Expert-level inorganic chemistry knowledge. Use when working with coordination chemistry, transition metals, crystal field theory, organometallics, main group chemistry, solid state chemistry, acid-base theory, or inorganic reaction mechanisms. Also use when the user mentions 'coordination complex', 'ligand', 'crystal field', 'transition metal', 'oxidation state', 'organometallic', 'Lewis acid', 'VSEPR', 'symmetry', 'point group', 'solid state', or 'catalysis'.
You are a world-class inorganic chemist with deep expertise in coordination chemistry, transition metal chemistry, organometallics, main group chemistry, solid state chemistry, symmetry, and inorganic reaction mechanisms.
Atomic radius:
Increases down group (more shells)
Decreases across period (more nuclear charge, same shell)
Lanthanide contraction: 4f electrons poor shielding →
5d elements smaller than expected → Zr/Hf similar size
Ionization energy:
Increases across period (more nuclear charge)
Decreases down group (outer electrons farther away)
Anomalies: Be > B (2s vs 2p), N > O (half-filled 2p stable)
Electronegativity:
F highest (4.0), Cs lowest (~0.7)
Increases across period, decreases down group
Oxidation states:
Transition metals: multiple states common (Fe: 0,+2,+3,+4,+6)
Main group: usually fixed (Na: +1, Mg: +2, Al: +3)
High OS: strong oxidizers (MnO₄⁻: Mn⁷⁺, Cr₂O₇²⁻: Cr⁶⁺)
Periodic trends summary:
→ (left to right): EN↑, IP↑, EA↑, radius↓, metallic character↓
↓ (top to bottom): EN↓, IP↓, EA↓, radius↑, metallic character↑
Coordination complex: metal center + ligands
[M(L)n]^charge notation
Coordination number (CN): number of donor atoms attached to metal
Common coordination numbers and geometries:
CN 2: linear (Ag⁺, Au⁺) — [Ag(NH₃)₂]⁺
CN 4: tetrahedral or square planar
Tetrahedral: d⁰, d⁵, d¹⁰, weak field
Square planar: d⁸ (Ni²⁺, Pd²⁺, Pt²⁺, Au³⁺), strong field
CN 6: octahedral (most common) — majority of TM complexes
Ligand types:
Monodentate: one donor atom (NH₃, Cl⁻, H₂O, CN⁻, CO)
Bidentate: two donor atoms (en, ox²⁻, bipy)
Tridentate: three (dien, terpy)
Tetradentate: four (trien, salen)
Hexadentate: six (EDTA⁴⁻)
Bridging: connects two metals (μ-Cl, μ-OH)
Chelate effect:
Chelating ligands form more stable complexes than monodentate
Entropic advantage: fewer molecules → higher entropy of reaction
EDTA forms very stable complexes (6 donor atoms)
Isomerism:
Structural isomers:
Ionization: [Co(NH₃)₅Br]SO₄ vs [Co(NH₃)₅SO₄]Br
Linkage: [Co(NH₃)₅NO₂]²⁺ (N-bonded) vs [Co(NH₃)₅ONO]²⁺ (O-bonded)
Stereoisomers:
Geometric (cis/trans, fac/mer)
Optical (Δ/Λ for tris-chelate octahedral)
d-orbital splitting in octahedral field:
eg (dx²-y², dz²): point directly at ligands → HIGHER energy
t₂g (dxy, dxz, dyz): point between ligands → LOWER energy
Crystal field splitting: Δo (10 Dq)
eg above average by 6 Dq (+0.6Δo)
t₂g below average by 4 Dq (-0.4Δo)
Strong vs weak field:
Strong field ligands: large Δo → low spin
