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Lattice Energy Calculator

Ready to calculate
U = −k·Z₊·|Z₋|/r·(correction).
4 Methods.
Madelung & Born presets.
100% Free.
No Data Stored.

How it Works

01Pick a Method

Kapustinskii (no structure data), Born-Landé, Born-Mayer, hard sphere — or run all four side by side.

02Enter Charges & r₀

Cation Z₊ and |anion Z₋|; inter-ionic distance r₀ in picometers (sum of Shannon ionic radii).

03Apply U = −k · Z₊·|Z₋|/r · (correction)

Madelung M for crystal structure, Born exponent n or ρ for repulsion. Built-in presets for both.

04Get U in kJ/mol, kcal/mol, eV

Output in 4 unit systems with full breakdown and side-by-side comparison across all four methods.

What is a Lattice Energy Calculator?

Lattice energy U is one of the most-cited quantities in inorganic chemistry — it is the energy released when one mole of an ionic compound forms from its constituent gaseous ions. It is the single quantity that controls the melting point, hardness, solubility, water-of-hydration thermochemistry, and reactivity of every ionic salt. Magnesium oxide melts at 2852 °C (U ≈ 3795 kJ/mol); cesium iodide at 632 °C (U ≈ 600 kJ/mol) — the 6.3× difference in U fully explains the 4× difference in melting point. Our Lattice Energy Calculator implements the four standard classical approximations in a single tool: Kapustinskii, Born-Landé, Born-Mayer, and hard-sphere (pure Coulomb).

Kapustinskii (1956) avoids the need for a Madelung constant by using the stoichiometry ν (total ions in the formula unit): U = −1202.5 · ν · Z₊ · |Z₋| / r · (1 − 34.5/r). It works for any ionic salt — an indispensable shortcut when the crystal structure is unknown. Born-Landé (1918) is the textbook standard: U = −138935 · M · Z₊ · |Z₋| / r · (1 − 1/n), where M is the Madelung constant for the crystal structure (NaCl 1.7476, CsCl 1.7627, fluorite 2.5194 ...) and n is the Born exponent (5-12 by noble-gas configuration). Born-Mayer (1932) replaces (1−1/n) with (1−ρ/r) where ρ ≈ 30 pm is a tabulated repulsion length — typically 1-3% closer to experimental Born-Haber values. Hard sphere drops the repulsion correction entirely; it gives the upper bound on |U|. Our "All" method runs the four side-by-side so you can pick the best fit for your data and cross-check.

Built-in Madelung presets for 9 common structures (rock salt, CsCl, zincblende, wurtzite, fluorite, rutile, antifluorite, perovskite); built-in Born-exponent presets for the 5 noble-gas configurations and common cation/anion averages. Inputs in picometers (Shannon ionic radii standard); outputs in kJ/mol, kcal/mol, and eV per ion pair. Designed for inorganic-chemistry students learning Born-Haber cycles, materials scientists screening ionic compounds for melting points and solubilities, geochemists modeling mineral stability, and any researcher comparing classical vs ab-initio lattice-energy values — runs entirely in your browser, no account, no data stored.

Pro Tip: Pair this with our Molarity Calculator for solution chemistry, our Grams to Moles Calculator for stoichiometry, or our Mass Percent Calculator for percent composition.

How to Use the Lattice Energy Calculator?

