Classification of Binary Hydrides

The ionic/covalent/metallic classification of hydrides is not a museum-piece taxonomy; it is the working vocabulary of several live technologies. Hydrogen storage for fuel-cell vehicles and stationary energy systems depends almost entirely on interstitial metal hydrides — alloys like LaNi₅ and FeTi absorb and release hydrogen reversibly near room temperature by exactly the interstitial-hole mechanism described here, and the search for better storage materials is largely a search for metals and alloys with the right combination of interstitial site size, hydrogen binding enthalpy, and reversibility. Complex hydride reducing agents used throughout organic and inorganic synthesis — lithium aluminium hydride (LiAlH₄) and sodium borohydride (NaBH₄) — are best understood as ionic salts of a covalent complex anion: Li⁺[AlH₄]⁻ and Na⁺[BH₄]⁻, where the outer cation-anion bonding is ionic (hence their ionic-solid-like handling properties and reactivity toward protic solvents) while the internal Al–H or B–H bonds are covalent, a hybrid case that only makes sense once the pure ionic and pure covalent limits are both understood. Industrial hydrogenation catalysis relies on the ability of Pd, Pt, Ni, and related metals to dissolve hydrogen interstitially and deliver it, atom by atom, to unsaturated substrates at a catalyst surface — the same metallic-hydride mechanism that makes palladium membranes useful for ultra-high-purity hydrogen separation (H₂ dissociates, dissolves as H atoms in the Pd lattice, diffuses through, and recombines on the far side, excluding essentially every other gas). In planetary science, the extreme pressures inside gas-giant interiors are believed to convert molecular H₂ into a metallic hydrogen phase — an extension of the metallic-hydride bonding logic to the pure element itself — implicated in the dynamo-generated magnetic fields of Jupiter and Saturn. And in materials chemistry, saline hydrides such as CaH₂ remain a standard laboratory desiccant and drying agent precisely because of the reaction $\mathrm{CaH_2 + 2H_2O \to Ca(OH)_2 + 2H_2}$ analyzed above — a direct, everyday consequence of hydrogen's identity as H⁻ in the ionic-hydride limit.

Ask the tutor: Why does aluminium, despite having a fairly high electronegativity for a metal (χ ≈ 1.61), form a polymeric, borderline-covalent hydride (AlH₃) rather than a clean ionic Al³⁺(H⁻)₃ lattice like calcium's?

Hydrogen has one proton and one electron. To complete a noble-gas-like duet (He configuration, 1s²) it needs one more electron; to reach the "no electrons" limit of a bare proton it must lose the one it has. Both extremes are accessible because hydrogen's ionization energy (1312 kJ mol⁻¹) is comparable to that of many nonmetals, while its electron affinity (−73 kJ mol⁻¹, forming H⁻) is comparable to a halogen's, though smaller. This dual identity — cation-former and anion-former — is why hydrogen has no fixed vertical "home" in the periodic table and is why the classification of its compounds cannot rely on simple valence-shell counting the way, say, halide or oxide classification can. Instead the deciding factor is always the relative electronegativity of hydrogen's partner. Picture the periodic table with hydrogen's electronegativity, χ(H) = 2.20, as a horizontal reference line. Elements whose electronegativity sits far below this line (χ < 1.5, the alkali and heavier alkaline-earth metals) are so much more willing to lose electrons than hydrogen that the bonding pair collapses fully onto hydrogen, generating H⁻ and M⁺ (or M²⁺) — an ionic hydride. Elements whose electronegativity sits close to or above hydrogen's (χ ≳ 2.0, essentially the whole p-block plus H itself in things like B–H and Si–H) share the bonding electrons in a two-center two-electron covalent bond, producing discrete molecules — a covalent (molecular) hydride. Elements in between, structurally speaking the transition metals with χ around 1.2–2.2 but with partially filled d orbitals available for metal–metal and metal–hydrogen bonding, absorb hydrogen atoms into the interstices of their existing close-packed or body-centered lattice without forming discrete H–M bonds pointing in fixed directions; the H 1s electron simply joins the metal's conduction band. This is the metallic (interstitial) hydride. The reason the map has exactly this shape, rather than some other split, comes down to competing energetics: lattice (Madelung) stabilization for the ionic route, bond-pair covalent stabilization for the molecular route, and band-structure/interstitial-site stabilization for the metallic route. Each mechanism wins in a different part of the periodic table because it depends on different atomic properties — ionization energy and lattice geometry for ionic hydrides, orbital overlap and hybridization for covalent hydrides, d-band availability and atomic radius ratio for metallic hydrides.

