Problem 13 Discuss the molecular orbital tr... [FREE SOLUTION]

Chapter 23: Problem 13

Discuss the molecular orbital treatment for an octahedral complex with the help of a suitable example.

Short Answer

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The molecular orbital treatment in an octahedral complex involves visualizing the structure of the complex, understanding the splitting of the metal ion's d orbitals into \(t_{2g}\) and \(e_{g}\) sets, populating these orbitals following the Aufbau principle and Hund's rule, and recognizing the energy gap between the orbitals. In a d3 octahedral complex as an example, 3 electrons occupy each of the \(t_{2g}\) orbitals and none in the \(e_{g}\) orbitals.

Step by step solution

Visualize the Octahedral Complex

Firstly, it's crucial to know how to visualize an octahedral complex. An octahedral complex is formed when a central metal atom or ion is surrounded by six ligands directed towards the corners of an octahedron. For example, consider a transition metal, M, surrounded by six identical ligands, L. In order to do so, draw a three-dimensional structure that shows the metal atom or ion at the center of the octahedron, while the six ligands are occupying the six corners.

Understand the Energy Levels and Orbitals

Secondly, it's necessary to understand that in an octahedral complex, the d orbitals of the metal ion and the atomic orbitals of the ligands combine to form molecular orbitals. These molecular orbitals are at different energy levels. The five d orbitals are split into two sets in an octahedral field: \(t_{2g}\) (dxy, dyz, dxz) and \(e_{g}\) (dx2-y2, dz2). The splitting of these orbitals are related to the crystal field splitting energy (\( \Delta_{o} \)). Express these energy levels in a diagram.

Populate the Molecular Orbitals

With both the molecular orbitals and splitting energy understood, it's time to populate the MOs. For that, follow the Aufbau principle, which states that electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states. According to the Hund's rule, if more than one orbital in a sublevel is available, electrons fill them singly first with parallel spins. Hence, fill electrons in \(t_{2g}\), and then in \(e_{g}\) if they're available.

Example Sketch of an Octahedral Complex

Let's make this more concrete by applying it to an example. Consider a d3 octahedral complex: it could be formed when a transition metal with 3 d electrons forms an octahedral complex with ligands. Based on the Aufbau principle and Hund's rule, three electrons will be filled singly into each of the \(t_{2g}\) orbitals, and none into the \(e_{g}\) orbitals. Represent this in the drawn energy level diagram.

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Discuss the molecular orbital treatment for an octahedral complex with the help of a suitable example.

Short Answer

Step by step solution

Visualize the Octahedral Complex

Understand the Energy Levels and Orbitals

Populate the Molecular Orbitals

Example Sketch of an Octahedral Complex

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