Orbital approach to the electronic structure of solids:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2012
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIII, 350 S. Ill., graph. Darst. 25 cm |
| ISBN: | 9780199534937 0199534934 9780198767053 |
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| 245 | 1 | 0 | |a Orbital approach to the electronic structure of solids |c Enric Canadell ; Marie-Liesse Doublet ; Christophe Iung |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2012 | |
| 300 | |a XIII, 350 S. |b Ill., graph. Darst. |c 25 cm | ||
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| adam_text | Contents
1
Elementary introduction to the transport
properties of solids
ι
1.1
Free electron model
1
1.1.1
One-dimensional system
2
1.1.2
Generalisation to a three-dimensional system
9
1.2
Conductivity of real solids
10
1.2.1
Factors influencing the conductivity
10
1.2.2
Band structure of real solids
11
1.2.3
Metallic behaviour
11
1.2.4
Semiconducting and insulating behaviour
12
1.2.5
Number of carriers
13
2
Electronic structure of molecules: use of symmetry
14
2.1
Molecular orbital theory
14
2.1.1
Born-Oppenheimer approximation
15
2.1.2
One-electron approximation
15
2.1.3
LC
АО
approximation
15
2.1.4
Secular equations and secular determinant
16
2.1.5
Basic features of the Hiickel and extended
Hiickel methods
17
2.1.6
Symmetry properties of the molecular
orbitais
18
2.2
A short review of the theory of symmetry point groups
19
2.2.1
Different symmetry point groups
19
2.2.2
Classes
21
2.2.3
Basis for an irreducible representation
22
2.3
Application to the study of the
π
system of regular
cyclobutadiene
25
2.3.1
Decomposition of the
Γ(ρζ)
basis
26
2.3.2
Determination of the basis elements for different
irreducible representations
27
2.3.3
Molecular orbital diagram of the
π
system of
regular cyclobutadiene
30
2.4
Transition metal complexes
30
2.4.1
Ligands and formal oxidation state
31
2.4.2
The MLf, octahedral complex
33
2.4.3
Distortions of a complex
39
Contents
3 Electronic
structure
of one-dimensional systems:
basic notions
44
3.1
В
loch and crystal
orbitais
45
3.1.1
В
loch
orbitais
46
3.1.2
Crystal
orbitais
49
3.2
Electronic structure of the model chain
Нп
51
3.2.1
Representation of the
СО(Г)
and CO(X) functions
51
3.2.2
Energy of the crystal
orbitais
in the Hiickel
approach
52
3.2.3
Band structure
54
3.2.4
Basis for an energy level E(±k)
55
3.2.5
Fermi level of the Hn chain
57
3.3
Electronic structure of the dimerised model chain (Fl·)),,
58
3.3.1
Formal determination of the band structure
58
3.3.2
Qualitative determination of the band structure
61
3.4
Comparison of the regular Hn and dimerised
(Н2)„
chains
63
3.4.1
Comparison of the band structures of the regular
Н„
chain generated by either a simple or a double unit cell
63
3.4.2
Dimerisation in the Hn chain: notion of distortion
in a periodic system
67
4 Firstorder
Peierls distortions in periodic
1
D
systems
72
4.1
Analysis of the model system
(Н05+)„
72
4.1.1
Effect of a tetramerisation on the Fermi level
73
4.1.2
Effect of a tetramerisation on the states near the
Fermi level
74
4.1.3
Effect of a tetramerisation on the band structure
76
4.2
Analysis of first-order Peierls distortion in terms of a charge
density wave
77
4.3
Nesting vector
81
4.4
Commensurate and incommensurate distortions
81
4.4.1
Commensurate distortion
81
4.4.2
Incommensurate distortion
83
4.4.3
Comparison
83
4.5
Conclusions
83
5
Application to iraws-polyacetylene
85
5.1
Electronic structure of
ethylene
86
5.2
Main aspects of the band structure for rrarcs-polyacetylene
87
5.3
Detailed analysis of the band structure of
íra/iç-polyacetylene
88
5.4
Determination of the band structure of
řraní-polyacetylene
using the fragment formalism
89
5.4.1
Calculation of the band structure by means of the
Hiickel approach
91
5.4.2
Qualitative determination of the band structure
92
5.5
