Stereoisomerism - Geometrical & Optical

Stereoisomerism — Same Bonds, Different Shapes

Stereoisomers have the same atoms bonded to the same partners (same connectivity) but a different arrangement in space. There are two kinds: geometrical (cis-trans) and optical (mirror-image) isomerism.

Stereoisomerism in complexes depends on the geometry and the type of ligands. A complex with all identical ligands (homoleptic, e.g. $[\text{Co(NH}_3)_6]^{3+}$) shows no geometrical isomerism; you need two or more kinds of ligand (heteroleptic).

Geometrical (cis-trans) Isomerism

Geometrical isomers differ in the relative positions of ligands around the metal.

**Square planar (CN = 4), type $[\text{MA}_2\text{B}_2]$: **

• cis — the two A ligands are adjacent (90° apart).
• trans — the two A ligands are opposite (180° apart).
• Classic example: cisplatin $[\text{Pt(NH}_3)_2\text{Cl}_2]$ — the cis isomer is the anticancer drug; the trans isomer is inactive.

Octahedral (CN = 6):

• $[\text{MA}_4\text{B}_2]$ type shows cis (the two B ligands adjacent) and trans (the B ligands opposite). E.g. $[\text{Co(NH}_3)_4\text{Cl}_2]^+$.
• $[\text{MA}_3\text{B}_3]$ type shows fac (3 alike on one triangular face) and mer (3 alike in a meridian).

Key Point: Tetrahedral complexes do NOT show geometrical isomerism — all four positions are equivalent, so there is no cis/trans distinction.

Optical Isomerism (Chirality)

Optical isomers are non-superimposable mirror images of each other — like your left and right hands. They are called enantiomers; one rotates plane-polarised light clockwise (dextro, d or +) and the other anticlockwise (laevo, l or −).

Optical isomerism is common in octahedral complexes containing bidentate (chelate) ligands:

• $[\text{Co(en)}_3]^{3+}$ — exists as two enantiomers (d and l forms). No plane of symmetry, so it is chiral.
• cis-$[\text{Co(en)}_2\text{Cl}_2]^+$ is optically active (chiral); the trans isomer has a plane of symmetry and is not optically active.

[NEET Important] A complex is optically active only if it has no plane of symmetry (no superimposable mirror image). The cis isomers of $[\text{M(en)}_2\text{X}_2]$ type are usually optically active; trans isomers usually are not (they have a symmetry plane).

Solved Examples

Example 1: cis and trans of cisplatin

Draw/describe the geometrical isomers of $[\text{Pt(NH}_3)_2\text{Cl}_2]$ (square planar).

Solution: cis — the two Cl (and the two NH$_3$) are adjacent (90°); this is the anticancer drug cisplatin. trans — the two Cl are opposite (180°); biologically inactive.

Example 2: Why no geometric isomers in tetrahedral

Why does a tetrahedral $[\text{MA}_2\text{B}_2]$ complex show no geometrical isomerism?

Solution: In a tetrahedron, all four corner positions are equivalent — there is no distinct opposite position — so there is no cis/trans distinction.

Example 3: Geometric isomers of an octahedral complex

How many geometrical isomers does $[\text{Co(NH}_3)_4\text{Cl}_2]^+$ show?

Solution: Two — cis (the two Cl adjacent) and trans (the two Cl opposite).

Example 4: fac and mer

What are fac and mer isomers, and for what type do they occur?

Solution: They occur for octahedral $[\text{MA}_3\text{B}_3]$ complexes. fac (facial): the three identical ligands occupy one triangular face. mer (meridional): the three identical ligands lie in a plane (meridian) through the metal.

Example 5: Optical activity of [Co(en)3]3+

Why is $[\text{Co(en)}_3]^{3+}$ optically active?

Solution: It has no plane of symmetry; its mirror image is non-superimposable, so it exists as two enantiomers (d and l) — it is chiral and optically active.

Example 6: cis vs trans optical activity

Which of cis- and trans-$[\text{Co(en)}_2\text{Cl}_2]^+$ is optically active?

Solution: The cis isomer is optically active (no plane of symmetry, chiral). The trans isomer has a plane of symmetry, so it is not optically active.

Example 7: Define enantiomers

What are enantiomers?

Solution: Enantiomers are a pair of non-superimposable mirror-image stereoisomers. They rotate plane-polarised light by equal amounts in opposite directions (one +/dextro, the other −/laevo).

Example 8: Geometrical isomerism condition

What kind of ligand set is needed for a complex to show geometrical isomerism?

Solution: The complex must be heteroleptic (contain two or more different kinds of ligand) and have a geometry (square planar or octahedral) that allows distinct cis/trans arrangements.

Example 9: Identify optical isomerism

Does $[\text{PtCl}_2(\text{en})]$ (square planar) show optical isomerism?

Solution: No. Square planar complexes generally have a plane of symmetry (the molecular plane), so they are usually not optically active. Optical isomerism is mainly seen in octahedral chelate complexes.

Example 10: Total stereoisomers

How many stereoisomers (geometrical + optical) does $[\text{Co(en)}_2\text{Cl}_2]^+$ have?

Solution: Three in total: the trans isomer (1, optically inactive) plus the cis isomer, which exists as a pair of enantiomers (2). So 1 + 2 = 3 stereoisomers.