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Why is the a term the ground term for a d3 electron configuration for a transition metal in an octahedral complex
Accepted Answer
The ground term for a d3 electron configuration in an octahedral complex is ⁴A2g. This is determined by the following steps:
1. Determining the possible microstates: For d3, there are 10 possible microstates (ways to arrange 3 electrons among 5 d orbitals).
2. Applying Hund's rules: The ground state will have the maximum spin multiplicity (S=3/2, with all three electrons unpaired) and the maximum total orbital angular momentum (L=3, corresponding to a ⁴F term).
3. Considering octahedral field splitting: In an octahedral field, the d orbitals split into two sets: eg (d_x^2-y^2, d_z^2) and t2g (d_xy, d_xz, d_yz). The t2g set is lower in energy. With 3 electrons, the configuration will be t2g^3.
4. Deriving the ground term: Since the t2g orbitals are degenerate, the ground term will be the one with the lowest L value for a given S value. The ⁴F term can split into ⁴A2g, ⁴T2g, and ⁴T1g terms under octahedral symmetry. The lowest energy term is ⁴A2g, making it the ground term.
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