Band gap opening at the Fermi level in /raru-polyacetylene
93
Contents xi
6
Handling the symmetry in
1
D
compounds
96
6.1
Analysis of the An system
96
6.1.1
Analysis of the cyclic An system
96
6.1.2
Analysis of the linear An system
101
6.1.3
Notion of group of
а к
point
104
6.2
Application to the determination of the band structure for the An
linear system, where A is an atom
104
6.2.1
Group of the different it points
105
6.2.2
Symmetry of the different Bloch
orbitais
105
6.2.3
Bands associated with
σ
-type overlaps
107
6.2.4
Complete band structure
108
6.3
Band structure of the hypothetical
(NaCl)„
chain
109
6.3.1
Group of the different
к
points
110
6.3.2
Bands associated with
σ
-type
overlaps
110
6.3.3
Complete band structure
112
6.4
Consequences of the existence of a glide plane
113
6.4.1
Using point group symmetry properties in
fram-polyacetylene
113
6.4.2
Complete space group (non-symmorphic) of
írúTíj-polyacetylene
115
6.4.3
Crystal
orbitais
of ira/js-polyacetylene by means of the
non-symmorphic space group
G
= Tn® Cjh ®
(£-
ga
} 117
6.4.4
Concluding remarks
119
6.5
Work plan for the study of a
1
D
system
120
7
Application to polyacene
122
7.1
Band structure near the Fermi level
123
7.1.1
Unit cell definition
123
7.1.2
Symmetry analysis of the chain
123
7.1.3
Appropriate fragment
orbitais
123
7.1.4
Crystal
orbitais
at the
Г
and X points
124
7.1.5
π
-type band structure of polyacene
126
7.2
Distortions in polyacene
128
7.2.1
Disappearance of the
σχ
v symmetry plane
128
7.2.2
Disappearance of the
σν;
symmetry plane
128
7.3
General remarks concerning Peierls distortions
130
7.3.1
First-order Peierls distortions
130
7.3.2
Second-order Peierls distortions
131
8
Electronic structure of selected inorganic chains
ш
8.1
KCP
133
8.1.1
Band structure of the eclipsed chain [P^CN^]12 01
134
8.1.2
Band structure of KCP (staggered chain)
139
8.1.3
Conclusions
142
8.2
(ML4Ľ)„
chains
143
8.2.1
Svmmetrv
143
Contents
8.2.2
Choice of the fragment
orbitais
to generate the
В
loch
orbitais
143
8.2.3
Analysis of the Bloch
orbitais
at the
Г
and X points
144
8.2.4
Symmetry of the Bloch
orbitais
144
8.2.5
Band structure
145
8.2.6
Study of the
(ReCl4N)„
chain
147
8.2.7
Electronic structure of the
(Pt(NH2Et)4Cl2+)„
chain
149
8.3
Suggested studies
153
9
Electronic structure of 2D and
3D
systems
157
9.1
Basic concepts
157
9.1.1
Direct and reciprocal lattices
157
9.1.2
Bloch and crystal
orbitais
159
9.1.3
Brillouin zone
161
9.1.4
Symmetry and the Brillouin zone
162
9.2
Analysis of the electronic structure of 2D model systems
166
9.2.1
The square lattice
i^. [H„]
system
166
9.2.2
The square lattice 2X
[А„]
system
169
9.2.3
л
-type band structure of hexagonal graphene layers
173
10
Density of states
18
1
10.1
Calculation and analysis of the density of states
181
10.1.1
Density of states
181
10.1.2
Projected density of states
183
10.1.3
Crystal orbital overlap population
185
10.2
Combined use of DOS and COOP: electronic structure of the
MPS3 layered phases
186
10.3
Step-by-step determination of the density of states: the
(Pt(NH3)4Cl)2+chain
188
10.4
Density of states and fragment molecular orbital interaction
analysis: application to the
[(С5ГІ5)М]
chains
193
10.5
Transition metal diborides with the
АІВт
structure type:
a
3D
case study
196
11
Fermi surface and low-dimensional metals
20З
11.1
Notion of Fermi surface
204
11.2
Nesting vector and electronic instabilities in low-dimensional
metals
207
11.3
Monoclinic
ТаЅз
versus NbSe3
210
11.3.1
Crystal structure and electron counting
211
11.3.2
Qualitative band structure
212
11.3.3
Qualitative Fermi surface: differences between
NbSe3 andTaSi
214
11.4
Molybdenum bronzes
215
Contents xiii
11.4.1
Octahedral distortions and tig level splitting in
МоОб
octahedra
216
11.4.2
M0O5 chain with corner-sharing octahedra: counting of 2p
oxygen antibonding contributions
217
11.4.3
A0.33M0O3 (A
=
K. Rb. Cs,
TI) 2D
red bronzes: metallic or
insulating?