Pick a Method: Kapustinskii when you do not know the crystal structure (most general). Born-Landé for textbook problems where Madelung and Born exponent are given. Born-Mayer for tighter agreement with Born-Haber experimental values (uses ρ ≈ 30 pm). Hard sphere for the pure-Coulomb upper bound. All to compare the four side-by-side.
Enter Cation Charge Z₊ and Anion Magnitude |Z₋|: Both as positive integers. Examples: NaCl → 1, 1; MgO → 2, 2; CaF₂ → 2, 1 (per fluoride); Al₂O₃ → 3, 2; Na₃PO₄ → 1, 3 (treating PO₄³⁻ as a formal trianion).
Enter Inter-ionic Distance r₀ in picometers: Sum of Shannon ionic radii. Look up on the Shannon table (Acta Cryst. A32, 1976). Examples: NaCl r(Na⁺) + r(Cl⁻) = 102 + 181 = 283 pm; KCl 138 + 181 = 319 pm; MgO 72 + 140 = 212 pm; CaF₂ 100 + 133 = 233 pm. Note: experimental r₀ from X-ray diffraction is typically within ±5 pm of Shannon-radius sums.
For Kapustinskii — Enter Stoichiometry ν: Total ions in the empirical formula unit. NaCl → 2 (1 Na⁺ + 1 Cl⁻); CaF₂ → 3 (1 Ca²⁺ + 2 F⁻); Al₂O₃ → 5 (2 Al³⁺ + 3 O²⁻); Mg(NO₃)₂ → 3 (treating NO₃⁻ as a single ion). Kapustinskii bakes Madelung-like geometry into ν, so no separate M is needed.
For Born-Landé / Mayer / Hard-sphere — Pick a Madelung Preset or Enter M: Built-in presets for rock salt (1.7476), CsCl (1.7627), zincblende (1.6381), wurtzite (1.6413), fluorite (2.5194), rutile (2.408), antifluorite (2.5194), perovskite (2.474). Or enter your own value if your structure is non-standard.
For Born-Landé — Pick a Born Exponent n: Average of cation and anion noble-gas configurations: He → 5, Ne → 7, Ar → 9, Kr → 10, Xe → 12. NaCl: Na⁺ has Ne config (7) and Cl⁻ has Ar config (9), average n = 8. KCl: K⁺ Ar (9) + Cl⁻ Ar (9) = 9. CsI: Cs⁺ Xe (12) + I⁻ Xe (12) = 12.
For Born-Mayer — Enter ρ (Repulsion Length): Typically 30 pm = 0.30 Å for ionic crystals. Some sources give 34.5 pm (Pauling) or 28-32 pm based on alkali-halide fits. The default 30 pm gives Born-Mayer values within ~1% of experimental Born-Haber for Group I/II halides.
Read U in Multiple Units + Side-by-Side Comparison: The result panel shows U in kJ/mol (primary), kcal/mol, and eV per ion pair. The "All methods" comparison lets you see how Kapustinskii / Born-Landé / Born-Mayer / hard-sphere differ for the same inputs (typically Born-Mayer ≈ Born-Landé ≈ Kapustinskii within 5-10% for simple salts; hard-sphere is 10-15% larger in magnitude).

How is lattice energy calculated?

Lattice energy is the prototypical solid-state thermodynamic quantity — it represents the Coulombic attraction between oppositely charged ions in the crystal, corrected for short-range repulsion when ion shells overlap. The four classical approximations differ only in how they treat the repulsion correction.

References: A.F. Kapustinskii (1956) Q. Rev. Chem. Soc. 10:283; M. Born & A. Landé (1918); M. Born & J.E. Mayer (1932); CRC Handbook of Chemistry & Physics.

Core Formulas (kJ/mol, r in pm)

Kapustinskii: U = −1202.5 · ν · Z₊ · |Z₋| / r · (1 − 34.5/r)

Born-Landé: U = −138935 · M · Z₊ · |Z₋| / r · (1 − 1/n)

Born-Mayer: U = −138935 · M · Z₊ · |Z₋| / r · (1 − ρ/r)

Hard sphere: U = −138935 · M · Z₊ · |Z₋| / r    (no repulsion)

Where 138935 kJ·pm/mol = N_A · e² / (4πε₀); 1202.5 kJ·pm/mol is the Kapustinskii prefactor (Madelung-equivalent built in via ν); 34.5 pm and 30 pm are characteristic repulsion lengths.

Worked Example — NaCl (rock salt)

Z₊ = 1, |Z₋| = 1, r = 283 pm, ν = 2, M = 1.7476, n = 8, ρ = 30 pm.

  • Kapustinskii: U = −1202.5 × 2 × 1 × 1 / 283 × (1 − 34.5/283) = −1202.5 × 2/283 × 0.878 = −746 kJ/mol.
  • Born-Landé: U = −138935 × 1.7476 × 1 × 1 / 283 × (1 − 1/8) = −858.0 × 0.875 = −750 kJ/mol.
  • Born-Mayer: U = −138935 × 1.7476 / 283 × (1 − 30/283) = −858.0 × 0.894 = −767 kJ/mol.
  • Hard sphere: U = −138935 × 1.7476 / 283 = −858 kJ/mol (upper bound).
  • Born-Haber experimental value: −787 kJ/mol. Born-Mayer (−767) is closest; Kapustinskii (−746) and Born-Landé (−750) are within 5%.

