Question

Consider an octahedral complex \(\mathrm{MA}_{3} \mathrm{~B}_{3}\). How many geometric isomers are expected for this compound? Will any of the isomers be optically active? If so, which ones?

Short answer

The octahedral complex MA3B3 has two geometric isomers, a facial (fac) isomer and a meridional (mer) isomer. However, both isomers are optically inactive as they possess a mirror plane of symmetry between the ligands A and B.

Step-by-step solution

Identify ligands and their arrangement around the metal center

In an octahedral complex, there are six coordinate positions for ligands in which three positions are occupied by A-type ligands (A) and three positions are occupied by B-type ligands (B). The metal center (M) can be located at the center of the octahedron.

Generate possible isomers for the complex

Two major geometric isomer types can be formed from an octahedral complex with MA3B3 composition: a facial (fac) isomer and a meridional (mer) isomer. To generate these isomers, we can systematically place ligands A and B around the metal center, maintaining the number of A ligands (3) and B ligands (3) in every structure. 1. Facial (fac) isomer: the A ligands and the B ligands each occupy one face of the octahedron. 2. Meridional (mer) isomer: the A ligands and the B ligands are positioned in a pairwise manner along the corners of the octahedron (an alternative interpretation of the mer arrangement is that the A ligands form a "tripod" by being placed on three alternating positions at a 90° angle from each other in the x, y, and z axis, the B ligands are placed in the empty sites in between the A ligands).

Determine optical activity of isomers

To determine if any of the isomers are optically active, we need to analyze the symmetry of the structures. Optically active compounds are enantiomers (chiral molecules) and have non-superimposable mirror images. In contrast, optically inactive compounds have superimposable mirror images (achiral molecules). 1. Facial (fac) isomer: This isomer has a mirror plane of symmetry between the A and B ligands, and thus isomers of the fac type are optically inactive. 2. Meridional (mer) isomer: This isomer also has a mirror plane of symmetry between the A and B ligands, and therefore isomers of the mer type are optically inactive as well.

Summarize the findings

The octahedral complex MA3B3 has two geometric isomers: a facial (fac) isomer and a meridional (mer) isomer. Both of these isomers are optically inactive due to the presence of a mirror plane of symmetry between the ligands A and B.

Key concepts

Octahedral Complexes

In coordination chemistry, an octahedral complex is formed when a central metal atom or ion is surrounded by six ligands. Ligands are molecules or ions that donate a pair of electrons to the metal, creating a coordination bond. The arrangement is highly symmetrical, resembling an octahedron shape.

For the chemical formula \(\text{MA}_3\text{B}_3\), we have six ligand positions, occupied by two types of ligands: A and B. The three ligand A's and three ligand B's can occupy these positions differently, forming different isomers.

Understanding how these ligands arrange themselves around the metal center is crucial for predicting and explaining the chemical behavior and properties of the complex. This arrangement influences the complex's color, reactivity, and magnetism. Making it clear why octahedral geometry is one of the most common and important in coordination chemistry.

Optical Activity in Chemistry

Optical activity refers to a molecule's ability to rotate the plane of polarized light. This characteristic is crucial for understanding many natural and synthetic compounds, especially in the field of stereochemistry.

A compound is optically active when it is chiral, meaning it has two non-superimposable mirror images called enantiomers. To determine if a complex is optically active, we check for symmetry.
If a compound has a plane of symmetry, it becomes achiral, meaning both its mirror images can be superimposed, making it optically inactive.

In the case of \(\text{MA}_3\text{B}_3\) octahedral complexes, both facial and meridional isomers possess a mirror plane due to the symmetrical arrangement of ligands. Thus, these isomers cannot rotate plane-polarized light and are optically inactive.

Facial and Meridional Isomers

In octahedral complexes like \(\text{MA}_3\text{B}_3\), the two primary geometric isomers are known as facial (fac) and meridional (mer) isomers. Each type has a distinct ligand arrangement that influences its properties and behavior.

- **Facial Isomer (fac)**: In this configuration, all three A ligands and all three B ligands occupy adjacent sites on one face of the octahedron. This arrangement forms a triangular face of ligands, like a triangle perched on one side of a die.
- **Meridional Isomer (mer)**: Here, the A and B ligands alternate around the octahedron, forming a "meridian" circle, connecting three alternating positions like the corners of a tripod. This arrangement is more diagonal and spread across different faces.

Both fac and mer isomers have significant mirror planes resulting in them being non-chiral and thus optically inactive.