Molecular orbitals of transition metal complexes

Foreword
Acknowledgements
Contents
Introduction
Chapter 1: Setting the scene
	1.1. Electron count in a complex: the covalent model
		1.1.1. Ligand classification (L or X)
			1.1.1.1. L-type ligands
			1.1.1.2. X-type ligands
			1.1.1.3. Ligands of LℓXx type
			1.1.1.4. Bridging ligands
		1.1.2. Electron count and the 18-electron rule
			1.1.2.1. Total number of electrons, the 18-electron rule
			1.1.2.2. Oxidation state
			1.1.2.3. dn Configuration of a metal
	1.2. An alternative model: the ionic model
		1.2.1. Lewis bases as ligands
		1.2.2. Equivalence of the covalent andionic models: examples
			1.2.2.1. Oxidation state and dn electronic configuration
			1.2.2.2. Total number of electrons
	1.3. Principles of orbital interactions
		1.3.1. Interaction between two orbitals withthe same energy
		1.3.2. Interaction between two orbitals withdifferent energies
		1.3.3. The role of symmetry
		1.3.4. σ and π interactions
	1.4. Metal orbitals
		1.4.1. Description of the valence orbitals
		1.4.2. Orbital energies
	1.5. Ligand orbitals
		1.5.1. A single ligand orbital: σ interactions
		1.5.2. Several orbitals: σ and π interactions
			1.5.2.1. Ligands of the AH2 type
			1.5.2.2. AH ligands
			1.5.2.3. Monoatomic ligands A
			1.5.2.4. Ligands with a π system: the example of CO
			1.5.2.5. π complexes
	1.6. Initial orbital approach to MLℓ complexes
		1.6.1. Simplified interaction diagram
		1.6.2. Strong-field and weak-field complexes
		1.6.3. Electronic configuration and the 18-electron rule
		1.6.4. Analogy with the octet rule
	Exercises
Chapter 2: Principal ligand fields: σ interactions
	2.1. Octahedral ML6 complexes
		2.1.1. Initial analysis of the metal–ligand orbital interactions
		2.1.2. Complete interaction diagram
			2.1.2.1. The symmetry of metal orbitals
			2.1.2.2. Symmetry-adapted orbitals on the ligands
			2.1.2.3. Interaction diagram
			2.1.2.4. Molecular orbitals and the definition of the d block
			2.1.2.5. Two other representations of the d block
			2.1.2.6. Weak fields and strong fields
		2.1.3. Electronic structure
			2.1.3.1. d6 diamagnetic complexes
			2.1.3.2. Other cases
	2.2. Square-planar ML4 complexes
		2.2.1. Characterization of the d block
		2.2.2. Electronic structure for 16-electron d8 complexes
	2.3. Square-based pyramidal ML5 complexes
		2.3.1. Characterization of the d block (metal in the basal plane)
			2.3.1.1. Derivation of the d orbitals from those of the octahedron
			2.3.1.2. Exact form of the z2 orbital
		2.3.2. Characterization of the d block (metal out of the basal plane)
		2.3.3. Electronic structure and geometry
			2.3.3.1. d8 or d6 diamagnetic complexes
			2.3.3.2. Other cases
			2.3.3.3. Electronic count and geometry
	2.4. Tetrahedral ML4 complexes
		2.4.1. Characterization of the d block
		2.4.2. Electronic structure
			2.4.2.1. d10 diamagnetic complexes
			2.4.2.2. Other cases
		2.4.3. ML4 complexes: square-planar or tetrahedral?
	2.5. Trigonal-bipyramidal ML5 complexes
		2.5.1. Characterization of the d block
		2.5.2. Electronic structure
			2.5.2.1. Diamagnetic d8 complexes
			2.5.2.2. Other cases
	2.6. Trigonal-planar ML3 complexes
		2.6.1. Characterization of the d block
		2.6.2. 16-electron d10 complexes
	2.7. Linear ML2 complexes
		2.7.1. Characterization of the d block
		2.7.2. Electronic structure
	2.8. Other complexes or MLn fragments