Worked Example — MgO (rock salt structure, large U)

Z₊ = 2, |Z₋| = 2, r = 212 pm, ν = 2, M = 1.7476, n = 7, ρ = 30 pm.

  • Born-Landé: U = −138935 × 1.7476 × 2 × 2 / 212 × (1 − 1/7) = −4582 × 0.857 = −3927 kJ/mol.
  • Born-Mayer: U = −138935 × 1.7476 × 4 / 212 × (1 − 30/212) = −4582 × 0.858 = −3933 kJ/mol.
  • Born-Haber experimental: −3795 kJ/mol. ~3% high — the small overestimate reflects partial covalency in MgO.
  • Note the 5× higher magnitude vs NaCl despite similar r — because Z₊ × |Z₋| changes from 1 to 4. This is why MgO melts at 2852 °C and NaCl at 801 °C.

Common Lattice Energies (Born-Haber experimental, kJ/mol)

  • Group I halides: LiF 1037, NaCl 787, KCl 717, RbCl 692, CsCl 657, CsI 600.
  • Group II oxides (rock salt): MgO 3795, CaO 3414, SrO 3217, BaO 3029.
  • Group II halides (fluorite for heavy): CaF₂ 2630, MgF₂ 2961, BaF₂ 2353.
  • Group III oxides: Al₂O₃ ~15,916 (sapphire — extreme).
  • Common nitrates / sulfates: NaNO₃ 763, K₂SO₄ ~2052, Na₂SO₄ ~1938.
  • Trend with charge: doubling charges quadruples U at fixed r (NaCl 787 → MgO 3795 = 4.8× when accounting for smaller r in MgO).
  • Trend with size: within Group I chlorides, U falls smoothly as r₀ rises (LiCl 853 → CsCl 657, ~25% drop).

Madelung Constants (dimensionless geometric factor)

  • Rock salt (NaCl, KCl, MgO): 1.7476.
  • Cesium chloride (CsCl, CsBr, NH₄Cl): 1.7627.
  • Zincblende (ZnS cubic, ZnO low-T): 1.6381.
  • Wurtzite (ZnS hex, AgI, BeO): 1.6413.
  • Fluorite (CaF₂, BaF₂, ThO₂): 2.5194.
  • Antifluorite (Na₂O, K₂O, Li₂O): 2.5194 (same as fluorite, just inverted).
  • Rutile (TiO₂, MnO₂): 2.408.
  • Perovskite (CaTiO₃, BaTiO₃): 2.474.
  • Corundum (Al₂O₃, Cr₂O₃): 4.172 (large because of 3+ cations).

Born Exponents by Noble-Gas Configuration

  • He config (Li⁺, Be²⁺, H⁻): n = 5.
  • Ne config (Na⁺, Mg²⁺, F⁻, O²⁻): n = 7.
  • Ar config (K⁺, Ca²⁺, Cl⁻, S²⁻): n = 9.
  • Kr config (Rb⁺, Sr²⁺, Br⁻): n = 10.
  • Xe config (Cs⁺, Ba²⁺, I⁻): n = 12.
  • Mixed-config crystals: use the average of cation and anion exponents. NaCl (Ne/Ar) → n = (7+9)/2 = 8. KBr (Ar/Kr) → n = (9+10)/2 = 9.5.
Real-World Example

Worked Example — Compute U for KCl Using Three Methods

Inputs. KCl is rock salt; Z₊ = 1, |Z₋| = 1, r₀ = 319 pm (= 138 pm K⁺ + 181 pm Cl⁻), ν = 2, M = 1.7476, n = 9 (K⁺ Ar config + Cl⁻ Ar config), ρ = 30 pm.

Kapustinskii.

  • U = −1202.5 × 2 × 1 × 1 / 319 × (1 − 34.5/319)
  • = −7.539 × (1 − 0.1081)
  • = −7.539 × 0.8919 = −672.4 kJ/mol.

Born-Landé.

  • U = −138935 × 1.7476 × 1 × 1 / 319 × (1 − 1/9)
  • = −761.3 × 0.8889 = −676.8 kJ/mol.

Born-Mayer.

  • U = −138935 × 1.7476 / 319 × (1 − 30/319)
  • = −761.3 × 0.9060 = −689.7 kJ/mol.

Comparison with Born-Haber experimental.

