Note: 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 H& -- #252 -- ckel and extended H& -- #252 -- ckel 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 & -- #960 -- system of regular cyclobutadiene -- 2.3.1 Decomposition of the & -- #915 -- (pz ) basis -- 2.3.2 Determination of the basis elements for different irreducible representations -- 2.3.3 Molecular orbital diagram of the & -- #960 -- 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(& -- #915) and CO(X) functions -- 3.2.2 Energy of the crystal orbitals in the H& -- #252 -- ckel approach -- 3.2.3 Band structure. , 3.2.4 Basis for an energy level E(& -- #177 -- 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 H& -- #252 -- ckel 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 & -- #963 -- -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 & -- #963 -- -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)] & -- #8855 -- C[sub(2h)] & -- #8855 -- {E, g& -- #963 -- } -- 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 & -- #915 -- and X points -- 7.1.5 & -- #956 -- -type band structure of polyacene -- 7.2 Distortions in polyacene -- 7.2.1 Disappearance of the & -- #963 -- [sub(xy)] symmetry plane -- 7.2.2 Disappearance of the & -- #963 -- [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-& -- #948 -- )-)] -- 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 & -- #915 -- 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(& -- #8734 -- )] [H[sub(n)]] system -- 9.2.2 The square lattice [sup(2)][sub(& -- #8734 -- )] [A[sub(n)]] system -- 9.2.3 & -- #956 -- -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 & -- #945 -- 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 H& -- #252 -- ckel 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.