Coordination Compounds · Lesson 5 of 12
Optical Isomerism
“Recognise non-superimposable mirror images and distinguish structural handedness from measured optical rotation.”
• Test coordination structures for chirality. • Construct mirror-related chelate arrangements. • Count optical subdivisions of geometrical classes. • Distinguish Δ/Λ descriptors from signs of optical rotation.
A mirror image can be a different molecule
Two objects are superimposable if a rotation and translation can make every part coincide without breaking bonds. An ideal square-planar complex can be matched to its mirror image, but three chelate rings wrapped around an octahedral metal may have a handed arrangement. Its mirror image contains the same atoms and metal–donor connections but the opposite twist. A rotation cannot exchange those two arrangements. Such structures are chiral, and the pair are enantiomers.
Stereoisomerism in which two structures are non-superimposable mirror images. A pure enantiomer can rotate plane-polarised light; an equal mixture of the two has cancelling rotations under the same conditions.
Do not use a two-dimensional crossing as the only chirality test. A crossing may be a projection artifact. Identify actual opposite vertices and which donors belong to each chelate, then compare the entire structure with its reflection. A plane of symmetry establishes achirality in the ideal structures used here. Absence of an obvious plane in a poor drawing does not by itself prove chirality.
Three bidentate ligands make a handed cage
For [Co(en)₃]³⁺, there are six N donors, grouped into three adjacent donor pairs. A useful exact description uses vertices ±x,±y,±z. One arrangement pairs (+x,+y), (−x,+z), (−y,−z). Reflecting x changes the first arrangement into the partner pairs (−x,+y), (+x,+z), (−y,−z). The coloured curves in the drawing identify which donors belong to the same en. These donor-pair patterns are equivalent under a reflection but not under any proper rotation of the octahedron.
The two helicities are commonly labelled Δ and Λ. These describe absolute spatial arrangement using a stated viewing convention. A polarimeter instead measures rotation sign, (+) or (−), sometimes called dextro and laevo. One cannot infer the sign from Δ or Λ alone: the sign can depend on wavelength and experimental conditions. Nor does a ligand need a chiral carbon atom for its complex to be chiral; the entire coordination arrangement can supply handedness.
Two chelates: why cis can be chiral
For octahedral [PtCl₂(en)₂]²⁺, put chlorides at adjacent +x,+y. The remaining donor positions can be paired as (−x,+z),(−y,−z), or as (−x,−z),(−y,+z). The two chelate patterns form a mirror pair. Moving chlorides to opposite +z,−z instead gives the trans geometry, which has an ideal symmetry operation allowing its mirror image to be superimposed. Thus there are two optical cis forms and one trans form, three stereoisomers in total.
Problem
Which is chiral: cis-[CrCl₂(C₂O₄)₂]³⁻ or trans-[CrCl₂(C₂O₄)₂]³⁻?
- 1.Each oxalate is bidentate, so both entities have CN 6. With two chlorides and four O donors, the metal is +3: x − 2 − 4 = −3.
- 2.The cis entity has two mirror-related chelate arrangements that cannot be matched by rotation. It therefore has an enantiomeric pair.
- 3.The ideal trans entity is achiral. Replacing en by symmetric oxalate preserves the relevant donor-pair topology, so the same cis/trans chirality reasoning applies.
When two different monodentate ligands are present
The entity [CoCl(NH₃)(en)₂]²⁺ has adjacent or opposite Cl and NH₃ positions. Its cis class has an optical pair, and its ideal trans class is achiral, again giving three stereoisomers. Because Cl and NH₃ differ, do not describe them as an identical pair; cis/trans still describes their 90°/180° relationship. Charge balance gives Co +3, and one Cl plus one NH₃ plus two en gives six donors.
For [Cr(NH₃)₂Cl₂(en)]⁺, there are three geometrical classes. Only the class in which both NH₃ ligands are cis and both chlorides are cis is chiral. The NH₃-trans and Cl-trans classes each have a reflection symmetry in the ideal model. The both-cis class splits into two optical forms, so all geometrical and optical possibilities total four stereoisomers. The same donor topology applies to the cobalt(III) analogue.
A practical counting method
First hold the geometry fixed; next impose the chelate pairings; then remove arrangements related by rotation; finally ask whether reflection produces a remaining distinct arrangement. This order avoids confusing an optical pair with a cis/trans pair. For tris(oxalato)chromate(III), there is one geometrical class but two optical forms. For a square-planar entity with four different achiral monodentate ligands, three geometrical isomers exist, but the ideal plane prevents an optical pair for each.
Problem
A solution contains equal amounts of the two enantiomers of [Co(en)₃]³⁺. Does zero rotation prove that the individual ions are achiral?
- 1.An individual ion may be chiral and rotate polarised light when present as one enantiomer.
- 2.In an equal mixture the two enantiomers have equal and opposite rotations under identical conditions. The net rotation is zero.
- 3.The sample is racemic; optical inactivity of a bulk sample is therefore not by itself proof of an achiral molecular structure.
The ideal donor arrangement is the level of detail considered here. Real en rings have conformations and can undergo motion, but introducing ring-conformation labels is unnecessary for identifying the principal coordination stereoisomers. Count the specified metal-centred geometry consistently rather than multiplying it by every instantaneous molecular vibration.
Quick Quiz
Quiz
Which entity has an optical pair in the ideal donor model?
Three chelate rings can wrap around the metal in two mirror-related helicities.
How many stereoisomers does [CoCl₂(en)₂]⁺ have?
Two cis enantiomers plus one achiral trans form give three.
What does zero rotation for a racemic sample mean?
A sample property can cancel even when its individual molecular entities are chiral.
Can Δ alone determine a positive polarimeter reading?
Absolute handedness does not fix the sign of rotation at a chosen wavelength.
How many geometrical classes occur for octahedral M(AA)A₂B₂?
A-trans, B-trans and both-cis are the three classes; the last can split into an optical pair.
Practice Problems
- Describe the optical pair of [Cr(C₂O₄)₃]³⁻ without relying on colour.
- List all principal stereoisomers of [PtCl₂(en)₂]²⁺.
- List all principal stereoisomers of [CoCl(NH₃)(en)₂]²⁺ and explain why the charge is +2.
- For [Cr(NH₃)₂Cl₂(en)]⁺ identify the optical class and total count.
- Explain why a molecule with no chiral carbon may be optically active.
- A student draws a square-planar MABCD, reflects the page and calls the reflection an optical isomer. Correct the reasoning.
1. Three identical bidentate oxalates give six O donors in an octahedron. 2. Use pairings (+x,+y),(−x,+z),(−y,−z) for one form and reflect x for the other. 3. Each chelate still joins adjacent vertices. 4. No proper rotation matches the pairings, so there are two enantiomers within one geometrical class.
Key Takeaways
• Enantiomers are non-superimposable mirror images. • An entire chelate arrangement can be chiral without chiral carbon atoms. • Tris-chelate octahedral entities have two principal helicities. • Cis M(AA)₂B₂ has an optical pair; the ideal trans form is achiral. • M(AA)A₂B₂ has three geometrical classes and four principal stereoisomers. • Δ/Λ configuration does not by itself determine optical-rotation sign. • A racemic sample can be optically inactive despite containing chiral ions.