Notice how the map is not a strict left-to-right function of the periodic table alone; it is a function of electronegativity, which happens to correlate with position but bends around anomalies (H itself, the metalloid diagonal, the lanthanides). Beryllium (χ = 1.57) and magnesium (χ = 1.31) sit right at the edge of the ionic block predicted by simple group membership, and both in fact form hydrides with substantial covalent, polymeric character (BeH₂, MgH₂) rather than clean rock-salt ionic lattices — a boundary case explored below. A second organizing picture is the stoichiometric ratio test. Because H⁻ is a simple monatomic anion, ionic hydrides obey ordinary ionic-formula rules: MH for Group 1 (charge-balancing M⁺ + H⁻), MH₂ for Group 2 (M²⁺ + 2H⁻). Covalent hydrides obey the 8 − N rule familiar from p-block valence: the number of H atoms bonded to a p-block element E equals (8 − N) where N is the group number in the old (1–18, mapped to old 1–8 for p-block) convention, giving CH₄ (N=4, 8−4=4), NH₃ (N=5, 8−5=3), H₂O (N=6, 8−6=2), HF (N=7, 8−7=1). Metallic hydrides obey neither rule cleanly: composition is set by how many interstitial holes get filled, which depends on temperature and hydrogen pressure, giving formulas like PdH₀.₆₀₋₀.₇₀ that are not small-integer ratios at all.

The classification can be captured in three quantitative relationships, each isolating the dominant energetic term for one hydride family.

1. The electronegativity-difference criterion.

where: Δχ is negative and large in magnitude for strongly electropositive E (ionic hydrides, H⁻ forms), close to zero or positive but modest for p-block E (covalent hydrides, shared pair), and Δχ is not the deciding variable at all for d-block E (band structure and radius ratio dominate instead — metallic hydrides). Reading: this is a diagnostic, not a rigorous bonding calculation — real hydrides show a continuum of ionic/covalent character, best estimated by the difference-squared expression below, but the sign and rough size of Δχ correctly sorts the overwhelming majority of the periodic table into the three families.

2. Percentage ionic character (Pauling's empirical formula).

where: Δχ is the electronegativity difference between E and H, and the formula is Pauling's original empirical estimate connecting bond dipole to electronegativity difference (it is a rule of thumb calibrated against dipole moment data, not a first-principles quantum-mechanical result). Reading: at Δχ ≈ 0 (as for C–H, χC = 2.55, giving Δχ = 0.35) the bond is essentially covalent (~3% ionic); at Δχ ≈ 1.5–1.8 (Na–H region) ionic character exceeds 65–70%, crossing into the regime where the solid is best described as a rock-salt lattice of discrete ions.

3. Lattice-energy criterion for the ionic route (Born–Landé framework).

where: $N_A$ is Avogadro's number, $M$ the Madelung constant for the structure type, $z_+, z_-$ the ionic charges, $e$ the electron charge, $r_0$ the equilibrium interionic distance, $\varepsilon_0$ the vacuum permittivity, and $n$ the Born exponent (compressibility factor). Reading: ionic hydride formation is only favorable when the lattice energy released by packing M⁺ and H⁻ ions together outweighs the energetic cost of forming H⁻ from H (endothermic by roughly 73 kJ mol⁻¹ electron affinity release, offset by the cost of ionizing M). Small, highly charged cations (Li⁺, Mg²⁺) generate large lattice energies and favor the ionic route even though they are not the most electropositive metals on a raw electronegativity scale — this is why LiH and the alkaline-earth hydrides Ca/Sr/BaH₂ are cleanly ionic while BeH₂, with its very small, highly polarizing Be²⁺, tips over into covalent, polymeric bonding instead (the Fajans'-rules effect).

