Transition metals are defined as elements that have an incomplete d subshell in either their elemental form or in any stable ion.

General configuration for first-row transition metals (Sc to Zn): [Ar] 3dˣ 4s² (x = 1 to 10).

For second and third rows: [Kr] 4dˣ 5s²; [Xe] 4f¹⁴ 5dˣ 6s².

Transition metals can exhibit a wide range of oxidation states, often differing by increments of +1.

General Trend: Lower oxidation states are more stable for elements with a higher nuclear charge (i.e., for later transition metals); higher oxidation states dominate early in the series.

Examples (First-Row Transition Metals):
- Sc: only +3 (Sc³⁺) is common.
- Ti: +2, +3, +4 (Ti⁴⁺ most stable).
- V: +2, +3, +4, +5 (V⁵⁺ in VO₃⁻, V₂O₅).
- Cr: +2, +3, +6 (Cr³⁺ in Cr₂O₃; Cr⁶⁺ in CrO₄²⁻, Cr₂O₇²⁻).
- Mn: +2, +4, +6, +7 (Mn⁷⁺ in MnO₄⁻).
- Fe: +2, +3 (Fe³⁺ in Fe₂O₃; Fe²⁺ in FeO).
- Co: +2, +3.
- Ni: +2, +3 (Ni³⁺ less common).
- Cu: +1, +2; d¹⁰ Cu⁺ and d⁹ Cu²⁺.
- Zn: only +2 (d¹⁰).

Transition metals form colourful aqueous ions and coordination complexes due to d–d electronic transitions and charge-transfer transitions.

Crystal Field Splitting: In an octahedral field, the five degenerate d orbitals split into two energy levels: t₂g (lower) and e_g (higher).

• When visible light is absorbed to promote an electron from t₂g → e_g, the complementary wavelength is transmitted/reflected → observed colour.

Factors Affecting Colour:
- Type of metal and its oxidation state (affects Δ_oct, the crystal field splitting energy).
- Nature of ligands (spectrochemical series: ligands that produce large Δ_oct → absorb higher-energy light; e.g., CN⁻ is strong field, H₂O is weak field).
- Geometry (octahedral vs. tetrahedral vs. square planar; tetrahedral complexes have smaller splitting → different colour).

Crystal Field Theory (CFT): Simplifies ligands as point charges that create an electrostatic field splitting the d orbitals.

• In an octahedral complex: ±0.4 Δ_oct for t₂g orbitals; +0.6 Δ_oct for e_g orbitals (relative to the barycentre).

Ligand Field Stabilization Energy (LFSE): Energy gained by placing electrons in the lower-energy set (t₂g) rather than in degenerate d orbitals.

• LFSE helps explain stability of certain oxidation states (e.g., d³ and low-spin d⁶ prefer octahedral geometry since t₂g is completely filled).
• When Δ_oct >> pairing energy → low-spin; when Δ_oct << pairing energy → high-spin.

Transition metals and their complexes are widely used as homogeneous and heterogeneous catalysts due to:

1. Variable Oxidation States: They can undergo redox cycles, temporarily changing oxidation state to facilitate electron transfer.
2. Ability to Adsorb Molecules: On solid metal surfaces (Pd, Pt, Ni, etc.), reactants adsorb onto vacant d orbitals, weakening bonds and accelerating reactions (e.g., hydrogenation, oxidation).
3. Formation of Labile Complexes: Coordination sites can open and close easily, allowing reactant molecules to bind, react, and detach.

Unpaired d electrons impart magnetic behaviour to transition-metal complexes:

1. Diamagnetism: All electrons are paired → weakly repelled by a magnetic field.
2. Examples: Zn²⁺ (d¹⁰), Cu⁺ (d¹⁰) in complexes.
3. Paramagnetism: One or more unpaired electrons → weakly attracted to a magnetic field.
4. Number of unpaired electrons (n) determines the magnetic moment: μ ≈ √[n(n+2)] (in Bohr magnetons).
5. Example: [Mn(H₂O)₆]²⁺ (d⁵ high-spin) has five unpaired electrons → strong paramagnet.
6. Ferromagnetism and Antiferromagnetism: Some transition metal oxides (e.g., Fe₃O₄, MnO) exhibit long-range ordering of magnetic moments at room temperature (ferromagnetic) or antiparallel alignment (antiferromagnetic).
7. Spin Crossover: Certain Fe²⁺ complexes (e.g., [Fe(phen)₂(NCS)₂]) can switch between high-spin and low-spin states upon changes in temperature or pressure, leading to dramatic changes in magnetism and colour.

Alloys: Solid solutions of two or more metals to achieve enhanced mechanical or chemical properties (e.g., stainless steel = Fe + C + Cr + Ni; brass = Cu + Zn).

• Transition metals like Fe, Ni, and Cu are key alloy components due to similar atomic radii allowing substitutional solid solutions.
• Intermetallic compounds (e.g., Ni₃Al, TiAl) have ordered stoichiometries, often high melting points and unique magnetism.

Across a period (Sc → Zn): Atomic radius decreases due to increasing Z_eff, despite addition of d electrons.

• Down a group (e.g., Sc → Y → La): Radius increases as n increases, but lanthanide contraction (ineffective shielding by 4f electrons) leads to a smaller-than-expected jump from 4d to 5d elements.