For each d electron configuration, state the number of...

For each $d$ electron configuration, state the number of unpaired electrons expected in octahedral complexes. Give an example complex for each case. (Two answers are possible for some of these cases.)
(a) $d^{2}$
(b) $d^{4}$
(c) $d^{6}$
(d) $d^{8}$

Key Concepts

Crystal Field Theory

This theory explains the splitting of the fivefold degenerate d orbitals into groups of different energies when a transition metal ion is surrounded by ligands in a specific geometry, such as octahedral coordination. The splitting results in the formation of lower-energy t2g orbitals and higher-energy eg orbitals, which forms the basis for understanding electron distribution in these complexes.

d Electron Configuration and Orbital Filling

The arrangement of electrons in the split d orbitals is determined by both the number of d electrons and the energy difference between the orbitals. Electrons fill the lower-energy t2g orbitals before occupying the higher-energy eg orbitals, but the exact configuration can vary depending on the competition between electron pairing energy and the crystal field splitting energy.

High Spin and Low Spin Complexes

Depending on the relative magnitudes of the ligand field splitting energy (?oct) and the electron pairing energy, octahedral complexes can adopt either high spin or low spin configurations. In high spin complexes, ?oct is small relative to the pairing energy, leading electrons to occupy higher energy orbitals unpaired, whereas in low spin complexes, a larger ?oct makes it energetically favorable for electrons to pair in the lower-energy orbitals.

Ligand Field Strength and Electron Pairing Energy

The type of ligands coordinated to the metal ion significantly influences the magnitude of the crystal field splitting. Strong field ligands produce larger splitting and can stabilize low spin configurations by promoting electron pairing in the t2g orbitals, while weak field ligands result in smaller splitting and favor high spin arrangements with more unpaired electrons. This interplay is critical for predicting the number of unpaired electrons in various d electron configurations.

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