Example 1 (foundational) — Classify CaH₂, PdH₀.₆, and PH₃ using electronegativity and structural criteria. Calcium: χ(Ca) = 1.00. Δχ = χ(Ca) − χ(H) = 1.00 − 2.20 = −1.20, so |Δχ| = 1.20, a large value dominated by Ca's low electronegativity. Applying Pauling's ionic-character formula,

This is a genuinely rough estimate (Pauling's formula is calibrated for diatomics, not extended solids), but combined with the structural fact that CaH₂ crystallizes in a distorted rock-salt-like (actually PbCl₂-type/orthorhombic) lattice made of discrete Ca²⁺ and H⁻ ions, and combined with the huge lattice energy expected for a 2+/1− ion pair (U ≈ −2400 kJ mol⁻¹, comparable in magnitude to CaF₂), the classification is unambiguous: CaH₂ is an ionic (saline) hydride. Diagnostic confirmation: CaH₂ reacts vigorously with water, $\mathrm{CaH_2 + 2H_2O \to Ca(OH)_2 + 2H_2}$, releasing H₂ from the H⁻ (a standard drying-agent reaction). Palladium: χ(Pd) = 2.20 — numerically identical to hydrogen's own electronegativity, which immediately signals that electronegativity difference is not the operative variable here (Δχ = 0.00 would, if you blindly applied the covalent-hydride formula, wrongly predict a perfectly nonpolar molecular hydride "PdH"). Instead the correct diagnostic is structural: Pd retains its face-centered cubic metal lattice, hydrogen atoms occupy octahedral holes, the material remains lustrous and electrically conducting as a solid, and the H:Pd ratio is a continuously variable, pressure-dependent quantity (commonly x ≈ 0.6–0.7 in "PdH$_x$" at 1 atm H₂, rising toward x ≈ 1 at higher pressure). This is the signature of a metallic/interstitial hydride — the electronegativity criterion simply does not apply to the d-block, where partly filled d-bands and interstitial site geometry, not Δχ, control hydrogen uptake. Phosphorus: χ(P) = 2.19, essentially identical to χ(H) = 2.20, giving Δχ ≈ −0.01 — an almost perfectly nonpolar bond, even more so than C–H. Structurally PH₃ is a discrete pyramidal molecule (C₃ᵥ symmetry, analogous to but with a smaller bond angle than NH₃, ~93.5° vs. 107.8°, because phosphorus's larger size and greater p-character in the bonding orbitals reduces lone-pair/bond-pair repulsion effects relative to N), obeying the 8 − N rule with N = 15 (old group Va) giving $8-5=3$ P–H bonds. It is a gas (b.p. −87.7 °C), non-conducting, and hydrolytically far more stable than the ionic hydrides — diagnostic confirmation of a covalent (molecular) hydride.

Example 2 (applied) — Estimate the enthalpy of formation of KH from a Born–Haber cycle and compare the lattice energy contribution to that of NaH. Using literature-typical values: ΔH_sub(K) = +89 kJ mol⁻¹, IE₁(K) = +419 kJ mol⁻¹, ½D(H–H) = +218 kJ mol⁻¹, EA(H) = −73 kJ mol⁻¹, and U(KH) ≈ −690 kJ mol⁻¹ (smaller in magnitude than NaH's −782 kJ mol⁻¹ because K⁺ is larger than Na⁺, r₀ increases, and lattice energy scales as 1/r₀).

This is close to the NaH result (−34 kJ mol⁻¹ from the earlier cycle) despite K having a substantially lower ionization energy than Na (419 vs. 496 kJ mol⁻¹) — the two effects (lower IE, favoring KH; smaller lattice energy from the larger K⁺, disfavoring KH) partly cancel. This is a genuinely useful check: it shows that ionic hydride stability down Group 1 is not simply "more ionic = more stable"; it is a balance of a shrinking ionization penalty and a shrinking lattice-energy reward, and the two nearly track together, which is why all alkali-metal hydrides (LiH through CsH) are comparably (modestly) exothermic to form and comparably reactive toward water, rather than showing a strong Li→Cs stability trend the way, say, fluoride lattice energies do. Limiting case: as the cation radius r₀ → ∞ (imagine a hypothetical superheavy alkali metal), the lattice energy term U → 0, and the sum $\Delta H_{\text{sub}} + IE_1 + \tfrac12 D(\text{H-H}) + EA(\text{H})$ (≈ +740 kJ mol⁻¹ using Na's sublimation/ionization values as a stand-in) would dominate and become strongly positive — the ionic hydride route would fail entirely, and hydrogen would either not react with such a metal or would have to find another mechanism (e.g. metallic dissolution) to be accommodated. This limiting case is precisely why lattice energy, not electronegativity difference alone, is the deeper reason ionic hydrides are confined to small, tightly-packing cations.

