crystals . . . . . . . 12
2.2.1 Translation and Point Symmetry of Bulk Crystals . . . . . . 12
2.2.2 Symmorphic and Nonsymmorphic Space Groups. . . . . . . 19
2.2.3 Orbits of Triperiodic Groups. Wyckoff Positions. . . . . . . 24
2.3 Bulk Crystal Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.1 Structures with Cubic Lattices. . . . . . . . . . . . . . . . . . . . 31
2.3.2 Structures with Tetragonal and Orthorhombic Lattices . . . 34
2.3.3 Structures with Hexagonal Lattices . . . . . . . . . . . . . . . . 39
2.4 Diperiodic (Layer) Symmetry Groups of Nanolayers . . . . . . . . . 44
2.4.1 Two Factorizations of the Layer Groups. . . . . . . . . . . . . 44
2.4.2 Orbits of Layer Groups . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.3 Slab Models of Nanolayers. . . . . . . . . . . . . . . . . . . . . . 51
2.5 Line and Rod Symmetry Groups of Stereo-Regular Polymers
and Monoperiodic Nanostructures . . . . . . . . . . . . . . . . . . . . . . 58
2.5.1 Different Factorization of Line and Rod Groups . . . . . . . 58
2.5.2 Rod Groups and their Settings as a Special
Geometric Realizations of Line Groups . . . . . . . . . . . . . 63
2.5.3 Orbits with Respect to Line and Rod Groups . . . . . . . . . 66
2.5.4 Nanotube Rolling Up from 2D Systems. . . . . . . . . . . . . 67
2.5.5 Hexagonal and Square Lattices. . . . . . . . . . . . . . . . . . . 71
2.5.6 Rectangular Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.5.7 Symmetry of Double and Multiwall Nanotubes. . . . . . . . 75
2.5.8 The Nanowires Construction . . . . . . . . . . . . . . . . . . . . 77
ix
x Contents
2.6 Symmetry of Crystalline Orbitals in Periodic Systems:
Space, Layer and Line Groups. . . . . . . . . . . . . . . . . . . . . . . . . 81
2.6.1 Symmetry of Molecular and Crystalline Orbitals. . . . . . . 81
2.6.2 Irreducible Representations of Space Groups.
Symmetry of Crystalline Orbitals of Bulk Crystals. . . . . . 83
2.6.3 Site Symmetry and Induced Representations
of Space Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.6.4 Irreducible Representations of Layer Groups.
Symmetry of Crystalline Orbitals. . . . . . . . . . . . . . . . . . 96
2.6.5 Irreducible Representations of Line Groups. . . . . . . . . . . 98
2.6.6 Site Symmetry for Line Groups of Families 4 and 8 . . . . 102
2.7 CRYSTAL Program. Use of Symmetry in First-Principles
LCAO Calculations of 3D, 2D, 1D Systems . . . . . . . . . . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3 First-Principles Simulations of Bulk Crystal and Nanolayer
Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.1 Basis Sets and Pseudopotentials in the Crystalline Electronic
Structure Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.1.1 Plane Wave and Localized Atomic Functions
Basis Sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.1.2 Gaussian Basis Sets for Solid State Calculations. . . . . . . 125
3.1.3 Effective Core Potentials . . . . . . . . . . . . . . . . . . . . . . . 133
3.2 LCAO Hartree-Fock Method for Periodic Systems. . . . . . . . . . . 144
3.2.1 Electron Correlation, One-Electron
and One-Determinant Approximations . . . . . . . . . . . . . . 144
3.2.2 LCAO Hartree-Fock Method for Periodic Systems . . . . . 147
3.3 Foundations of Density Functional Theory . . . . . . . . . . . . . . . . 153
3.3.1 Density Functional Theory. . . . . . . . . . . . . . . . . . . . . . 153
3.3.2 The Kohn–Sham Single-particle Equations. . . . . . . . . . . 156
3.3.3 Climbing the Jacob’s Ladder
for Exchange-Correlation Functionals. . . . . . . . . . . . . . . 159
3.4 LCAO and Density Functional Tight Binding (DFTB)
Methods for Periodic Systems. . . . . . . . . . . . . . . . . . . . . . . . . 169
3.4.1 LCAO DFT Method for Periodic Systems . . . . . . . . . . . 169
3.4.2 Exchange-Correlation Functionals for Periodic
Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
3.4.3 Density Functional Tight Binding (DFTB) Method . . . . . 178
3.5 Plane Wave Hartree-Fock and DFT Methods
for Periodic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
3.5.1 Projector Augmented-Wave Method . . . . . . . . . . . . . . . 183
3.5.2 Plane Wave Hartree-Fock Method
for Periodic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 184
3.5.3 Plane Wave Density Functional Method
for Periodic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 187