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Chapter 23: Problem 13

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

Short Answer

Expert verified
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

01

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.
02

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.
03

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.
04

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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Most popular questions from this chapter

Discuss Sidgwick's concept of effective atomic number with the help of suitable example.

Explain the following: (a) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) is paramagnetic and coloured. (b) \(\left(\mathrm{Ni}(\mathrm{CN})_{4}\right)^{2-}\) is square planar, but \(\left[\mathrm{Ni}(\mathrm{Cl})_{4}\right]^{2-}\) is tetrahedral. (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) is more stable than \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\), while \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is more stable than \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (d) Octahedral complexes are less stable than the square planar complexes. (e) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) is a low-spin complex, but \(\left[\mathrm{CoF}_{6}\right]^{3-}\) is high-spin complex.

What are the limitations of valence bond theory?

Draw molecular orbital diagram of a square planar complex showing only \(\pi\) -bonding.

How does ligand field theory describe the origin of charge transfer spectra in coordination complexes.
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