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Imagine a chemist in the early twentieth century holding two salts. Both analyse as exactly CoCl₃·4NH₃. One is green, the other violet. Same elements, same proportions, same molar mass, yet plainly different substances. Explaining pairs like this was one of the puzzles that led Alfred Werner to his theory of coordination compounds, and it earned him the Nobel Prize in Chemistry in 1913. His answer was that the atoms are the same but their arrangement around the metal is not. The two cobalt salts are isomers.
Isomerism in complexes follows the same big idea as isomerism in organic chemistry: same formula, different structure. But the metal centre adds new twists. Ligands can sit inside or outside the coordination sphere, some ligands can bond through more than one atom, and octahedral geometry allows arrangements that a tetrahedral carbon atom never could. This post builds a mental toolkit for spotting and counting these isomers. If complexes are new to you, start with coordination compounds: an introduction.
The two families
Every kind of isomer in a complex falls into one of two families:
| Family | What differs | Bonds broken to interconvert? |
|---|---|---|
| Structural (constitutional) isomers | Which atoms are bonded to the metal | Yes: different connections |
| Stereoisomers | Only the spatial arrangement of the same connections | Yes, but every isomer has the same set of metal–ligand bonds |
A useful analogy is a dinner table. Structural isomerism is about who is invited to the table at all (and who is left standing by the wall). Stereoisomerism is about the seating plan: the same guests, arranged differently.
Structural isomerism
Ionisation isomers
Square brackets in a formula mark the coordination sphere, the ligands actually bonded to the metal. Anything outside the brackets is a counter-ion, held only by ionic attraction. Two complexes are ionisation isomers when an anion swaps places between those two positions:
- [Co(NH₃)₅Br]SO₄: bromide is bonded to cobalt; sulfate is the free counter-ion.
- [Co(NH₃)₅(SO₄)]Br: sulfate is bonded to cobalt; bromide is free.
The difference shows up in simple tests. Add barium chloride solution to the first and a white barium sulfate precipitate forms at once, because free sulfate ions are present. Add silver nitrate to the second and a cream silver bromide precipitate appears. Each salt only “shows” the ion that is outside the brackets.
Hydrate (solvate) isomers
This is the same idea, but with water playing the swapping role. Hydrated chromium(III) chloride, CrCl₃·6H₂O, exists as three distinct solids:
| Formula | Chloride ions bonded to Cr | Free Cl⁻ per formula unit | mol AgCl precipitated per mol |
|---|---|---|---|
| [Cr(H₂O)₆]Cl₃ | 0 | 3 | 3 |
| [Cr(H₂O)₅Cl]Cl₂·H₂O | 1 | 2 | 2 |
| [Cr(H₂O)₄Cl₂]Cl·2H₂O | 2 | 1 | 1 |
They also differ in colour, because swapping a water ligand for chloride changes the d-orbital splitting. Counting the moles of silver chloride that precipitate quickly with silver nitrate is a classic way to tell them apart, and it is exactly the sort of evidence Werner used. (Water that is not bonded to the metal is lattice water; see hydrates and water of crystallisation.)
Linkage isomers
Some ligands have two different atoms that could each donate a lone pair. These are called ambidentate ligands, and they can bond through either end, but only one end at a time:
- Nitrite, NO₂⁻, can bond through nitrogen (nitrito-κN, older name nitro) or through an oxygen (nitrito-κO, older name nitrito).
- Thiocyanate, SCN⁻, can bond through sulfur (thiocyanato-κS) or nitrogen (thiocyanato-κN, often called isothiocyanato).
- Cyanide, CN⁻, almost always bonds through carbon, but bridging and N-bonded examples exist.
So [Co(NH₃)₅(NO₂)]²⁺ exists as an N-bonded and an O-bonded form, with different colours. Think of a two-pin plug that fits a socket either way round: the plug and the socket are identical, but which pin makes contact changes what you get.
A handy rule of thumb from hard–soft acid–base ideas: softer metals tend to prefer the softer sulfur end of thiocyanate, while harder metal ions prefer the nitrogen end.
Coordination isomers
These need a salt in which both the cation and the anion are complexes. The ligands can then be distributed between the two metals in different ways:
- [Co(NH₃)₆][Cr(CN)₆]: ammonia around cobalt, cyanide around chromium.
- [Cr(NH₃)₆][Co(CN)₆]: the ligand sets have swapped metals.
Same overall formula, different complex ions, and so different properties.
Stereoisomerism
Now the same bonds exist in every isomer, and only the geometry differs. Whether stereoisomers are possible at all depends on the shape of the complex, so shape comes first.
Tetrahedral complexes: usually nothing to find
In a tetrahedron, every corner is adjacent to every other corner. With two A ligands and two B ligands (MA₂B₂), there is only one way to arrange them: any two positions you choose are equivalent to any other two. So tetrahedral MA₂B₂ complexes show no cis–trans isomerism. This is the same reason CH₂Cl₂ has only one form. (A tetrahedral complex with four different ligands could in principle be chiral, but such complexes are rarely stable enough in solution to separate.)
Square planar complexes: cis and trans
A square has two kinds of relationship between corners: adjacent (90° apart) and opposite (180° apart). So a square planar MA₂B₂ complex has two isomers:
- cis: the two B ligands are side by side.
- trans: the two B ligands are across from each other.
