Which complexes exhibit geometric isomerism? a. \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5}(\mathrm{OH})\right]^{2+}\) b. \(\left[\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\) c. \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{2}\right]^{+}\) d. \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{3}\right]^{-}\) e. \(\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}(\mathrm{CN})_{2}\right]\)

Coordination chemistry is the branch of chemistry that deals with coordination compounds where a central metal atom or ion is surrounded by molecules or anions, known as ligands. These ligands can donate pairs of electrons to the metal, forming coordinate covalent bonds. The total number of ligands attached to the central metal is known as the coordination number, which plays a critical role in determining the geometry and possible isomerism of the complex.
Coordination complexes exhibit a variety of properties and structures, which are influenced by the types of ligands, the oxidation state of the central metal, and the coordination geometry. Understanding these factors helps predict the reactivity, color, and magnetic properties of the complex, making coordination chemistry a fundamental topic in inorganic chemistry.

Octahedral geometry is one of the most common coordination geometries in coordination chemistry, where six ligands symmetrically surround a central metal ion, akin to the vertices of an octahedron. An octahedral complex has a coordination number of six.
In an octahedral arrangement, the ligands can generate distinct patterns in space that lead to geometric isomerism. Due to the octahedral symmetry, every ligand position is related to each other through symmetry operations. Nonetheless, when there are different types of ligands, it becomes possible for these ligands to adopt different relative positions, leading to the existence of geometric isomers.

Square planar geometry is another important coordination geometry, especially for metal ions with a d8 electron configuration, such as nickel(II), palladium(II), platinum(II), and gold(III). This geometry occurs less frequently than octahedral geometry and is characterized by a central metal ion surrounded by four ligands positioned at the corners of a square plane, with the metal ion at the center of the square. This geometry is related to the octahedral geometry but with two opposite ligands removed.
Square planar complexes can exhibit cis and trans isomerism, similar to octahedral complexes, but with a different spatial arrangement of ligands. This leads to unique chemical and physical properties, often exploited in the field of medicinal chemistry and homogenous catalysis.

Cis and trans isomers are two types of geometric isomers that can be found in coordination complexes with square planar or octahedral geometries. Cis isomers have similar ligands adjacent to each other, while trans isomers have similar ligands across from each other or at 180 degrees. Geometric isomerism is crucial because it can greatly influence the chemical properties of a complex, including its reactivity, solubility, and biological activity.
In medicinal chemistry, for instance, cisplatin (a square planar complex) is a well-known anticancer drug, while its trans isomer is pharmacologically inactive. This illustrates the importance of correctly identifying and synthesizing the desired geometric isomer in coordination chemistry.

Bidentate ligands have two donor sites that allow them to bind to a central metal atom or ion at two points simultaneously. This 'double-toothed' binding creates a ring of atoms including the metal ion, termed a chelate ring, which can lead to enhanced stability of the coordination complex compared to complexes with monodentate ligands.
For geometric isomerism to occur with bidentate ligands in an octahedral complex, the metal must also be bound to other ligands that allow for variability in their spatial arrangement. The presence of bidentate ligands can often lead to more complex isomerism, as seen in the example of the ethylenediamine ligand (en) in complex b from the exercise, which allows for both cis and trans configurations relative to other ligands in the complex.