Revision sheet: Transition Metal Complexes and Bonding

📋 Course Outline

1. Transition metals and complexes
2. Spectrochemical series and crystal field theory
3. Molecular orbital theory and SALCs
4. Octahedral sigma-donor complexes
5. Ligand field splitting and electron count
6. 18-electron rule and square planar complexes
7. Electron counting methods
8. Organometallic synthesis routes
9. CO bonding and IR shifts
10. Ligand hapticity and bridging modes

📖 1. Transition metals and complexes

🔑 Key Concepts & Definitions

• Transition metal complex : A transition metal complex is a bonding interaction between a Lewis acid metal centre and a Lewis base ligand.
• Lewis acid Lewis base view : In the Lewis acid–base view, the metal accepts electron density while the ligand donates it to form coordinate bonding.
• Oxidation state of metal : The formal oxidation state of the metal centre is a bookkeeping charge used to characterise electron density and counting.
• d n electron count : The d n count is the number of d electrons on the metal after applying the formal oxidation state.
• Coordination number and shape : Coordination number and shape describe the ligand arrangement around the metal centre that determines which orbitals interact.

📝 Essential Points

• A TM complex can be represented as a coordinate bond between a metal Lewis acid and a ligand Lewis base.
• For characterisation, four descriptors are used: formal oxidation state, d n electron count, coordination number/shape, and magnetic moment.

💡 Memory Hook

Lewis acid grabs, ligand gives; then count d electrons to predict geometry and magnetism.

📖 2. Spectrochemical series and crystal field theory

🔑 Key Concepts & Definitions

• Spectrochemical series : The spectrochemical series ranks ligands by the strength of their ligand field splitting they produce on a metal.
• Ligand field splitting energy : Ligand field splitting energy is the gap between metal d-orbital sets created by the surrounding ligands.
• Crystal field theory : Crystal field theory explains complex bonding by replacing metal–ligand effects with a splitting of metal d orbitals by ligand fields.

📝 Essential Points

• The given spectrochemical series order is I− < Br− < S2− < Cl− < F− < OH− < O2− < OH2 < py < NH3 < en < bpy < PPh3 < CN− < CO.

💡 Memory Hook

Spectrochemical series: weak field ends with I−, strongest shown by CO.

📖 3. Molecular orbital theory and SALCs

🔑 Key Concepts & Definitions

• Molecular orbital theory : Molecular orbital theory builds molecular orbitals from linear combinations of atomic orbitals.
• Symmetry Adapted Linear Combinations (SALCs) : SALCs are symmetry-matched linear combinations of atomic orbitals used to construct molecular orbital diagrams.
• Bonding vs antibonding overlap : Bonding MOs form from in-phase overlap, while antibonding MOs form from out-of-phase overlap.
• gerade and ungerade : Gerade (g) orbitals have inversion symmetry and ungerade (u) orbitals are non-centrosymmetric.
• Antibonding marker : An asterisk (*) denotes an antibonding orbital in the orbital labelling used for MOs.

📝 Essential Points

• For H2, in-phase overlap gives a bonding MO and out-of-phase overlap gives an antibonding MO denoted σu*.
• In the provided conventions, π overlap uses a nodal-plane notation, u means non-centrosymmetric, g means centrosymmetric, and * means antibonding.

💡 Memory Hook

AO combinations: + makes bonding, − makes antibonding; g/u tracks symmetry, * tracks antibonding.

📖 4. Octahedral sigma-donor complexes

🔑 Key Concepts & Definitions

• Sigma-donor ligand : A sigma-donor ligand bonds to the metal by forming σ bonds with appropriate symmetry for overlap.
• Octahedral metal valence orbitals : For an octahedral complex, the metal valence orbitals available for bonding include n+1s, n+1p, and nd orbitals.
• eg and t2g sets : In octahedral symmetry, d orbitals split into an eg set and a t2g set with different spatial orientations.
• eg orientation : The eg orbitals point along the x, y, z axes in the octahedral model used.
• t2g orientation : The t2g orbitals point between the x, y, z axes in the octahedral model used.

📝 Essential Points

• For octahedral complexes with only σ-donor ligands, example σ-donors listed include NH3 and CH3−.
• The d(eg) orbitals point along x, y, z axes and the d(t2g) orbitals point between x, y, z axes.
• No symmetry-matched ligand linear combinations can overlap with the metal t2g orbitals for the σ-donor-only case, so they remain non-bonding.

💡 Memory Hook

σ-only ligands: eg can “shake hands” with metal d orbitals, t2g stays untouched.

📖 5. Ligand field splitting and electron count

🔑 Key Concepts & Definitions

• Delta o (Δo) : Δo is the ligand field splitting energy gap between the t2g set and the antibonding eg* set in an octahedral complex model.
• Non-bonding t2g orbitals : Non-bonding t2g orbitals remain based on the metal and are unchanged by σ-donor complex formation.
• eg antibonding character* : The eg* orbitals are largely metal-based and are closer in energy to the metal orbitals than to the ligand orbitals.
• Pure σ-donor complexes electron range : Pure σ-donor octahedral complexes can accommodate electrons in either t2g or eg* depending on the metal d-electron count.