219
11.4.4
Ao 3MOO3 (A
=
K, Rb, Tl) blue bronzes: 2D solids with
pseudo-
ID behaviour
224
11.4.5
Looking for ID systems where there seem to be none: the
concept of hidden nesting
227
11.5
Low-dimensional molecular conductors
232
11.5.1
An archetypal molecular metal: (TMTSF)2PF6
234
11.5.2
Chemically modifying the electronic structure of molecular
conductors
235
11.5.3
Structurally complex materials with simple band structures
238
11.5.4
A case study: ID vs 2D character of the carriers in some a
phases of BEDT-TTF
242
11.5.5
Electronic structure and folding: how to relate the band
structure and Fermi surface of different salts of
the same family
247
12
Electron repulsion
256
12.1
From the Hiickel model to the Hubbard model
256
12.1.1
The delocalised picture of
Ht
256
12.1.2
The localised picture of H2
260
12.1.3
From the molecule to the solid state
266
12.1.4
Application to one-band systems
269
12.2
Mean-field approaches
273
12.2.1
The many-body problem
273
12.2.2
The Hartree-Fock method
274
12.2.3
Density functional theory
281
12.3
Conclusion
287
Solutions for exercises
291
Appendix: Character tables
342
Index
345
Elaborating on an approach that fills the gap between the different languages of the physics and
chemistry communities, this book provides an intuitive yet sound understanding of how the structure
and properties of solids may be related. The natural link is provided by the band theory approach
to the electronic structure of solids. The chemically insightful concept of orbital interaction
and the essential machinery of band theory are used throughout the book to build links between
the crystal and electronic structure of periodic systems. In such a way, it is shown how important
tools for understanding properties of solids like the density of states, the Fermi surface, etc. can be
qualitatively sketched and used to either understand the results of quantitative calculations
orto
ration¬
alize experimental observations. Extensive use of the orbital interaction approach appears to be a very
efficient way of building bridges between physically and chemically based notions to understand the
structure and properties of solids.
is a Research Professor at CSIC
- Institut
de Ciencia
de Materials de Barcelona,
is
a
Research
Director at
CNRS
-
Institut Charles
Gerhardt,
Montpellier,
is a Professor at the
Université de Montpellier- Institut Charles
Gerhardt.
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534937
|
| any_adam_object | 1 |
| author | Canadell, Enric Doublet, Marie-Liesse Iung, Christophe |
| author_GND | (DE-588)1022551752 (DE-588)1022553356 (DE-588)1022553690 |
| author_facet | Canadell, Enric Doublet, Marie-Liesse Iung, Christophe |
| author_role | aut aut aut |
| author_sort | Canadell, Enric |
| author_variant | e c ec m l d mld c i ci |
| building | Verbundindex |
| bvnumber | BV039881016 |
| classification_rvk | UP 3600 |
| classification_tum | CHE 152f CHE 194f |
| ctrlnum | (OCoLC)751831973 (DE-599)BSZ356144747 |
| dewey-full | 530.41 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.41 |
| dewey-search | 530.41 |
| dewey-sort | 3530.41 |
| dewey-tens | 530 - Physics |
| discipline | Physik Chemie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039881016 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:13:18Z |
| institution | BVB |
| isbn | 9780199534937 0199534934 9780198767053 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024740253 |
| oclc_num | 751831973 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 |
| physical | XIII, 350 S. Ill., graph. Darst. 25 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Canadell, Enric Verfasser (DE-588)1022551752 aut Orbital approach to the electronic structure of solids Enric Canadell ; Marie-Liesse Doublet ; Christophe Iung 1. publ. Oxford [u.a.] Oxford Univ. Press 2012 XIII, 350 S. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Orbital (DE-588)4127528-7 gnd rswk-swf Elektronenstruktur (DE-588)4129531-6 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Solids Electronic structure Molecular orbitals Festkörper (DE-588)4016918-2 s Elektronenstruktur (DE-588)4129531-6 s Orbital (DE-588)4127528-7 s DE-604 Doublet, Marie-Liesse Verfasser (DE-588)1022553356 aut Iung, Christophe Verfasser (DE-588)1022553690 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024740253&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024740253&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Canadell, Enric Doublet, Marie-Liesse Iung, Christophe Orbital approach to the electronic structure of solids Orbital (DE-588)4127528-7 gnd Elektronenstruktur (DE-588)4129531-6 gnd Festkörper (DE-588)4016918-2 gnd |
| subject_GND | (DE-588)4127528-7 (DE-588)4129531-6 (DE-588)4016918-2 |
| title | Orbital approach to the electronic structure of solids |
| title_auth | Orbital approach to the electronic structure of solids |
| title_exact_search | Orbital approach to the electronic structure of solids |
| title_full | Orbital approach to the electronic structure of solids Enric Canadell ; Marie-Liesse Doublet ; Christophe Iung |
| title_fullStr | Orbital approach to the electronic structure of solids Enric Canadell ; Marie-Liesse Doublet ; Christophe Iung |
| title_full_unstemmed | Orbital approach to the electronic structure of solids Enric Canadell ; Marie-Liesse Doublet ; Christophe Iung |
| title_short | Orbital approach to the electronic structure of solids |
| title_sort | orbital approach to the electronic structure of solids |
| topic | Orbital (DE-588)4127528-7 gnd Elektronenstruktur (DE-588)4129531-6 gnd Festkörper (DE-588)4016918-2 gnd |
| topic_facet | Orbital Elektronenstruktur Festkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024740253&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024740253&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT canadellenric orbitalapproachtotheelectronicstructureofsolids AT doubletmarieliesse orbitalapproachtotheelectronicstructureofsolids AT iungchristophe orbitalapproachtotheelectronicstructureofsolids |