  • Experimental U(KCl) = −717 kJ/mol (Born-Haber cycle).
  • Kapustinskii: 6.2% low. Born-Landé: 5.6% low. Born-Mayer: 3.8% low. Hard-sphere: 6.2% high (−762).
  • Take-away: Born-Mayer is the most accurate of the four classical models for Group I halides; Kapustinskii is remarkable given how little input it needs.

Who Should Use the Lattice Energy Calculator?

1
Compute U for Group I/II halides and oxides; compare to Born-Haber cycle values; demonstrate why high-charge / small-ion compounds (MgO, Al₂O₃) have extreme melting points and hardness.
2
Higher U → higher melting point and Mohs hardness. Use the calculator to rank candidate ionic compounds for refractory applications (MgO 2852 °C, ZrO₂ 2715 °C) before fabrication.
3
Solubility ∝ |ΔH_solvation| − |U|. Use U from this calculator with hydration enthalpies (Latimer) to predict whether a salt is water-soluble. (Why MgSO₄ is freely soluble but BaSO₄ is not — the Ba²⁺ hydration enthalpy cannot overcome U(BaSO₄) = 2374 kJ/mol.)
4
U drives mineral phase relations — corundum (Al₂O₃) is stable at higher T than simpler oxides because of its enormous |U| ≈ 15,916 kJ/mol. Compute U for proposed mineral compositions when modeling magma crystallization.
5
Compare classical U values with experimental Born-Haber values to teach the role of Madelung geometry, Born exponent, and the breakdown of pure-ionic models for covalently-influenced compounds (AgI, CuI, CdS).
6
When U is known (Born-Haber) and ions are known, the calculator inverts to give the Madelung constant — letting you discriminate between candidate structures (rock salt vs CsCl vs zincblende, all with similar r but different M).
7
Compounds with very high U are kinetically and thermodynamically inert; very low U are reactive (Cs⁺ salts, large polyatomic anions). Use U to rank candidate materials for high-temperature batteries, ionic-liquid precursors, and stable storage forms.

Technical Reference

Sign Convention. By IUPAC convention, lattice energy U is the energy of the process M⁺(g) + X⁻(g) → MX(s) and is therefore NEGATIVE (energy released when gaseous ions form the crystal). Many older texts and supplier datasheets report |U| as a positive number labeled "lattice energy" or "lattice enthalpy" — typically referring to the reverse dissociation process MX(s) → M⁺(g) + X⁻(g). When comparing values from different sources, always check the sign convention. The calculator follows IUPAC (negative U) but reports |U| in the breakdown for convenience.

Constants Used. The Coulomb prefactor for Born-Landé / Born-Mayer / hard-sphere is N_A · e² / (4πε₀) = 138935 kJ·pm/mol. Equivalently 1389.35 kJ·Å/mol, or 14.4 eV·Å per ion pair. The Kapustinskii prefactor is 1202.5 kJ·pm/mol, which equals (138935 × 0.88 × ⟨M⟩ / ν_ref) — the constant 0.88 absorbs the (1 − 1/n_avg) factor and ⟨M⟩/ν_ref absorbs the structure-averaged Madelung. The Kapustinskii (1 − 34.5/r) correction is the Goldschmidt-tolerance-adjusted equivalent of the Born-Landé (1 − 1/n).

Madelung Constant — Definition. M = Σ_ij ±(z_i · z_j) · r₀/r_ij summed over all ion pairs in the lattice (i ≠ j), where r₀ is the nearest-neighbor distance. M is dimensionless and depends only on the geometry of the lattice. Calculation is done by direct summation (Evjen method) or Ewald summation for ionic-conductor work. Tabulated values are accurate to 5+ decimal places: NaCl 1.74756, CsCl 1.76267, ZnS 1.63806 (cubic), CaF₂ 2.51939. The original Madelung paper (1918) computed NaCl by hand to 1.74; modern computer values are within 0.001%.

Born Exponent — Origin. The Born repulsion potential is V_rep ∝ B/r^n. At equilibrium r₀, the attractive (Coulomb, ∝ 1/r) and repulsive (∝ 1/r^n) forces balance. Differentiation of the total energy with respect to r and setting to zero at r = r₀ gives the (1 − 1/n) factor in Born-Landé. Born exponents are determined experimentally from compressibility measurements: more easily compressed crystals have lower n (n = 5 for LiF) and stiffer crystals have higher n (n = 12 for CsI). Pauling tabulated noble-gas-config values that have been reproduced in every inorganic textbook since.

