Inorganic Chemistry: The Rest of the Periodic Table

A ruby is aluminium oxide with a sprinkling of chromium. An emerald is a beryllium aluminium silicate with a sprinkling of chromium. Same impurity atom, same ion (Cr³⁺), yet one stone is deep red and the other deep green. It is not a trick of the light or the cut. It is the surroundings: six oxygen atoms packed round each chromium, pressed a little more tightly in the ruby than in the emerald.

That one fact opens most of inorganic chemistry. Organic chemistry covers carbon's compounds, which is a huge neighbourhood. Inorganic covers everything else: the other 90-odd elements and how they combine. Metals sit at the centre of it, wrapped in a shell of neighbours. Some end up in a crystal, some in a catalyst bed the size of a house, and some at the heart of a protein in your blood. The same few ideas sort all of them.

Complexes: a metal and its ligands

A transition metal ion rarely stands alone. It collects molecules or ions called ligands that each donate a pair of electrons to it, and the result is a coordination complex. The number of donor atoms is the coordination number, and six is most common, arranged at the corners of an octahedron. Square planar (four) and tetrahedral (four) are the other common shapes.

Alfred Werner, at Zürich, worked out the idea in the 1890s without any way of seeing a molecule, by counting. Cobalt(III) chloride combined with ammonia in several different, differently coloured solids. When he added silver nitrate to a solution, silver chloride precipitated, but only from the chloride ions that were free. In one compound all three chlorides came out, in another only two, in another only one. Werner's explanation: ammonia and some chlorides are bound to the cobalt in an inner sphere, six in all, and the rest float free outside. He received the 1913 Nobel Prize in Chemistry. Try to predict it before looking.

Many complexes come in mirror-image pairs, and Werner showed in the years before the First World War that this is true of purely inorganic ones too. Complexes also matter for health: cisplatin, a square-planar platinum(II) complex found in the 1960s when Barnett Rosenberg noticed that platinum electrodes stopped bacteria dividing, became a widely used cancer drug. That is a description, not medical advice.

Crystal field theory: why complexes have colour and magnetism

A free metal ion has five d orbitals of equal energy. Surround it with six ligands at the corners of an octahedron and the electrons in the d orbitals are repelled by them. Two of the five orbitals point straight at the ligands and rise in energy (the e_g pair); three point between them and sink (the t_2g trio). Hans Bethe laid the theory down in 1929. The gap between the sets is called Δ_o, and it is small, comparable to the energy of visible light.

This gap does two things at once. Colour: an electron can hop from t_2g to e_g by absorbing a photon of exactly energy Δ_o, taking that colour out of white light. Magnetism: electrons would rather sit alone in separate orbitals with parallel spins, but if Δ_o is large they will pair up in the lower set instead. So whether the metal ends up with many unpaired electrons (high spin) or few (low spin) depends on a contest:

Ligands have a pecking order, the spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO, from weak field to strong. Iron(II) is d⁶: with water ligands (weak) it is high spin with four unpaired electrons, with cyanide (strong) all six pair up and it is low spin and non-magnetic. Set Δ_o and P yourself and watch the electrons rearrange.

The colour follows from the gap. For chromium(III), a d³ ion, the lowest-energy absorption is exactly Δ_o, so the arithmetic is simple: wavelength = 1 ÷ wavenumber. Swapping the ligands in a Cr³⁺ complex moves the gap and so the colour. The same logic explains the ruby and emerald: in corundum the oxygens press a little closer to the chromium, making Δ_o larger and shifting the absorbed light so the stone looks red; in beryl the field is slightly weaker and it looks green.

Symmetry and point groups

Every molecule has a set of moves that leave it looking unchanged: rotate it by a certain angle about an axis, reflect it across a plane, invert it through its centre. Together with "do nothing" these moves obey the rules of a group: do two in a row and you get another one, each has an undo, and the order of combining follows the associative law. This is exactly the structure of Abstract Algebra (34/73), and chemists give the groups names such as C_2v (water) and T_d (methane).

Counting the moves has consequences you can predict before calculating anything. A molecule can only have a permanent dipole if no symmetry move swaps the ends. A molecule can only be handed (chiral) if it has no mirror planes or inversion centre. And the orbitals, the vibrations and which spectral lines are allowed all sort themselves by how they behave under those moves. Water has four operations (identity, one two-fold rotation and two mirror planes), a group of order 4 with the same structure as the Klein four-group. Ammonia has six, the same structure as the symmetric group S₃ (all shuffles of three things). Methane has 24, the same group as all the ways to shuffle four things (S₄). An octahedral complex has 48.

Solids: atoms stacked in a repeating cell

A crystal is a pattern repeating in three dimensions, and the repeat is its unit cell. Knowing the cell edge a and what sits in it is enough to compute things you can weigh. The three simplest packings of identical spheres are simple cubic (each atom touches 6 others, 52.4% of space filled), body-centred cubic (8 neighbours, 68.0%) and face-centred cubic (12 neighbours, 74.0%, the densest a stack of equal spheres can get). Copper, aluminium and gold are face-centred; iron at room temperature and tungsten are body-centred; table salt is an interleaved lattice of sodium and chloride ions; diamond is carbon in a more open arrangement.

Worked: copper is face-centred cubic with a = 361.5 pm and four atoms per cell. 4 × 63.546 g/mol ÷ (6.022 × 10²³ × (3.615 × 10⁻⁸ cm)³) = 8.96 g/cm³, which is the measured density of copper. The numbers on paper and on the balance agree, which is how X-ray diffraction results are checked. Crystals are also where the energy-storage story lives: the cathode of the lithium-ion battery is a layered oxide of cobalt and lithium, work for which John Goodenough, Stanley Whittingham and Akira Yoshino received the 2019 Nobel Prize in Chemistry. And in 2025 Susumu Kitagawa, Richard Robson and Omar Yaghi were recognised for metal–organic frameworks, crystals that are mostly empty space.