Weak field ligands: small Δo → high spin
Pairing energy P: cost to pair electrons in same orbital
Spectrochemical series (increasing Δo):
I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < bipy < CN⁻ < CO
Halides, O-donors: weak field
N-donors, CO, CN⁻: strong field
Crystal field stabilization energy (CFSE):
CFSE = n(t₂g)×(-0.4Δo) + n(eg)×(+0.6Δo) - P(if paired)
d-orbital splitting:
Tetrahedral: Δt = 4/9 Δo (opposite splitting, t₂ above e)
Square planar: from octahedral, remove two axial ligands
Colors:
Complex absorbs complementary color to what we see
Color wheel: red-green, orange-blue, yellow-violet
d-d transitions: allowed but weak (Laporte forbidden)
Charge transfer: intense colors (MnO₄⁻ purple, CrO₄²⁻ yellow)
Magnetism:
Unpaired electrons → paramagnetic
μ = √(n(n+2)) BM (n = unpaired electrons)
All paired → diamagnetic
High spin d⁵ (Fe³⁺): 5 unpaired, μ = 5.92 BM
Low spin d⁶ (Fe²⁺, CO): 0 unpaired, diamagnetic
18-Electron Rule:
Stable organometallics tend to have 18 electrons
(analogous to noble gas configuration)
Count: metal d electrons + electrons from all ligands
Ligand electron contributions:
2e donors: CO, PR₃, NH₃, H₂O, RNC, alkene (η²)
2e donors (anionic): H⁻, Cl⁻, R⁻, OR⁻, NR₂⁻
4e donors: butadiene (η⁴), cyclobutadiene (η⁴)
5e donors: Cp⁻ (η⁵-cyclopentadienyl)
6e donors: benzene (η⁶), CO₃²⁻
Examples:
Cr(CO)₆: Cr⁰ (6e) + 6 CO (12e) = 18e ✓
Fe(CO)₅: Fe⁰ (8e) + 5 CO (10e) = 18e ✓
Ni(CO)₄: Ni⁰ (10e) + 4 CO (8e) = 18e ✓
Cp₂Fe (ferrocene): Fe²⁺ (6e) + 2 Cp⁻ (10e) = 16e (18 with ionic)
Key reactions:
Oxidative addition:
M(n) + X-Y → M(n+2)(X)(Y)
Metal oxidation state increases by 2, CN increases by 2
Requires: coordinatively unsaturated, electron-rich metal
Reductive elimination:
M(X)(Y) → M + X-Y (reverse of OA)
Forms C-C, C-H, C-X bonds
Requires: X,Y cis to each other
Migratory insertion:
M-CO + M-R → M-COR (1,2-insertion)
CO insertion into M-C bond
β-hydride elimination:
M-CH₂CH₃ → M-H + CH₂=CH₂
Requires: β-H, empty coordination site, syn coplanar geometry
Major decomposition pathway for alkyl complexes
Catalytic cycles:
Hydrogenation (Wilkinson's catalyst RhCl(PPh₃)₃):
OA (H₂) → alkene coordination → insertion → RE (alkane)
Hydroformylation (oxo process):
CO + H₂ + alkene → aldehyde (Rh or Co catalyst)
Wacker process:
CH₂=CH₂ + O₂ → CH₃CHO (Pd catalyst)
Heck, Suzuki, Negishi: Pd-catalyzed C-C couplings
Symmetry elements:
E: identity (all molecules)
Cn: rotation axis (n-fold: 360°/n)
σ: mirror plane (σh: horizontal, σv: vertical, σd: dihedral)
i: inversion center
Sn: improper rotation axis
Point groups:
C₁: no symmetry (chiral molecules)
Cs: only σ
Ci: only i
Cn: only Cn axis
Cnv: Cn + nσv (H₂O: C₂v, NH₃: C₃v)
Cnh: Cn + σh
Dn: Cn + nC₂⊥
Dnh: Dn + σh (BF₃: D₃h, benzene: D₆h)
Dnd: Dn + nσd (allene: D₂d, ferrocene staggered: D₅d)
T, Td, Th: tetrahedral (CH₄: Td)
O, Oh: octahedral (SF₆: Oh)
Ih: icosahedral (buckminsterfullerene C₆₀: Ih)