		2.8.1. Pyramidal ML3 complexes
		2.8.2. ‘T-shaped’ ML3 complexes
		2.8.3. ‘Butterfly’ ML4 complexes
		2.8.4. Bent ML2 complexes
		2.8.5. ML complexes
	Exercises
	Appendix A: polarization of the d orbitals
		2.A1. Three-orbital interaction diagram
		2.A2. Polarization by a p orbital: TBP ML5 complexes
		2.A3. Polarization by the s orbital: linear ML2 complexes
		2.A4. Polarization by the s orbital and by a p orbital: SBP ML5 complexes
	Appendix B: orbital energies
Chapter 3: π-type interactions
	3.1. π-donor ligands: general properties
		3.1.1. The nature of the π orbital on the ligand
		3.1.2. ‘Single-face’ and ‘double-face’ π-donors
		3.1.3. Perturbation of the d orbitals: the general interaction diagram
		3.1.4. A first example: the octahedral complex [ML5Cl]
			3.1.4.1. Perturbation of the d block
			3.1.4.2. The influence of the electronic configuration on the π-donor character of the Cl ligand
	3.2. π-acceptor ligands: general properties
		3.2.1. The nature of the π orbital on the ligand
		3.2.2. ‘Single-face’ and ‘double-face’ π-acceptors
		3.2.3. Perturbation of the d orbitals: the general interaction diagram
		3.2.4. A first example: the octahedral complex [ML5CO]
			3.2.4.1. Interaction diagram
			3.2.4.2. The metal–carbonyl bond: donation and back-donation interactions
	3.3. Complexes with several π-donor orπ-acceptor ligands
		3.3.1. The trans-[ML4Cl2] octahedral complex
			3.3.1.1. π-type orbitals on the ligands
			3.3.1.2. Taking symmetry into account: initial analysis
			3.3.1.3. Taking symmetry into account: the use of group theory
			3.3.1.4. The interaction diagram
		3.3.2. The trans-[ML4(CO)2] octahedral complex
		3.3.3. Construction of the d-block orbitals ‘by hand’
			3.3.3.1. The trans-[ML4 Cl2] and trans-[ML4(CO)2] complexes revisited
			3.3.3.2. mer-[ML3 (CO)3] complexes
			3.3.3.3. A rigorous or an approximate method?
		3.3.4. [MCl6] and [M(CO)6] octahedral complexes
			3.3.4.1. The d block in [MCl6] and [M(CO)6] complexes
			3.3.4.2. Strong-field and weak-field complexes
	3.4. π complexes: the example of ethylene
		3.4.1. Orbital interactions: the Dewar–Chatt–Duncanson model
			3.4.1.1. σ or π interactions?
			3.4.1.2. The Dewar–Chatt–Duncanson model
		3.4.2. Electronic structure of a d6 complex [ML5(η2-C2H4)]
			3.4.2.1. The complete interaction diagram
			3.4.2.2. A molecular ethylene complex or a metallacyclopropane?
		3.4.3. Metallocenes Cp2M
			3.4.3.1. The π system of the cyclopentadienyl ligand
			3.4.3.2. Cp2M complexes: the ferrocene example
		3.4.4. Cp2MLn complexes
			3.4.4.1. The bent Cp2M fragment
			3.4.4.2. Cp2MLn complexes (n = 2, 3)
	3.5. π interactions and electron counting
	Exercises
	Appendix C: the carbonyl ligand, a double-face π-acceptor
Chapter 4: Applications
	4.1. Conformational problems
		4.1.1. d8-[ML4(η2-C2H4)] complexes
		4.1.2. d6-[ML5(η2-C2H4)] complexes: staggered or eclipsed conformation?
		4.1.3. d6-[ML4(η2-C2H4)2] complexes: coupling of two π-acceptor ligands
		4.1.4. Orientation of H2 in the ‘Kubas complex [W(CO)3(PR3)2(η2-H2)]
			4.1.4.1. Orbital interactions in a d6-[ML5(η2-H2)] complex
			4.1.4.2. Orientation of H2 in the Kubas complex
	4.2. ‘Abnormal’ bond angles
		4.2.1. Agostic interactions
			4.2.1.1. Introduction
			4.2.1.2. An agostic methyl group: the complex [Ti(Cl)3(Me2P−−(CH2)2−−PMe2)(CH3)]
			4.2.2. d6 ML5 complexes: a ‘T-shaped’ or ‘Y-shaped’ geometry?