📝 Essential Points

• For an octahedral σ-donor complex, the t2g set is non-bonding so whether it is occupied does not affect stability in the model used.
• In the σ-donor-only scenario, complex electron numbers span from 12 electrons (d0 metal) up to 22 electrons (d10 metal).
• In W(CH3)6, Δo is described as the energy gap between t2g and eg* rather than the eg–t2g gap because the eg* orbitals are closer in energy to the metal levels.

💡 Memory Hook

Δo refers to t2g → eg* (not eg → t2g) in this σ-donor MO picture.

📖 6. 18-electron rule and square planar complexes

🔑 Key Concepts & Definitions

• 18-electron rule : The 18-electron rule states that many complexes are stabilized when their valence electron count reaches 18.
• Square planar structure : Square planar structure is a geometry adopted by certain transition-metal complexes instead of octahedral coordination.
• 16-electron rule : The 16-electron rule states an electron-count target of 16 for the late transition-metal square planar exception described.
• pi-acceptor ligands : π-acceptor ligands stabilise metal orbital sets by withdrawing electron density via π backbonding.

📝 Essential Points

• Complexes with low oxidation state metals (−2 to +2) tend to obey the 18-electron rule and prefer π-acceptor ligands.
• The stated exception is late transition metals with 8 d-electrons, which adopt square planar structures with 16 electrons.
• Metals in higher oxidation states (+3 to +8) prefer pure σ-donors and/or π-donors, which cause only small d-splitting so complexes may not obey the 18-electron rule.

💡 Memory Hook

Low oxidation → π-acceptors → usually 18e; late d8 → square planar → 16e.

📖 7. Electron counting methods

🔑 Key Concepts & Definitions

• Valence electrons in counting : In electron counting, valence electrons come from metal d electrons plus electrons donated by ligands.
• Covalent method : The covalent method treats the metal as having its zero oxidation state and treats anionic ligands as radicals.
• Ionic method : The ionic method assigns oxidation states so the ligand charges are used to determine electron donation in an electron-count total.
• Metal group number in covalent method : In the covalent method, the metal electron contribution equals its group number on the periodic table.

📝 Essential Points

• In the covalent method, all ligands and the metal are considered neutral, so the metal is taken as zero oxidation state.
• In the covalent method, electrons for the metal equal its periodic table group number, and anionic ligands such as CH3− are treated as radicals.
• To apply the 18-electron rule, if the complex has a charge you add or remove electrons to match the total count.
• In the given covalent examples, W0 = 6e− and 6×CH3 (6×2e−) give a total of 12e− from ligands, with charge-adjusted totals reaching 18e− for the shown cases.

💡 Memory Hook

Covalent counting: neutral metal (0 oxidation) + group number metal electrons + radicals for anionic ligands.

📖 8. Organometallic synthesis routes

🔑 Key Concepts & Definitions

• Thermodynamic favourability : Thermodynamic favourability means the reaction must have ΔG negative to proceed under the stated synthesis context.
• Ligand substitution routes : Ligand substitution is a route to build organometallic complexes by replacing ligands on a metal centre.
• Thermal substitution : Thermal substitution is ligand exchange driven by thermal conditions, with a note that a gas product affects the entropy.
• Photochemical substitution of CO : Photochemical substitution of CO is ligand exchange induced by UV excitation that weakens metal–CO bonding.
• Nucleophilic substitution of anionic ligands : Nucleophilic substitution is a route to form M–C bonds using anionic C-donor ligands and is driven by salt lattice energy.

📝 Essential Points

• The synthesis will not work unless thermodynamically favourable, using ΔG = ΔH − TΔS.
• One way to make ΔG negative is to make ΔH very negative by forming stable products or by-products with large bond or lattice energies.
• UV excitation moves an electron from t2g to eg* in W–CO complexes, weakening M–CO bonding and increasing the CO substitution rate by a factor of 10^16.
• Photochemical excitation causes dissociation of the most weakly bound ligand, and further photolysis never causes CO to dissociate in the scenario described (THF is the dissociating ligand).
• For M–C formation with anionic C-donor ligands, the reaction is driven by the high lattice energy of the salt product, where LiBr(s) has a lattice energy given as −807 kJ mol−1 and the overall ΔH is strongly negative in the example.

💡 Memory Hook

UV: t2g → eg* weakens M–CO; nucleophilic M–C: lattice energy makes ΔG behave.

📖 9. CO bonding and IR shifts

🔑 Key Concepts & Definitions

• CO as a C donor : In CO bonding descriptions used here, the C lone pair is identified as donating into a metal-based orbital to strengthen the C–O bond.
• C–O bond strengthening and weakening : CO coordination can strengthen or weaken the C–O bond depending on whether metal donation goes into orbitals that are slightly or strongly antibonding.
• IR stretching frequency νCO : The IR stretching frequency νCO is used as a measurable proxy for C–O bond strength in CO complexes.
• pi-donation and pi-acceptance balance : Metal electron density controls how much donation into the CO π* antibonding orbital occurs, changing C–O bond strength and νCO.