Example 3 (exam/competition level) — A student is given an unlabelled binary hydride, MH_n, that: (a) is a white crystalline solid; (b) does not conduct electricity as a solid but conducts as a melt; (c) reacts with D₂O to release HD gas (not D₂ or H₂ exclusively); (d) has an empirical formula corresponding to M:H = 1:1. Identify the class of hydride and the diagnostic significance of each observation, then predict which specific hydride this most likely is if M is found (by mass spectrometry of the melt) to have atomic mass close to 40 and charge 2+ in the melt — reconcile this against the 1:1 stoichiometry. Observation (a), a white crystalline solid with no molecular volatility, immediately rules out a covalent/molecular hydride (which would typically be a gas, liquid, or low-melting molecular solid) and is consistent with either ionic or metallic; observation (b), conducting only when molten, is the classic ionic-solid signature (ions are locked in a rigid lattice in the solid but become mobile charge carriers on melting) — this specifically rules out metallic hydrides, which conduct in both the solid and molten states because delocalized band electrons don't require melting to become mobile. So the compound is confirmed ionic. Observation (c) is the diagnostic ionic-hydride water(here heavy-water) test: the H⁻ ion is itself a strong reducing agent and Brønsted base, so it reacts with D₂O by abstracting a deuteron,

releasing the mixed isotopologue HD rather than pure H₂ or D₂ — direct proof that the hydrogen in the solid was present as H⁻ (from the solid MH_n) reacting with the D of D₂O, not simply exchanging with solvent H atoms. A covalent hydride's H, by contrast, would typically not show this clean 1:1 HD signature in a simple ionic-mechanism sense (though some covalent E–H bonds do exchange by different mechanisms; the clean stoichiometric HD release specifically diagnoses an H⁻ nucleophile/base reacting via deuteron abstraction). Now reconcile mass and charge with stoichiometry: if M carries a 2+ charge in the melt (confirmed by mass spectrometry) but the empirical formula is M:H = 1:1, charge balance seems to fail for a simple ionic salt M²⁺(H⁻)₂ (expected M:H = 1:2). The resolution is that the empirical formula 1:1 with M²⁺ present is inconsistent with a simple binary hydride MH — this is exactly the pattern seen in complex or non-stoichiometric ionic hydrides, and points to the student having actually measured, for instance, a partially decomposed or oxide-contaminated sample, or (more likely intended here) that the "1:1" analytical result was a units/typo trap and the real formula, consistent with M²⁺ and H⁻, must be MH₂. With atomic mass ≈ 40 and charge 2+, M is calcium (40.08 u, Ca²⁺), and the compound is CaH₂, matching every other observation: white crystalline ionic solid, non-conducting until molten, HD release with D₂O via H⁻ + D₂O → HD + OD⁻, and (correctly) M:H = 1:2, not 1:1 — the exercise's "trap" is designed to force the reconciliation step, showing that charge-balance stoichiometry is a harder constraint than a possibly miscounted empirical-formula ratio.

Linus Pauling was trained as a structural chemist and crystallographer at Caltech, and his electronegativity scale grew directly out of his X-ray and electron-diffraction work on bond lengths and his thermochemical analysis of bond energies. He was awarded the Nobel Prize in Chemistry in 1954 "for his research into the nature of the chemical bond," and later the Nobel Peace Prize in 1962 — making him, to date, the only person to receive two unshared Nobel Prizes. His electronegativity values (still called the Pauling scale) remain the default reference numbers used throughout inorganic chemistry, including every Δχ figure quoted in this article.