Born-Mayer ρ — Origin. Born & Mayer (1932) replaced the power-law repulsion with an exponential V_rep ∝ B · exp(−r/ρ), which is more physical for closed-shell ion overlap. ρ is the e-folding length of the repulsive potential (~30 pm = 0.30 Å for typical alkali halides). The Born-Mayer correction (1 − ρ/r) is the equivalent of (1 − 1/n) at the equilibrium distance. ρ values for individual ion pairs are tabulated in Pauling (1960) and Mayer-Mayer (1933); 30 pm is a reasonable default within ±10% for most common ionic compounds.

Beyond Classical Models. For high-precision lattice energies, modern approaches use periodic DFT (typically B3LYP, PBE0, or HSE06 with dispersion corrections) or many-body MP2/CCSD(T) embedded in a frozen lattice. Quantum-mechanical results agree with Born-Haber experimental U to within 1-2% for simple binary salts and 3-5% for complex oxides. The classical models in this calculator are useful for predictive screening and pedagogy; they are NOT a substitute for ab-initio calculation in research-grade work where 20-50 kJ/mol matters.

Polarization and Dispersion Corrections. The classical formulas treat ions as rigid charged spheres. Real ions polarize each other (especially large soft anions: I⁻, Br⁻, S²⁻ → covalent character) and exhibit dispersion (van der Waals) attraction. Polarization corrections per Fajans rules are largest for high-charge cations with small radii (Be²⁺, Al³⁺) and large polarizable anions (I⁻ ≫ F⁻). For AgI vs NaCl with the same charges and similar r₀, classical U overestimates AgI |U| by ~15% because Ag-I is significantly covalent. Dispersion adds ~5-15 kJ/mol — small relative to typical |U| of 600-3000 kJ/mol but meaningful for precise Born-Haber comparisons.

Born-Haber Cycle — Experimental U. The Born-Haber cycle constructs U from a sum of measurable steps: M(s) → M(g) (sublimation), M(g) → M⁺(g) + e⁻ (ionization energy), ½X₂(g) → X(g) (atomization), X(g) + e⁻ → X⁻(g) (electron affinity), and the formation enthalpy ΔH_f° of the salt. The cycle gives U accurate to ±1-2 kJ/mol for most binary salts. When Born-Haber and classical U disagree by more than 5%, it usually indicates significant covalent character, polarization, or the wrong crystal structure assumption.

Conclusion

Lattice energy is the master quantity for ionic-solid thermochemistry — once you know U, you know melting point, hardness, solubility limits, and water-of-hydration thermochemistry to within ±20%. The four classical models in this calculator span the full range of available approximations: Kapustinskii for general use without structural data; Born-Landé for textbook Born-exponent problems; Born-Mayer for tightest agreement with Born-Haber; hard sphere for the upper-bound check. Run "All" mode to see the four side-by-side and pick the value closest to your reference.

The two pitfalls to remember: (1) Sign conventions vary — IUPAC defines U as negative (energy released on lattice formation); textbook tables often report |U| as a positive number. Check before comparing. (2) Classical models assume pure ionic bonding — they overestimate |U| by 5-20% for compounds with covalent character (AgI, CuI, CdS, the late-transition-metal salts). When a Born-Haber experimental value is available, prefer it; classical formulas are most useful for predictive screening of compounds that have not yet been measured.

Frequently Asked Questions

What is the Lattice Energy Calculator?
It implements the four classical lattice-energy approximations in a single tool: Kapustinskii (no Madelung needed, uses stoichiometry ν), Born-Landé (Madelung M and Born exponent n), Born-Mayer (Madelung M and repulsion length ρ ≈ 30 pm), and hard sphere (pure Coulomb, upper bound). Built-in Madelung presets for 9 common structures (rock salt, CsCl, zincblende, wurtzite, fluorite, rutile, etc.) and Born-exponent presets for the 5 noble-gas configurations. Input charges Z₊ and |Z₋| with inter-ionic distance r₀ in picometers; outputs U in kJ/mol, kcal/mol, and eV per ion pair.

Pro Tip: Pair this with our Molarity Calculator for solution chemistry.