📝 Essential Points

• The 3σ orbital is the C lone pair and is slightly C–O antibonding, so donating into it slightly strengthens the C–O bond.
• The 2π* orbital is more strongly antibonding, so metal electron density placed in it substantially weakens the C–O bond.
• νCO is influenced by metal oxidation state because greater metal electron density increases π-donation into CO 2π* and weakens C–O.
• νCO is also affected by other ligands: good donors enhance π-donation into CO 2π* while other π-acceptors like phosphines have the opposite effect.
• νCO depends on CO coordination mode because more metals coordinated to CO means more metal electron density donated into CO 2π*, weakening C–O.

💡 Memory Hook

More metal→more backbonding into CO 2π*→weaker C–O→νCO shifts lower.

📖 10. Ligand hapticity and bridging modes

🔑 Key Concepts & Definitions

• Hapticity (hapto number ηn) : Hapticity ηn is the number of atoms within an unsaturated ligand that are bonded to the metal.
• Monohapto and trihapto allyl : Allyl can bind through one carbon (η1) or through three carbons (η3) depending on bonding mode.
• Cyclopentadienyl binding : Cyclopentadienyl can bind as η1 using one carbon or as η5 using all five carbons.
• Bridging ligands : Bridging ligands connect more than one metal, and their formula must encode both hapticity and bridging.
• h and m nomenclature : The h- and m- nomenclature describes ligand bonding mode when a ligand is both polyhapto and bridging.

📝 Essential Points

• For allyl, η1-allyl and η3-allyl denote bonding using one versus three ligand carbon atoms.
• For cyclopentadienyl, η1-cyclopentadienyl and η5-cyclopentadienyl denote bonding using one versus five ligand carbon atoms.
• When a ligand is both polyhapto and bridging, the η and bridge descriptors must be combined in the formula to describe the bonding mode.
• The provided example states CO can bond through both carbon and oxygen atoms in metal cluster complexes, requiring mode description via the notation system.

💡 Memory Hook

η counts bonded atoms; h/m tags how it bridges; η1 vs η3 (allyl) and η1 vs η5 (Cp) are the standard contrasts.

📊 Synthesis Tables

Covalent vs ionic electron counting

Method	Metal electron count assumption	Ligand treatment
Covalent	Metal taken as zero oxidation state; metal electrons equal periodic group number	Anionic ligands treated as radicals (e.g., CH3−)
Ionic	Oxidation state is assigned so metal and ligand charges determine donation	Ligand electron donation is set using the ionic view (covalent vs ionic distinction governs totals)

⚠️ Common Pitfalls & Confusions

1. Mixing up Δo with the eg–t2g gap is easy because eg* is largely metal-based and is used to define the gap in this model.
2. Assuming occupied t2g orbitals always change stability is wrong for σ-donor octahedral complexes because t2g is non-bonding there.
3. Treating CO coordination as always strengthening the C–O bond is incorrect because stronger antibonding 2π* occupation weakens C–O.
4. Applying the 18-electron rule to complexes of high oxidation state metals is unreliable because they can prefer σ/π-donor ligands with small splitting and need not hit 18.
5. Confusing hapticity with ligand charge or ligand identity is a common mistake because ηn counts only bonded atoms within the ligand.
6. Using UV photolysis intuition to dissociate multiple CO ligands is incorrect because only the most weakly bound ligand dissociates further photolysis in the described scenario.
7. For electron counting, forgetting to adjust totals for complex charge will break agreement with the 18-electron target in the examples.

✅ Exam Checklist

1. Identify a transition metal complex as Lewis acid (metal) / Lewis base (ligand) bonding and list the four characterisation descriptors.
2. Reproduce the given spectrochemical series order from I− to CO.
3. Explain how SALCs and symmetry labels (g/u, π, *, nodal planes) are used to build MO diagrams.
4. For an octahedral σ-donor-only case, state which metal d set is non-bonding and why (no symmetry-matched ligand combination overlaps).
5. Define Δo as the t2g to eg* gap and state why it is not the eg–t2g gap in the provided explanation.
6. State the electron-number range for complexes with only σ-donor ligands (12 to 22) and the role of weak σ-donation.
7. Apply the 18-electron rule conditions and state the stated square planar 16-electron exception for late d8 metals.
8. Choose covalent vs ionic electron counting and correctly account for metal electrons and radical treatment of anionic ligands in the covalent method.
9. Compute how complex charge requires adding or removing electrons in electron counting (as described for the 18-electron rule use).
10. Describe the three synthesis routes: thermal/photochemical ligand substitution and nucleophilic substitution for M–C bond formation, including the thermodynamic driver.
11. Connect CO bonding to IR shifts by linking metal oxidation state and ligand effects to π-donation into CO 2π* and the resulting νCO trend.
12. Use hapticity notation ηn to classify allyl (η1 vs η3) and cyclopentadienyl (η1 vs η5) bonding, and state how bridging mode notation must be combined for polyhapto bridging ligands.