Stereoisomerism: Geometrical (cis-trans) Isomerism

Geometrical (cis-trans) isomers have exactly the same set of ligands bonded to the metal in exactly the same way (they are not structural isomers), but differ in how those ligands are spatially arranged around the metal centre. This kind of isomerism is possible in square planar and octahedral complexes, but not in tetrahedral ones (in a tetrahedral $\text{MA}_2\text{B}_2$ complex, every pair of like ligands is automatically equivalent, at the same $109.5^{\circ}$ angle, so no distinct arrangements exist).

For a square planar $\text{MA}_2\text{B}_2$ complex such as $[\text{Pt}(\text{NH}_3)_2\text{Cl}_2]$, two distinct isomers exist. In the cis isomer, the two identical ligands (here, the two $\text{NH}_3$ molecules, and separately the two $\text{Cl}^-$ ions) occupy adjacent corners of the square, $90^{\circ}$ apart. In the trans isomer, they occupy opposite corners, $180^{\circ}$ apart. Because the cis isomer is spatially asymmetric (its $\text{NH}_3$-side and $\text{Cl}$-side dipole contributions do not cancel), it possesses a net molecular dipole moment, whereas the trans isomer's higher symmetry makes its two Pt-Cl bond dipoles cancel exactly against each other (and likewise its two Pt-N bond dipoles), giving it zero net dipole moment. This particular pair of isomers is of major pharmacological importance: cis-$[\text{Pt}(\text{NH}_3)_2\text{Cl}_2]$, universally known as cisplatin, is a widely used anticancer drug that works by binding to and cross-linking DNA inside rapidly dividing cancer cells; its geometrical isomer, trans-$[\text{Pt}(\text{NH}_3)_2\text{Cl}_2]$ (transplatin), is essentially inactive as an anticancer agent — a striking illustration of how profoundly a purely spatial difference, with no change in chemical formula at all, can affect biological activity.

For an octahedral complex, geometrical isomerism is possible whenever at least two ligands of one kind and at least two of another are present. In an $\text{MA}_4\text{B}_2$-type complex such as $[\text{Co}(\text{NH}_3)_4\text{Cl}_2]^+$, the two $\text{Cl}^-$ ligands can occupy either adjacent positions ($90^{\circ}$ apart, the cis isomer, coloured violet) or diametrically opposite positions ($180^{\circ}$ apart, the trans isomer, coloured green) among the six octahedral vertices, with the four $\text{NH}_3$ ligands filling the remaining positions in each case. …