What is the Kapustinskii equation?
U = −1202.5 · ν · Z₊ · |Z₋| / r · (1 − 34.5/r) in kJ/mol with r in pm. Kapustinskii (1956) noted that the ratio of the Madelung constant to the number of ions in the formula unit is approximately the same for all common ionic structures (~0.874 for rock salt, CsCl, fluorite ÷ ν), so multiplying by ν instead of M gives a structure-independent estimate within ~5%. Strength: works for any salt, even when the structure is unknown. Weakness: ~5% systematic error for non-rock-salt structures (zincblende, wurtzite — Madelung lower than rock salt).
What is the Born-Landé equation?
U = −(N_A · M · |Z₊| · |Z₋| · e²) / (4πε₀ · r₀) · (1 − 1/n). Numerically U (kJ/mol) = −138935 · M · Z₊ · |Z₋| / r · (1 − 1/n) with r in pm. M is the Madelung constant (geometric, depending on crystal structure) and n is the Born exponent (5-12 by noble-gas configuration). The (1 − 1/n) term accounts for the short-range repulsion at the equilibrium distance. Born-Landé (1918) is the textbook standard and matches Born-Haber experimental values for Group I/II halides within 5%.
What is the Born-Mayer equation?
U = −138935 · M · |Z₊| · |Z₋| / r · (1 − ρ/r), where ρ is a tabulated repulsion length (typically 30 pm = 0.30 Å for alkali halides). Born & Mayer (1932) replaced the power-law repulsion of Born-Landé with an exponential, giving (1 − ρ/r) at equilibrium instead of (1 − 1/n). Born-Mayer is typically 1-3% closer to Born-Haber experimental U than Born-Landé. Default ρ = 30 pm works for most ionic crystals; the alternative Pauling value 34.5 pm gives slightly larger |U|.
What is the Madelung constant?
The dimensionless geometric factor that captures how all the ions in the lattice contribute to the Coulomb energy at a reference site. Defined as M = Σ ±(z_i · z_j) · r₀/r_ij summed over all ion pairs (excluding the self-term). Values: rock salt 1.7476, CsCl 1.7627, zincblende 1.6381, wurtzite 1.6413, fluorite 2.5194, rutile 2.408, perovskite 2.474, corundum 4.172. Madelung constants are not added but tabulated by structure type — rock salt and CsCl differ by less than 1% despite different geometries because both are close-packed ionic; zincblende is lower because of the tetrahedral coordination.
What is the Born exponent and how do I pick it?
The Born exponent n is the inverse-power exponent in the Born repulsion potential V_rep ∝ B/r^n. It is determined experimentally from compressibility measurements and tabulated by the noble-gas electronic configuration of the ion: He config (Li⁺, Be²⁺, H⁻) n = 5; Ne (Na⁺, Mg²⁺, F⁻, O²⁻) n = 7; Ar (K⁺, Ca²⁺, Cl⁻, S²⁻) n = 9; Kr (Rb⁺, Sr²⁺, Br⁻) n = 10; Xe (Cs⁺, Ba²⁺, I⁻) n = 12. For mixed crystals, use the average of the cation and anion exponents. NaCl: (Ne 7 + Ar 9)/2 = 8. CsI: (Xe 12 + Xe 12)/2 = 12.
Why is lattice energy negative? Why do textbooks report it as positive?
Sign convention. By IUPAC convention, U is the energy CHANGE for the process M⁺(g) + X⁻(g) → MX(s) — energy is released, so U < 0. Many older textbooks and supplier datasheets report the magnitude |U| as a positive "lattice energy" referring to the reverse dissociation MX(s) → M⁺(g) + X⁻(g). Both refer to the same physical quantity; just check the sign convention before comparing numbers. NaCl: IUPAC U = −787 kJ/mol; textbook |U| = +787 kJ/mol.
What is the lattice energy of NaCl?
−787 kJ/mol (Born-Haber experimental). Math by Born-Mayer: r₀ = 102 + 181 = 283 pm; M = 1.7476 (rock salt); ρ = 30 pm: U = −138935 × 1.7476 / 283 × (1 − 30/283) = −858 × 0.894 = −767 kJ/mol — within 3% of experimental. Born-Landé with n = 8 gives −750 kJ/mol (5% low). Kapustinskii gives −746 (5% low). Hard-sphere gives −858 (10% high — overestimate because no repulsion correction).
What is the lattice energy of MgO?
−3795 kJ/mol (Born-Haber experimental). The 4.8× larger magnitude vs NaCl despite similar coordination (both rock salt) is driven by Z₊·|Z₋| = 2×2 = 4 (vs 1×1 for NaCl) plus shorter r₀ (212 pm Mg-O vs 283 pm Na-Cl). This enormous lattice energy explains MgO's extreme melting point (2852 °C vs 801 °C for NaCl) and its use as a high-T refractory ceramic. Born-Mayer prediction (−3933) is 3.6% high — the small overestimate reflects partial covalent character in the Mg-O bond.