Determining point group:
1. Linear? → C∞v or D∞h
2. Multiple high-order axes? → T, O, or I
3. Find principal axis Cn
4. nC₂⊥ to Cn? → D type
5. σh? → Cnh or Dnh
6. nσv or nσd? → Cnv or Dnd
Character tables:
Irreducible representations label symmetry of orbitals/vibrations
A, B: non-degenerate; E: doubly degenerate; T: triply degenerate
Subscripts: 1 (symmetric to C₂), 2 (antisymmetric)
Superscripts: ′ (symmetric to σh), ″ (antisymmetric)
g (gerade): symmetric to i; u (ungerade): antisymmetric to i
Applications:
Selection rules: IR active if change in dipole (same symmetry as x,y,z)
Raman active: change in polarizability (quadratic functions)
MO theory: only orbitals of same symmetry can mix
Arrhenius: acids produce H⁺, bases produce OH⁻ (aqueous only)
Bronsted-Lowry:
Acid: proton donor, Base: proton acceptor
Conjugate pairs: HA/A⁻, BH⁺/B
Lewis:
Acid: electron pair acceptor (BF₃, AlCl₃, H⁺, metal ions)
Base: electron pair donor (NH₃, F⁻, OH⁻, lone pair donors)
HSAB (Hard and Soft Acids and Bases):
Hard acids: small, high charge, not polarizable (H⁺, Li⁺, Mg²⁺, Al³⁺, Cr³⁺)
Soft acids: large, low charge, polarizable (Cu⁺, Ag⁺, Pd²⁺, Pt²⁺, Hg²⁺)
Hard bases: small, high EN, not polarizable (F⁻, OH⁻, H₂O, NH₃, CO₃²⁻)
Soft bases: large, low EN, polarizable (I⁻, RS⁻, CN⁻, CO, PR₃)
Principle: Hard prefers Hard, Soft prefers Soft
AgF (soft/hard): unstable, AgI (soft/soft): very stable
Fe³⁺ (hard) prefers F⁻, O²⁻; Fe²⁺ (borderline) also S²⁻
Applications: predicting stability, solubility, reactivity
Acidity in inorganic:
Binary hydrides: acidity increases across period, down group
HF < HCl < HBr < HI (bond strength dominates down group)
Oxoacids: more O on central atom → stronger acid
H₂SO₄ > H₂SO₃, HNO₃ > HNO₂, HClO₄ > HClO₃ > HClO₂ > HClO
def main_group_reactions():
return {
'Group 1 (Alkali metals)': {
'reactions': '2M + 2H₂O → 2MOH + H₂↑',
'trend': 'Reactivity increases down group (Cs most reactive)',
'flame colors': 'Li: red, Na: yellow, K: violet, Rb: red-violet'
},
'Group 2 (Alkaline earths)': {
'reactions': 'M + 2H₂O → M(OH)₂ + H₂↑ (Ca, Sr, Ba)',
'CaCO₃': 'CaCO₃ → CaO + CO₂ (calcination at 900°C)',
'hardness': 'Temporary (HCO₃⁻) and permanent (SO₄²⁻) hardness'
},
'Group 13': {
'Al': 'Amphoteric: reacts with both acids and bases',
'B': 'Electron deficient, Lewis acid, forms boranes',
'BF₃': 'Classic Lewis acid, forms adducts BF₃·NH₃'
},
'Group 14': {
'C': 'Allotropes: diamond, graphite, fullerenes, graphene',
'Si': 'SiO₂ network solid, silicates, silicones',
'Sn/Pb': 'Amphoteric oxides, +2 and +4 states'
},
'Group 15 (Pnictogens)': {
'N₂': 'Triple bond (945 kJ/mol), very unreactive',
'NO': 'Radical, bent geometry, important signaling molecule',
'HNO₃': 'Strong acid, oxidizing agent (Cu, Ag dissolve)',
'P allotropes': 'White P₄ (reactive), red P (polymeric), black P'
},
'Group 16 (Chalcogens)': {
'O₃': 'Ozone: bent, 117°, oxidizing, UV absorption',
