As I was reading about nephelauxetic effects, which is the effect that atomic d-orbitals are bigger in a complex than in gaseous metal ions. The Racah interelectronic repulsion parameter gets smaller, indicating that doubly occupied d-orbitals are bigger in complexes than in an atom (why only doubly occupied though, shouldn't there also be less repulsion between, lets say singly occupied d-orbitals?). I wondered what reasons there could be for that. The two most cited reasons are:

  1. decreased effective nuclear charge, partially neutralized by the ligand sphere
  2. formation of covalent bond character with the ligand

The first option seems fine enough for me, but 2) makes little sense for me. The ligand field splitting arises because the partially filled d-orbitals want to avoid the double occupied ligand orbitals, therefore assuming a position where the electronic repulsion is smallest.

Why would they form covalent bonds then, or is that just a consequence of MO theory that we have to acccept?

  • 1
    $\begingroup$ There's practically no such thing as gaseous metal ions - you need plasma for any significant amount of "free" metal ions (a nitpick). $\endgroup$
    – Mithoron
    Aug 26, 2023 at 21:47

1 Answer 1


The Racah repulsion parameters are smaller in a transition metal complex than in a free atomic ion because

  1. Decreased effective nuclear charge: As the effective charge localized at the metal decreases, the orbitals increase in size (they're pulled in less tightly). This larger size means the electron density is more diffuse so electrons feel less repulsion from each other

  2. Ligand covalency: Mixing between the d orbitals and the ligand orbitals causes the wavefunction to extend further. This delocalization also increases the general interelectron distance, leading to less repulsion.

Your point about ligands repelling d orbitals comes from a crystal field understanding of metal–ligand interactions rather than a ligand field understanding. Crystal field theory tries to explain all of coordination chemistry using repulsion, and it turns out it's just too simplistic. The fact that crystal field theory ignores all metal–ligand bonding (covalency) is one of the major failings of crystal field theory (it's the reason it can't justify the spectroscopic series or the nephelauxetic series). This failure is the reason chemists gradually moved to ligand field theory.

Ligand field theory explains d orbital splitting using orbital overlap and covalent mixing of orbitals — not using repulsion. This is very reminiscent of diatomic MO diagrams, where localized orbitals overlap in constructive (bonding) and destructive (antibonding) patterns. Repulsion is treated separately through Racah parameters (just like crystal field theory). An advantage of this approach is that you can start to look at the interplay of covalency, symmetry (sigma/pi), 10Dq, B, and C.

So I suppose the short answer is that: you can't ignore MO theory like crystal field theory does. If you take into account the molecular orbitals, then bullet (2) makes sense.


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