The famous example is [Pt(NH₃)₂Cl₂] (see platinum). The cis isomer, cisplatin, is a widely used anticancer drug; the trans isomer, transplatin, is far less effective. The geometry matters because cisplatin, after losing its chloride ligands inside cells, binds to two neighbouring sites on DNA, and only the cis arrangement puts the two free positions close enough together to do that.
Octahedral MA₄B₂: cis and trans again
In an octahedron, any two positions are either 90° apart (cis) or 180° apart (trans). An MA₄B₂ complex therefore has exactly two geometric isomers. Werner’s green and violet salts are the pair of [Co(NH₃)₄Cl₂]⁺ ions: in the trans form the two chlorides are opposite; in the cis form they are neighbours.
Octahedral MA₃B₃: fac and mer
Three identical ligands on an octahedron can be arranged in two ways:
- fac (facial): the three B ligands occupy the corners of one triangular face, all mutually cis at 90°.
- mer (meridional): the three B ligands lie in a line around a “meridian” of the octahedron, so two of them are trans to each other.
A good way to picture this is a globe. Mark three points clustered around the North Pole and they sit on one face: that’s fac. Mark three points running over the top from one side of the equator to the other and they follow a line of longitude: that’s mer. [Co(NH₃)₃(NO₂)₃] is a standard textbook example with both forms.
Optical isomerism
A complex is chiral when its mirror image cannot be superimposed on it. The two forms are enantiomers. They have identical melting points, colours and most chemical properties, but they rotate plane-polarised light in opposite directions and can behave differently towards other chiral molecules, including enzymes and DNA.
The classic chiral complexes contain bidentate ligands such as 1,2-diaminoethane (en). In [Co(en)₃]³⁺ the three en ligands wrap around the metal like the blades of a propeller. A propeller can be left-handed or right-handed, and no rotation turns one into the other. These two forms are labelled Δ (delta, right-handed twist) and Λ (lambda, left-handed twist).
A subtler case is [Co(en)₂Cl₂]⁺:
- The trans isomer has a mirror plane running through the Co and the two en ligands, so it is achiral.
- The cis isomer has no mirror plane, so it exists as a pair of enantiomers.
That gives three stereoisomers in total: trans, Δ-cis and Λ-cis. This example appears in exams precisely because it combines geometric and optical isomerism in one ion.
A method for counting isomers
When you meet an unfamiliar formula, work through these questions in order:
- What is the coordination number, and so the likely shape? Four means tetrahedral or square planar; six means octahedral.
- Could any ligand swap in or out of the coordination sphere? Look for counter-ions or water outside the brackets (ionisation or hydrate isomers).
- Are there ambidentate ligands? NO₂⁻ and SCN⁻ signal possible linkage isomers.
- Are there two or more of one ligand type on a square planar or octahedral centre? Check for cis–trans or fac–mer.
- For each geometric isomer, is there a mirror plane? If not, it has an enantiomer. Bidentate ligands in cis arrangements are the usual culprits.
Building a physical model with a ball-and-stick kit, or even six labelled sticky notes on an orange, is the most reliable check. Drawing octahedra on paper makes it very easy to count the same isomer twice.
Common mistakes
- Counting rotations as isomers. Rotating a cis-MA₄B₂ octahedron so that the B ligands move to different positions does not make a new isomer. In an octahedron all cis pairs are equivalent, and so are all trans pairs.
- Expecting cis–trans isomers for tetrahedral complexes. A tetrahedron has no “opposite” corners, so MA₂B₂ has only one form.
- Assuming any complex with bidentate ligands is chiral. trans-[Co(en)₂Cl₂]⁺ has a mirror plane and is achiral. Always test for symmetry rather than relying on the ligand list.
- Confusing linkage isomers with ionisation isomers. In linkage isomerism the same ligand stays bonded but changes its donor atom; in ionisation isomerism a different ion moves in or out of the brackets.
- Thinking optical isomers need carbon. Chirality is about the shape of the whole ion. [Co(en)₃]³⁺ is chiral because of its propeller arrangement around the metal, not because of a stereocentre in the ligand.
- Mixing up structural and geometric isomers in counts. If a question asks for “stereoisomers”, don’t include linkage or hydrate isomers.
Why isomerism matters
Isomerism in complexes is not just a naming exercise. Different isomers can have different colours, reactivities, solubilities and biological effects. The contrast between cisplatin and transplatin is the headline example, but the same principle runs through catalysis, where a chiral metal complex can make one enantiomer of a product preferentially, and through bioinorganic chemistry, where the precise arrangement of donor atoms around a metal in a protein controls what that metal does. Many metal–ligand bonds are dative bonds (see coordinate covalent bonds), and their directions in space are what make all of these arrangements possible.
Key takeaways
- Isomers of complexes have the same formula but different structures; they split into structural isomers and stereoisomers.
- Structural types: ionisation (anion swaps in or out of the brackets), hydrate (water swaps), linkage (ambidentate ligand changes donor atom) and coordination (ligands swap between two complex ions).
- Geometric isomers: cis–trans for square planar MA₂B₂ and octahedral MA₄B₂; fac–mer for octahedral MA₃B₃. Tetrahedral MA₂B₂ has none.
- Optical isomers are non-superimposable mirror images; [Co(en)₃]³⁺ (Δ and Λ) and cis-[Co(en)₂Cl₂]⁺ are standard examples, while the trans form is achiral.
- Isomers can behave very differently: cisplatin is an anticancer drug; its trans isomer is far less active.
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