				4.2.2.1. Correlation diagram Y←TBP→T (σ interactions only)
				4.2.2.2. The role of π-type interactions
	4.3. Carbene complexes
		4.3.1. Ambiguity in the electron count for carbene complexes
		4.3.2. Two limiting cases: Fischer carbenes and Schrock carbenes
			4.3.2.1. Two interaction schemes for back-donation
			4.3.2.2. Fischer carbenes and Schrock carbenes
	4.4. Bimetallic complexes: from a single to a quadruple bond
		4.4.1. σ, π, and δ interactions
		4.4.2. M2L10 complexes
		4.4.3. The [Re2(Cl)8]2− complex: a staggered or an eclipsed conformation?
	4.5. The reductive elimination reaction
		4.5.1. Definition
		4.5.2. Simplified model for the reaction [LnMR2] → [LnM] + R−−R
		4.5.3. An example: d8-[L2MR2] → d10-[L2M] + R−−R.
		4.5.3.1. Correlation diagram for the highest-symmetry mechanism (C2v)
		4.5.3.2. Use of the correlation diagram: influence of the nature of the metal
	4.6. Principal references used for each section (§) of this chapter
	Exercises
Chapter 5: The isolobal analogy
	5.1. The analogy between fragments of octahedral ML6 and of tetrahedral CH4
		5.1.1. Fragment orbitals by the valence-bond method
		5.1.2. Fragment molecular orbitals
	5.2. Other analogous fragments
	5.3. Applications
		5.3.1. Metal–metal bonds
		5.3.2. Conformational problems
	5.4. Limitations
	Exercises
Chapter 6: Elements of group theory and applications
	6.1. Symmetry elements and symmetry operations
		6.1.1. Reflection planes
		6.1.2. Inversion centre
		6.1.3. Rotation axes
		6.1.4. Improper rotation axes
	6.2. Symmetry groups
		6.2.1. Definitions
		6.2.2. Determination of the symmetry point group
		6.2.3. Basis of an irreducible representation
			6.2.3.1. Basis for a representation
			6.2.3.2. Basis for an irreducible representation
			6.2.3.3. H2O as an example
		6.2.4. Characters
			6.2.4.1. Representation of the group
			6.2.4.2. Characters: the C3v point group
		6.2.5. Character tables
			6.2.5.1. Character table for the C2v point group
			6.2.5.2. Character table for the C3v point group
	6.3. The reduction formula
		6.3.1. The reduction formula
		6.3.2. Characters of a reducible representation
		6.3.3. Applications
			6.3.3.1. H2O as an example
			6.3.3.2. NH3 as an example
		6.3.4. Direct products
	6.4. Symmetry-adapted orbitals
		6.4.1. Projection operator
		6.4.2. Application
			6.4.2.1. The ΓH basis in H2O
			6.4.2.2. The ΓH basis in NH3
	6.5. Construction of MO: H2O as an example
		6.5.1. Symmetry and overlap
		6.5.2. Molecular orbitals for H2O
	6.6. Symmetry-adapted orbitals in several MLn complexes
		6.6.1. Square-planar ML4 complexes
			6.6.1.1. Reduction of the Γσ representation
			6.6.1.2. Symmetry-adapted orbitals
		6.6.2. Tetrahedral ML4 complexes
			6.6.2.1. Reduction of the Γσ representation
			6.6.2.2. Symmetry-adapted orbitals
		6.6.3. Trigonal-planar ML3 complexes
			6.6.3.1. Reduction of the representation Γσ
			6.6.3.2. Symmetry-adapted orbitals
		6.6.4. Trigonal-bipyramidal ML5 complexes
			6.6.4.1. Reduction of the representation Γσ
			6.6.4.2. Symmetry-adapted orbitals
		6.6.5. Octahedral ML6 complexes
			6.6.5.1. Reduction of the Γσ representation
			6.6.5.2. Symmetry-adapted orbitals
		6.6.6. Trigonal-planar ML3 complexes with a ‘π system’ on the ligands
			6.6.6.1. Reduction of the representations Γp||  and Γp⊥
			6.6.6.2. Symmetry-adapted orbitals
	Exercises
Answers to the exercises (in skeletal form)
	Chapter 1: Setting the scene
	Chapter 2: Principal ligand fields: σ interactions
	Chapter 3: π-type interactions
	Chapter 4: Applications
	Chapter 5: The isolobal analogy
	Chapter 6: Elements of group theory and applications
Bibliography
Index