Question

What does a closed shell mean?

Answer 1

It means there are no unpaired electrons. So the only filled orbitals are:

`ul(uarr darr)`

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On the other hand, open-shell species have unpaired electrons in their ground-state electron configuration, i.e. something like:

`underbrace(ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr)))_(2p)`

In group theory,

• closed-shell atoms are said to have a `""^(1) "S"_0` (singlet-S-zero) state.
• closed-shell molecules have a `""^(1) Sigma_g^+` (singlet-sigma-gerade plus) state.

That's just another way to say that there are zero unpaired electrons in all occupied orbitals.

Atoms like `"Kr"` (noble gas), `"Zn"^(2+)` (argon configuration), etc. are closed-shell.

`"O"_2^(2-)` is an example of a closed-shell molecule, whereas `"O"_2` is an open-shell molecule.

Various open-shell cases exist. For instance... only a few homonuclear diatomics are open-shell:

• `"O"_2` ground state: `""^(3)Sigma_g^(-)`, open shell

`underbrace(ul(uarr color(white)(darr))" "ul(uarr color(white)(darr)))_(1pi_g^"*", " "2pi_g^"*")`

• `"O"_2^(+)` ground state: `""^2 Pi_g`, open shell

`underbrace(ul(uarr color(white)(darr))" "ul(color(white)(uarr darr)))_(1pi_g^"*", " "2pi_g^"*")`

• `"B"_2^(+)` ground state: `""^2 Pi_u`, open shell

`underbrace(ul(uarr color(white)(darr))" "ul(color(white)(uarr darr)))_(1pi_u, " "2pi_u)`