Catalysts in industry

Many of the largest chemical processes on Earth are inorganic catalysts doing one job over and over. Fritz Haber showed in the laboratory in 1909 that nitrogen and hydrogen would combine to ammonia over a metal catalyst, and Carl Bosch at BASF scaled it into a plant; both received Nobel prizes (Haber 1918, Bosch 1931). Roughly half of the world's population is fed with the help of nitrogen fertiliser made this way, by one widely cited estimate. Haber's legacy is double-edged: he also directed Germany's gas-warfare programme in the First World War, and scholars still argue about how to weigh the two.

The ammonia reaction is the balance of the previous piece's ideas. It releases heat but lowers entropy, so a low temperature favours the product and a high one favours the reactants (see Physical Chemistry, 35/40). But at low temperature it is far too slow. Iron catalyst plus a few hundred degrees and high pressure is the compromise. A catalyst changes the speed but not the equilibrium. Other pillars:

Process	Catalyst	Makes
Haber–Bosch	Iron, with promoter oxides	Ammonia, for fertiliser
Contact process	Vanadium(V) oxide	Sulfur trioxide, for sulfuric acid
Catalytic converter	Platinum, palladium, rhodium	Cleaner car exhaust
Ziegler–Natta (Nobel 1963)	Titanium chloride with an aluminium alkyl	Polyethylene, polypropylene
Wilkinson's catalyst	A rhodium complex	Selective hydrogenation

Geoffrey Wilkinson and Ernst Otto Fischer shared the 1973 Nobel Prize for the chemistry of organometallic "sandwich" compounds. Most of these catalysts are used in tiny amounts and for a long time, so the metals' cost and supply, and whether they can be recovered, are part of the design.

Bioinorganic chemistry: iron in blood, magnesium in leaves

Life uses metals too. In haemoglobin, each of four protein chains cradles a flat ring called haem with an iron(II) ion at its centre. The iron binds an oxygen molecule in the lungs and lets go in the tissues. The trick, worked out by Max Perutz (Nobel 1962, shared with John Kendrew), is that the four sites help each other: when one binds oxygen the protein shifts shape, and the next binds more easily. Perutz's mechanism has been refined since, but the outcome stands. Plot saturation against oxygen pressure and you get an S-shaped curve, unlike myoglobin, which holds a single site and gives a simple hyperbola. Carbon monoxide binds the same iron far more tightly than oxygen does, which is why a working smoke and CO alarm is worth having.

Chlorophyll uses a ring of nearly the same family with a magnesium ion at the centre. Magnesium here has no d-electrons to play with, so it acts as a stable anchor holding the ring flat while the ring itself absorbs light. Richard Willstätter received the 1915 Nobel Prize for work on plant pigments, chlorophyll above all. Other metals do other jobs: cobalt in vitamin B₁₂, zinc in the enzyme that moves carbon dioxide in and out of blood, copper in the blue blood of octopuses.

What a graduate just sees

• A metal in a compound is a metal plus its surroundings. Change the ligands and you change the colour, magnetism and reactivity.
• Colour is a d-electron hopping across a gap; the photon taken out of white light is the one whose energy matches the gap.
• High or low spin is a contest between the splitting Δ_o and the pairing cost P.
• Counting symmetry operations tells you, before any calculation, whether a molecule can be polar or chiral.
• A crystal is one cell repeated, so its density is Z·M ÷ (N_Aa³).
• Close-packed stacks fill 74% of space and have 12 neighbours.
• A catalyst changes the rate, never the equilibrium, and many are metals in a shell of ligands.
• The same chemistry runs blood, leaves and fertiliser plants: a metal ion in a ring or a lattice, tuned by what surrounds it.

Where it shows up next

• Biochemistry (35/43): metalloenzymes use iron, zinc, copper and cobalt exactly as above; the geometry and the d-count explain what each can do.
• Condensed Matter Physics (34/87): crystals reappear as bands and semiconductors; the lattice here is the stage for the electrons there.
• Materials Science and Manufacturing (34/13): alloys, ceramics and battery electrodes are applied solid-state inorganic chemistry. For the battery side, see Batteries (29/08).
• In the world: fertiliser plants, catalytic converters, pigments and glass, solar cells, fuel cells, MRI contrast agents, cancer drugs, and the question of where scarce metals like cobalt, platinum and rhodium come from and how they are recycled.

If you want to go deeper

• 📘 Textbook. Mark Weller, Tina Overton, Jonathan Rourke and Fraser Armstrong, Inorganic Chemistry (Oxford University Press, 7th edition, 2018), the current edition of the long-running Shriver & Atkins text. Broad, with a good run of descriptive chemistry.
• 📘 Textbook. Gary Miessler, Paul Fischer and Donald Tarr, Inorganic Chemistry (Pearson). A symmetry- and bonding-first approach.
• 📘 Gentler. Peter Atkins, The Periodic Kingdom (1995), a tour of the table as a landscape, and Sam Kean, The Disappearing Spoon (2010), element stories (anecdotes: read for fun, check the rest).
• 🌐 Free course. MIT OpenCourseWare 5.05 Principles of Inorganic Chemistry III (Spring 2005, main-group chemistry with synthesis, structure and bonding), with 5.111SC Principles of Chemical Science as an introduction.