Orbital Approach to the Electronic Structure of Solids

Name: Orbital Approach to the Electronic Structure of Solids
Brand: Oxford University Press
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Marie-Liesse Doublet Christophe Iung Enric Canadell(Autor*in)

Oxford University Press

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Erschienen am 12. Januar 2012

365 Seiten

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978-0-19-162690-6 (ISBN)

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Inhalt

Cover
Contents
1 Elementary introduction to the transport properties of solids
1.1 Free electron model
1.1.1 One-dimensional system
1.1.2 Generalisation to a three-dimensional system
1.2 Conductivity of real solids
1.2.1 Factors influencing the conductivity
1.2.2 Band structure of real solids
1.2.3 Metallic behaviour
1.2.4 Semiconducting and insulating behaviour
1.2.5 Number of carriers
2 Electronic structure of molecules: use of symmetry
2.1 Molecular orbital theory
2.1.1 Born-Oppenheimer approximation
2.1.2 One-electron approximation
2.1.3 LCAO approximation
2.1.4 Secular equations and secular determinant
2.1.5 Basic features of the Hückel and extended Hückel methods
2.1.6 Symmetry properties of the molecular orbitals
2.2 A short review of the theory of symmetry point groups
2.2.1 Different symmetry point groups
2.2.2 Classes
2.2.3 Basis for an irreducible representation
2.3 Application to the study of the p system of regular cyclobutadiene
2.3.1 Decomposition of the G (pz ) basis
2.3.2 Determination of the basis elements for different irreducible representations
2.3.3 Molecular orbital diagram of the p system of regular cyclobutadiene
2.4 Transition metal complexes
2.4.1 Ligands and formal oxidation state
2.4.2 The ML[sub(6)] octahedral complex
2.4.3 Distortions of a complex
3 Electronic structure of one-dimensional systems: basic notions
3.1 Bloch and crystal orbitals
3.1.1 Bloch orbitals
3.1.2 Crystal orbitals
3.2 Electronic structure of the model chain H[sub(n)]
3.2.1 Representation of the CO(G) and CO(X) functions
3.2.2 Energy of the crystal orbitals in the Hückel approach
3.2.3 Band structure
3.2.4 Basis for an energy level E(±k)
3.2.5 Fermi level of the H[sub(n)] chain
3.3 Electronic structure of the dimerised model chain (H[sub(2)])[sub(n')]
3.3.1 Formal determination of the band structure
3.3.2 Qualitative determination of the band structure
3.4 Comparison of the regular H[sub(n)] and dimerised (H[sub(2)])[sub(n')] chains
3.4.1 Comparison of the band structures of the regular H[sub(n)] chain generated by either a simple or a double unit cell
3.4.2 Dimerisation in the H[sub(n)] chain: notion of distortion in a periodic system
4 First-order Peierls distortions in periodic 1D systems
4.1 Analysis of the model system (H[sup(0.5+)])[sub(n)]
4.1.1 Effect of a tetramerisation on the Fermi level
4.1.2 Effect of a tetramerisation on the states near the Fermi level
4.1.3 Effect of a tetramerisation on the band structure
4.2 Analysis of first-order Peierls distortion in terms of a charge density wave
4.3 Nesting vector
4.4 Commensurate and incommensurate distortions
4.4.1 Commensurate distortion
4.4.2 Incommensurate distortion
4.4.3 Comparison
4.5 Conclusions
5 Application to trans-polyacetylene
5.1 Electronic structure of ethylene
5.2 Main aspects of the band structure for trans-polyacetylene
5.3 Detailed analysis of the band structure of trans-polyacetylene
5.4 Determination of the band structure of trans-polyacetylene using the fragment formalism
5.4.1 Calculation of the band structure by means of the Hückel approach
5.4.2 Qualitative determination of the band structure
5.5 Band gap opening at the Fermi level in trans-polyacetylene
6 Handling the symmetry in 1D compounds
6.1 Analysis of the A[sub(n)] system
6.1.1 Analysis of the cyclic A[sub(n)] system
6.1.2 Analysis of the linear A[sub(n)] system
6.1.3 Notion of group of a k point
6.2 Application to the determination of the band structure for the A[sub(n)] linear system, where A is an atom
6.2.1 Group of the different k points
6.2.2 Symmetry of the different Bloch orbitals
6.2.3 Bands associated with s-type overlaps
6.2.4 Complete band structure
6.3 Band structure of the hypothetical (NaCl)[sub(n)] chain
6.3.1 Group of the different k points
6.3.2 Bands associated with s-type overlaps
6.3.3 Complete band structure