'H₂O': 'Anomalous properties: H-bonding, high bp/mp',
'H₂SO₄': 'Dehydrating agent, strong diprotic acid, oleum'
},
'Group 17 (Halogens)': {
'F₂': 'Most electronegative, most oxidizing, attacks glass',
'Cl₂': 'Cl₂ + H₂O → HCl + HOCl (disproportionation)',
'interhalides': 'ClF, BrF₃, IF₇ (high coordination possible for heavy)'
},
'Group 18 (Noble gases)': {
'reactivity': 'Kr, Xe: can form compounds with F, O',
'XeF₂': 'Linear, sp³d, 3 lone pairs',
'XeF₄': 'Square planar',
'XeO₃': 'Pyramidal, explosive'
}
}
Crystal structures:
Rock salt (NaCl): FCC anions, octahedral holes for cations
radius ratio: 0.414-0.732
Cesium chloride (CsCl): simple cubic, cubic holes
radius ratio: > 0.732
Zinc blende (ZnS): FCC S²⁻, tetrahedral holes for Zn²⁺
radius ratio: 0.225-0.414
Fluorite (CaF₂): FCC Ca²⁺, all tetrahedral holes for F⁻
Perovskite (CaTiO₃): mixed oxide, superconductor-related structures
Spinel (AB₂O₄): complex oxide, magnetic materials
Lattice energy:
U = -Mz⁺z⁻e²NA/4πε₀r₀ × (1 - 1/n) (Born-Mayer)
M = Madelung constant (depends on structure)
NaCl: M = 1.748, CsCl: M = 1.763, ZnS: M = 1.638
Born-Haber cycle: uses lattice energy thermodynamically
Defects:
Schottky: equal cation and anion vacancies (ionic radius similar)
Frenkel: cation displaced to interstitial site (small cation)
Non-stoichiometry: Fe₁₋ₓO (wustite), variable composition
Band theory (solid state):
Metals: partially filled band (or overlap)
Insulators: large band gap (>4 eV)
Semiconductors: small gap (1-3 eV)
Doping: n-type (donor) or p-type (acceptor)
Essential metal ions in biology:
Na⁺, K⁺: nerve impulse, osmotic balance
Ca²⁺: muscle contraction, signaling, bone
Mg²⁺: ATP cofactor, chlorophyll center
Fe: hemoglobin (O₂ transport), cytochromes (electron transfer)
Zn: carbonic anhydrase, carboxypeptidase (structural/catalytic)
Cu: cytochrome c oxidase, plastocyanin, ceruloplasmin
Co: vitamin B₁₂ (cobalamin), coenzyme
Mo: nitrogenase (N₂ fixation), xanthine oxidase
Mn: photosystem II (O₂ evolution), arginase
Hemoglobin:
Fe²⁺ in porphyrin ring (heme)
High spin (deoxy) → low spin (oxy): σ-donor O₂
Cooperative binding: sigmoidal O₂ saturation curve
CO binds 240× stronger than O₂ → CO poisoning
Nitrogen fixation:
N₂ + 8H⁺ + 8e⁻ + 16 ATP → 2NH₃ + H₂ + 16 ADP + 16 Pi
Nitrogenase enzyme: Fe-Mo cofactor (FeMoco)
Industrial: Haber-Bosch (Fe catalyst, 450°C, 200 atm)
| Pitfall | Fix |
|---|---|
| Oxidation state in complex | Count electrons carefully: metal charge = complex charge - ligand charges |
| CFSE calculation sign | t₂g electrons negative, eg electrons positive contribution |
| 18-electron rule exceptions | d⁸ square planar complexes stable at 16e (Rh, Ir, Pd, Pt) |
| Point group assignment | Systematic: linear? → high symmetry? → Cn? → C₂⊥? → σ? |
| Hard/soft prediction | HSAB predicts stability, not solubility alone |
| Geometric vs optical isomers | Square planar: cis/trans but NOT optical; octahedral tris-chelate: optical |