Question

What are high and low spin complexes in crystal field theory?

Answer 1

It just categorizes, qualitatively, how the metal `d` orbitals are filled in crystal field theory after they are split by what the theory proposes are the ligand-induced electron repulsions.

The usual Hund's rule and Aufbau Principle apply.

Examples of low-spin `d^6` complexes are `["Cr"("CN")_6]^(3-)` and `"Cr"("CO")_6`, and examples of high-spin `d^6` complexes are `["CrCl"_6]^(3-)` and `"Cr"("H"_2"O")_6`.

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I assume you know the basic facets of crystal field theory:

1. Ligands come in, and their important orbitals interact with the metal `d` orbitals.
2. Electrons repel electrons to destabilize certain metal `d` orbitals. In an octahedral field, these are known as the `e_g^"*"` orbitals.
3. Electrons are attracted to the electropositive metal center to stabilize certain metal `d` orbitals. In an octahedral field, these are known as the `t_(2g)` orbitals.

The crystal field splitting energy is called `Delta_o` in an octahedral field for simplicity, and the resultant `d` orbital splitting is:

`uarrE" "color(white)({(" "" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "e_g^"*")),(color(black)(Delta_o)),(" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "t_(2g))):})`

Orbitals close in energy simultaneously fill more easily and vice versa. And so, depending on the magnitude of `Delta_o`, there are two cases. Take a `d^6` configuration as an example...

• When `Delta_o` is large, the complex is likely low-spin:

`uarrE" "color(white)({(" "" "color(black)(ul(color(white)(uarr darr))" "ul(color(white)(uarr darr))" "e_g^"*")),(),(),(),(),(color(black)(Delta_o)),(),(),(),(),(" "color(black)(ul(uarr darr)" "ul(uarr darr)" "ul(uarr darr)" "t_(2g))):})`

• When `Delta_o` is small, the complex is likely high-spin:

`uarrE" "color(white)({(" "" "color(black)(ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "e_g^"*")),(),(color(black)(Delta_o)),(),(" "color(black)(ul(uarr darr)" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "t_(2g))):})`

Of course, I am exaggerating the energy scale, but hopefully that brings the point across.

• High spin complexes half-fill the lower energy `bbd` orbitals first, and THEN move up to the higher energy `d` orbitals to half-fill those next, before pairing starts occurring, BECAUSE those orbitals are so similar in energy to the lower energy orbitals.
• Low spin complexes fill the lower energy orbitals completely first, before moving on to the higher energy orbitals, BECAUSE those orbitals are so much higher in energy.