6.4 Consequences of the existence of a glide plane
6.4.1 Using point group symmetry properties in trans-polyacetylene
6.4.2 Complete space group (non-symmorphic) of trans-polyacetylene
6.4.3 Crystal orbitals of trans-polyacetylene by means of the non-symmorphic space group G = T[sub(n)] ? C[sub(2h)] ? {E, gs }
6.4.4 Concluding remarks
6.5 Work plan for the study of a 1D system
7 Application to polyacene
7.1 Band structure near the Fermi level
7.1.1 Unit cell definition
7.1.2 Symmetry analysis of the chain
7.1.3 Appropriate fragment orbitals
7.1.4 Crystal orbitals at the G and X points
7.1.5 µ-type band structure of polyacene
7.2 Distortions in polyacene
7.2.1 Disappearance of the s[sub(xy)] symmetry plane
7.2.2 Disappearance of the s[sub(yz)] symmetry plane
7.3 General remarks concerning Peierls distortions
7.3.1 First-order Peierls distortions
7.3.2 Second-order Peierls distortions
8 Electronic structure of selected inorganic chains
8.1 KCP
8.1.1 Band structure of the eclipsed chain [Pt(CN)[sub(4)]][sup((2-d)-)]
8.1.2 Band structure of KCP (staggered chain)
8.1.3 Conclusions
8.2 (ML[sub(4)]L')[sub(n)] chains
8.2.1 Symmetry
8.2.2 Choice of the fragment orbitals to generate the Bloch orbitals
8.2.3 Analysis of the Bloch orbitals at the G and X points
8.2.4 Symmetry of the Bloch orbitals
8.2.5 Band structure
8.2.6 Study of the (ReCl[sub(4)]N)[sub(n)] chain
8.2.7 Electronic structure of the (Pt(NH[sub(2)]Et)[sub(4)]Cl[sup(2+)])[sub(n)] chain
8.3 Suggested studies
9 Electronic structure of 2D and 3D systems
9.1 Basic concepts
9.1.1 Direct and reciprocal lattices
9.1.2 Bloch and crystal orbitals
9.1.3 Brillouin zone
9.1.4 Symmetry and the Brillouin zone
9.2 Analysis of the electronic structure of 2D model systems
9.2.1 The square lattice [sup(2)][sub(8)] [H[sub(n)]] system
9.2.2 The square lattice [sup(2)][sub(8)] [A[sub(n)]] system
9.2.3 µ-type band structure of hexagonal graphene layers
10 Density of states
10.1 Calculation and analysis of the density of states
10.1.1 Density of states
10.1.2 Projected density of states
10.1.3 Crystal orbital overlap population
10.2 Combined use of DOS and COOP: electronic structure of the MPS[sub(3)] layered phases
10.3 Step-by-step determination of the density of states: the (Pt(NH[sub(3)])[sub(4)]Cl)[sup(2+)] chain
10.4 Density of states and fragment molecular orbital interaction analysis: application to the [(C[sub(5)]H[sub(5)])M] chains
10.5 Transition metal diborides with the AlB[sub(2)] structure type: a 3D case study
11 Fermi surface and low-dimensional metals
11.1 Notion of Fermi surface
11.2 Nesting vector and electronic instabilities in low-dimensional metals
11.3 Monoclinic TaS[sub(3)] versus NbSe[sub(3)]
11.3.1 Crystal structure and electron counting
11.3.2 Qualitative band structure
11.3.3 Qualitative Fermi surface: differences between NbSe[sub(3)] and TaS[sub(3)]
11.4 Molybdenum bronzes
11.4.1 Octahedral distortions and t[sub(2g)] level splitting in MoO[sub(6)] octahedra
11.4.2 MoO[sub(5)] chain with corner-sharing octahedra: counting of 2[sub(p)]oxygen antibonding contributions
11.4.3 A[sub(0.33)]MoO[sub(3)] (A = K, Rb, Cs, Tl) 2D red bronzes: metallic or insulating?
11.4.4 A[sub(0.3)]MoO[sub(3)] (A = K, Rb, Tl) blue bronzes: 2D solids with pseudo-1D behaviour
11.4.5 Looking for 1D systems where there seem to be none: the concept of hidden nesting
11.5 Low-dimensional molecular conductors
11.5.1 An archetypal molecular metal: (TMTSF)[sub(2)]PF[sub(6)]
11.5.2 Chemically modifying the electronic structure of molecular conductors
11.5.3 Structurally complex materials with simple band structures
11.5.4 A case study: 1D vs 2D character of the carriers in some a phases of BEDT-TTF
11.5.5 Electronic structure and folding: how to relate the band structure and Fermi surface of different salts of the same family
12 Electron repulsion
12.1 From the Hückel model to the Hubbard model
12.1.1 The delocalised picture of H[sub(2)]
12.1.2 The localised picture of H[sub(2)]
12.1.3 From the molecule to the solid state
12.1.4 Application to one-band systems
12.2 Mean-field approaches
12.2.1 The many-body problem
12.2.2 The Hartree-Fock method
12.2.3 Density functional theory
12.3 Conclusion
Solutions for exercises
Appendix: Character tables
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W

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