Which one of the following complexes shows optical isomerism? (en=ethylenediamine)

For optical isomerism a molecule must be chiral, that is, it must not possess any element of symmetry such as a plane of symmetry, a centre of symmetry, or an improper axis of rotation. In octahedral coordination compounds, chirality most often appears when the complex contains at least two unsymmetrical bidentate ligands arranged so that the whole ion has no internal mirror plane.

We now examine each of the four given complexes one by one.

Option A is trans $$[Co(en)_2Cl_2]^+$$ (the outside chloride ion is the counter-ion and does not affect symmetry). In the trans form the two chloride ligands occupy opposite (180°) positions. This places one $$Cl^-$$ above and the other exactly below the plane formed by the four nitrogen donors. Because of this arrangement there exists a vertical plane passing through the metal and both chlorides, so the ion possesses a plane of symmetry. A molecule that has a symmetry plane cannot be chiral. Hence the trans isomer is optically inactive.

Option B is $$[Co(NH_3)_4Cl_2]^+$$. Here all six ligands are monodentate; four are identical $$NH_3$$ and two are identical $$Cl^-$$. The complex can exist as cis and trans geometrical isomers. In the cis form the two chlorides are adjacent; in the trans form they are opposite. For an octahedral $$MA_4B_2$$ ion, whether cis or trans, one can always find either a mirror plane (for the cis form) or a centre of symmetry (for the trans form). Therefore neither isomer is chiral, and no optical activity is possible.

Option C is $$[Co(NH_3)_3Cl_3]$$. This is an $$MA_3B_3$$ type octahedral complex. It exhibits facial (fac) and meridional (mer) geometrical isomers, but both fac and mer have symmetry elements (a three-fold rotational axis plus mirror planes for fac, and a mirror plane for mer). Consequently, the complex is achiral and shows no optical isomerism.

Option D is cis $$[Co(en)_2Cl_2]^+$$. The two ethylenediamine ligands are unsymmetrical bidentate ligands that each occupy two adjacent positions, forming two five-membered rings with the cobalt ion. In the cis form the two chloride ligands are also adjacent. Because the two $$en$$ chelate rings twist in a definitive handed manner, the whole ion lacks a plane or centre of symmetry and consequently exists in two non-superimposable mirror-image configurations, conventionally labelled $$\Delta$$ and $$\Lambda$$. These two forms rotate plane-polarised light in opposite directions, so optical activity is observed.

Among the four choices, only the cis $$[Co(en)_2Cl_2]^+$$ ion fulfils the necessary condition of having no symmetry element and thus can show optical isomerism.

Hence, the correct answer is Option D.