Paramagnetism: substances with unpaired electrons are attracted to a magnetic field. Magnetic moment $\mu = \sqrt{n(n+2)}$ BM where $n$ = number of unpaired electrons. n=1: $\mu=1.73$ BM. n=2: $\mu=2.83$ BM. n=3: $\mu=3.87$ BM. n=4: $\mu=4.90$ BM. n=5: $\mu=5.92$ BM (high spin Mn²⁺, Fe³⁺). Diamagnetism: all electrons paired → weak repulsion from magnetic field. The spin-only formula gives reasonable approximation for first-row transition metals; orbital contribution becomes significant for second and third row. Measuring magnetic moment by Gouy method tells us the number of unpaired electrons and hence the spin state (high spin vs low spin).

Octahedral weak field (small Δo): d electrons fill orbitals with maximum unpaired spins (Hund rule). d1: 1 unpaired. d2: 2. d3: 3. d4: 4 (high spin). d5: 5 (high spin, Fe3+, Mn2+). d6: 4 (high spin, Fe2+). d7: 3 (Co2+). d8: 2 (Ni2+). d9: 1 (Cu2+). d10: 0 (Zn2+). Octahedral strong field (large Δo): electrons pair in t2g first. d4 → 2 unpaired (low spin). d5 → 1. d6 → 0 (Co3+ with CN-). d7 → 1. d8 → 2 (same as weak field — t2g6 eg2 in both cases!). d9 → 1. d10 → 0. So d8 is special: same number of unpaired (2) in both weak and strong field octahedral! The magnetic moment alone cannot distinguish high spin from low spin for d8.

Ni2+ (d8) forms complexes with different geometries: Tetrahedral (sp3): with weak field ligands (Cl-, Br-, I-, SCN-). [NiCl4]2-: tetrahedral, 2 unpaired, paramagnetic. μ = 2.83 BM. Square planar (dsp2): with strong field ligands (CN-, CO, en). [Ni(CN)4]2-: square planar, 0 unpaired, diamagnetic. The geometry preference: in tetrahedral, the crystal field stabilisation is smaller (Δt = 4/9 Δo) — insufficient to force pairing. In square planar: very large crystal field stabilisation for d8 configuration (can be > pairing energy) → all electrons pair in 4 lower orbitals → dsp2 hybridisation. Ni0 (d10): tetrahedral with CO → [Ni(CO)4]. d10 has all electrons paired regardless of field strength.

Transition metal complexes absorb visible light by d-d transitions (electron jumps from t2g to eg in octahedral complex). Selection rules: Laporte rule: transitions between orbitals of same parity (g→g or u→u) are forbidden. For octahedral: d-d transitions are g→g (forbidden) but occur weakly due to vibrational distortion. Spin selection rule: transitions between states of different spin multiplicity are forbidden. [Ti(H2O)6]3+: simplest case, d1, one d-d transition, one absorption band. [Cu(H2O)6]2+: d9, one "hole" in d9 acts like d1. Many-electron cases (d2-d8): multiple electronic states, complex spectra described by Tanabe-Sugano diagrams. Charge transfer (CT) spectra: much more intense than d-d (Laporte allowed). MnO4- intense purple = CT (not d-d).

Organometallic compounds: direct metal-carbon bond. Examples: [Ni(CO)4] (nickel tetracarbonyl), [Fe(CO)5] (iron pentacarbonyl), [Cr(CO)6] (chromium hexacarbonyl), ferrocene [Fe(C5H5)2]. 18-electron rule: stable organometallics obey the 18-electron rule (all valence orbitals filled). [Ni(CO)4]: Ni0 has 10 d electrons, 4 CO each donate 2 electrons → 10 + 8 = 18. Stable. Ferrocene: Fe2+ (6 e) + 2 Cp- (5 e each) = 6+10 = 16? No: Fe2+ d6 = 6 electrons + each C5H5- donates 6 π electrons = 6+6+6=18. Sandwich compound: metal between two cyclopentadienyl rings. Important industrial organometallics: [RhCl(PPh3)3] (Wilkinson catalyst, hydrogenation), [TiCl4+Al(C2H5)3] (Ziegler-Natta, alkene polymerisation), [PdCl2] (Wacker, CH2=CH2 → CH3CHO).

Transition metals show variable valency due to small energy difference between (n-1)d and ns orbitals. Both lose electrons in ionisation. Fe: +2, +3 (can be +4, +6 in special cases like FeO4²⁻). Cu: +1, +2. Mn: +2, +3, +4, +6, +7. Cr: +2, +3, +6. The colour of transition metal complexes arises from d-d transitions. Ti3+ (d1): purple. Cr3+ (d3): green/blue. Mn2+ (d5 high spin): very pale pink (transition forbidden, very weak). Fe3+ (d5 high spin): pale yellow-brown. Co2+ (d7): pink/red. Ni2+ (d8): green/blue. Cu2+ (d9): blue. Zn2+ (d10): colourless (no d-d transitions possible). The colour observed is complementary to absorbed colour.

Magnetic moment $\mu_{spin-only} = \sqrt{n(n+2)}$ Bohr Magnetons (BM) where n = number of unpaired electrons. For [NiCl4]2- (n=2): μ = √(2×4) = √8 = 2.83 BM. For [Ni(H2O)6]2+ (n=2): μ = 2.83 BM. For diamagnetic [Ni(CN)4]2- (n=0): μ = 0 BM. For [Ni(CO)4] (d10, n=0): μ = 0 BM. Experimental magnetic moment of [NiCl4]2- ≈ 3.2-3.4 BM (slightly higher than spin-only due to orbital contribution). This confirms the spin-only formula gives approximate values for first-row transition metals. Higher BM than spin-only: orbital contribution significant (e.g., Co2+ complex: spin-only gives 3.87 BM but experimental ≈ 4.1-5.2 BM for tetrahedral complexes due to large T1 ground state orbital contribution).

Pearson HSAB theory: Lewis acids (metal ions) and Lewis bases (ligands) classified as hard or soft. Hard acids: high charge, small size, low polarisability. Mg2+, Fe3+, Cr3+, Co3+, Al3+, H+. Hard bases: high electronegativity, small, low polarisability. F-, OH-, H2O, NH3, Cl-. Soft acids: low charge, large, highly polarisable. Ni0, Pt2+, Pd2+, Cu+, Au+, Hg2+. Soft bases: large, polarisable, low electronegativity. CN-, CO, PR3, I-, RS-. Rule: hard acid + hard base = stable (ionic interaction). Soft + soft = stable (covalent/back-bonding). Mixed = less stable. Applications: Hg2+ (soft acid) prefers CN-, I-, RS- (soft bases) — explains Hg toxicity (binds to thiol groups -SH in enzymes). Fe3+ (hard) binds F- strongly. Ni0 (soft) forms stable [Ni(CO)4]. HSAB explains selectivity in biological systems, extraction chemistry, catalysis.