Which method should I use?
Kapustinskii when you don't know the crystal structure or have no Madelung table — surprisingly accurate (~5% off) for any salt. Born-Landé for textbook problems where Madelung and Born exponent are given; standard inorganic-chemistry curriculum. Born-Mayer for tightest agreement with Born-Haber experimental values (typically 1-3% closer than Born-Landé). Hard sphere as the upper-bound check — the difference between hard-sphere and any of the corrected methods (~10-15%) is the magnitude of the Born repulsion at r₀. All mode to compare the four side-by-side; the spread tells you how robust the answer is.
Why does my classical lattice energy disagree with the Born-Haber value?
Several common reasons: (1) Covalent character — AgI, CuI, CdS, ZnS have significant covalency; classical pure-ionic models overestimate |U| by 5-20%. (2) Wrong Madelung constant — using rock salt when the structure is actually zincblende (M differs by ~6%). (3) Wrong Born exponent — using n = 9 for KCl when literature gives n = 9.5 (mixed Ar/Kr); ~1% effect. (4) r₀ from sum of Shannon radii vs measured — typically within ±5 pm but can shift U by 2-3%. (5) Polarization and dispersion corrections not included in classical models — typically 5-15 kJ/mol, important for precise comparison. (6) Hydrate, double-salt, or non-stoichiometric phase with different Madelung. When Born-Haber experimental data exists, prefer it over classical estimates.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE chemistry team built this calculator to handle every classical lattice-energy approximation in a single tool. <strong>Lattice energy U</strong> is the energy released when gaseous ions condense into the crystal lattice — it determines melting point, hardness, solubility, and water-of-hydration thermochemistry for every ionic compound. The four built-in methods cover the full literature: <strong>(1) Kapustinskii</strong> — uses stoichiometry ν instead of an explicit Madelung constant, ideal when the structure is unknown; <strong>(2) Born-Landé</strong> — uses Madelung M and Born exponent n (5-12 by noble-gas configuration), the textbook standard; <strong>(3) Born-Mayer</strong> — replaces (1−1/n) with (1−ρ/r) for tighter agreement with experiment, ρ ≈ 30 pm; <strong>(4) Hard sphere</strong> — pure Coulomb without repulsion, gives the upper bound. <strong>All-mode</strong> runs the four side-by-side for instant cross-checking. Built-in Madelung presets for 9 common structures (rock salt, CsCl, zincblende, wurtzite, fluorite, rutile, antifluorite, perovskite). Inputs accept charges Z₊ and |Z₋| with Shannon ionic radii r₀ in picometers; outputs in kJ/mol, kcal/mol, and eV per ion pair.

Kapustinskii (1956), Born-Landé (1918), Born-Mayer (1932)Standard solid-state and inorganic chemistry referencesCRC Handbook of Chemistry and Physics; Shannon ionic radii (1976)

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Lattice energy U is reported as NEGATIVE (energy released when gaseous ions form the crystal); many texts use positive |U| for the reverse dissociation — check sign conventions when comparing. Classical models (Kapustinskii, Born-Landé, Born-Mayer, hard sphere) assume purely ionic bonding and overestimate |U| by 5-20% for compounds with covalent character (AgI, CuI, CdS). For research-grade values, prefer Born-Haber experimental U or periodic-DFT calculations. Madelung constants depend on crystal structure (NaCl 1.7476 vs CsCl 1.7627 vs zincblende 1.6381); Born exponents (5-12) come from noble-gas configurations and compressibility measurements. References: A.F. Kapustinskii (1956) Q. Rev. Chem. Soc. 10:283; M. Born &amp; A. Landé (1918); M. Born &amp; J.E. Mayer (1932); CRC Handbook; Shannon (1976) ionic radii.