Chemical Bonding and Structure: Ionic Solids, VSEPR, MO Theory and Coordination Compounds

2.1Ionic bonding and lattice energy

An ionic bond forms by electron transfer followed by electrostatic attraction in a crystal lattice. It is favoured by a low ionisation enthalpy of the metal, a high electron affinity of the non-metal and, above all, a high lattice energy, which pays for the energy spent in making the ions.

Lattice energy

Lattice energy U is the energy released when one mole of the crystal forms from its gaseous ions (or, as an enthalpy, the energy needed to separate it). It cannot be measured directly; it is calculated (Born–Landé) or found from a Born–Haber cycle.

• To use it you need the Madelung constant M (from the structure type), the interionic distance r₀, the ionic charges and the Born exponent n (repulsion, 5–12; from compressibility). Kapustinskii’s equation estimates U without knowing the structure.
• U ∝ z₊z₋/(r₊ + r₋): higher charges and smaller ions give higher lattice energy and higher melting points. MgO ≫ NaCl; BeO > MgO > CaO > SrO > BaO.
• Madelung constant sums all attractions and repulsions of an ion with the whole lattice. It rises with coordination number: ZnS (CN 4) 1.638 < NaCl (CN 6) 1.748 < CsCl (CN 8) 1.763; fluorite 2.519, rutile 2.408. The nearest neighbours make the largest contribution.

Born–Haber cycle

• The cycle explains which formulas exist. NaCl₂ would have a large lattice energy (≈ −2180 kJ mol⁻¹), but forming Na²⁺ means breaking the Ne core (IE₂ ≈ 4562 kJ mol⁻¹), so Δ_fH would be strongly positive.
• Solubility of an ionic solid depends on both lattice enthalpy (to be overcome) and solvation (hydration) enthalpy (released). It dissolves when hydration roughly matches or exceeds the lattice energy.

2.2Radius ratio rules and simple crystal structures

In an ionic crystal each cation tries to touch as many anions as possible without the anions touching each other. The limiting value of r₊/r₋ decides the coordination number:

• NaCl: 0.95/1.81 = 0.525 → Na⁺ in octahedral holes (CN 6:6). For AB₂ with CN 6 for A (e.g. r(A⁴⁺)/r(O²⁻) = 63/140 = 0.45) the structure is rutile (6:3); with CN 8 it is fluorite (8:4).
• ZnS: Zn²⁺ fills half the tetrahedral holes of S²⁻ (CN 4:4). Zinc blende (sphalerite): S²⁻ in ccp. Wurtzite: S²⁻ in hcp.
• The rule often fails: real ions are not hard spheres, radii vary with CN, near a limiting value two structures have similar energies, and covalency changes everything. ZnS has r₊/r₋ ≈ 0.52 (predicting CN 6) yet adopts CN 4, because Zn²⁺ (18-electron shell) and the large S²⁻ give considerable covalent character.
• Packing of metals: ccp (fcc) and hcp both have CN 12 and 74 % packing; bcc has CN 8 (68 %); simple cubic CN 6 (52.4 %).

2.3Polarisation and Fajans’ rules

A cation distorts the electron cloud of a neighbouring anion; the shared electron density gives an ionic bond partial covalent character. Covalent character increases when:

• the cation is small and highly charged (high polarising power, charge/size): Na⁺ < Mg²⁺ < Al³⁺;
• the anion is large and highly charged (high polarisability): F⁻ < Cl⁻ < Br⁻ < I⁻;
• the cation has an 18-electron or (18 + 2) shell (Cu⁺, Ag⁺, Zn²⁺, Pb²⁺) rather than a noble-gas shell: d electrons shield the nucleus poorly. CuCl is more covalent than NaCl though the ions are of similar size.

• So A⁺ with F⁻ gives the most ionic halide and A³⁺ with I⁻ the most covalent. LiI and BeCl₂ are covalent; BaCl₂ is more ionic than PbCl₂, NCl₃ or Cl₂O.
• Consequences: lower melting point, lower solubility in water, higher solubility in organic solvents, colour (AgI yellow), and easier thermal decomposition of salts of large anions.

2.4Defects in solids

• AgBr shows both Schottky and Frenkel defects.
• Metal excess (F-centres): heating NaCl in sodium vapour gives Na_1+δCl. Na atoms ionise at the surface; Cl⁻ ions diffuse out, leaving anion vacancies that trap the released electrons. An electron in an anion vacancy is an F-centre (Farbe, colour): NaCl turns yellow, KCl violet, LiCl pink. Heated ZnO (Zn²⁺ and electrons in interstitial sites) turns yellow.
• Metal deficiency: FeO is really Fe_0.95O; some Fe²⁺ become Fe³⁺ to keep neutrality.
• Controlled valency semiconductor: doping NiO with Li₂O in air. Each Li⁺ on a Ni²⁺ site is balanced by one Ni²⁺ → Ni³⁺. The Ni³⁺ sites act as positive holes, so conductivity rises (p-type).
• Non-stoichiometric compounds conduct, are often coloured and are used as semiconductors and catalysts.
• Magnetism: paramagnetic (unpaired electrons, attracted), diamagnetic (all paired, weakly repelled), ferromagnetic (unpaired spins aligned in domains, permanent magnetism: Fe, Co, Ni, Gd; Gd with seven unpaired 4f electrons is ferromagnetic below about 20 °C), antiferromagnetic (MnO) and ferrimagnetic (Fe₃O₄).