Question

How might one draw atomic and molecular orbital diagrams?

Answer 1

I will use oxygen (`"O"_2(g)`) as an example.

With oxygen, you know that the atomic orbital potential energies go in the following order:

`V_(1s)` `"<<"` `V_(2s) < V_(2p)`

So the atomic orbital diagram is simply those orbitals in that order of energy. Note that the `1s` orbitals are significantly lower in energy than the `2s` orbitals.

For the homonuclear diatomic `"O"_2`, we simply have two copies of this atomic orbital diagram far apart at first. Fill those with oxygen's 8 electrons (2 core + 6 valence).

Now we have two of the same atomic orbital diagrams laid out:

Then, for the molecular orbital diagram, we examine how these atomic orbitals interact with each other in a linear combination of atomic orbitals (LCAO). Here's how this goes (of course, the `ns` are compatible with the `ns`).

Taking the internuclear axis as the `z`-axis, we have:

• `"AO"_(1s) + "AO"_(1s) = sigma_(1s) + sigma_(1s)^"*"` (strong head-on overlap)
• `"AO"_(2s) + "AO"_(2s) = sigma_(2s) + sigma_(2s)^"*"` (strong head-on overlap)
• `"AO"_(2p_x) + "AO"_(2p_x) = pi_(2p_x) + pi_(2p_x)^"*"` (weak sidelong overlap)
• `"AO"_(2p_y) + "AO"_(2p_y) = pi_(2p_y) + pi_(2p_y)^"*"` (weak sidelong overlap)
• `"AO"_(2p_z) + "AO"_(2p_z) = sigma_(2p_z) + sigma_(2p_z)^"*"` (strong head-on overlap)

Thus, we take 10 atomic orbitals and generate 10 molecular orbitals, in accordance with the conservation of orbitals.

Based on the amount of orbital overlap, the relative changes in energy differ going from the atomic orbital to the molecular orbital. Greater overlap = greater change in energy.

That's why the `sigma_(2p_z)` molecular orbitals are lower in energy than the `pi_(2p_x)` and `pi_(2p_y)` molecular orbitals.

And finally, just fill in the electrons in accordance with Hund's rule, the Pauli Exclusion Principle, and the Aufbau Principle.

You get 8 electrons from each oxygen, so you get 16 total:

And indeed, this agrees with other MO diagrams of `"O"_2(g)`.

This is known as triplet (`""^3 Sigma`) oxygen, the ground-state of oxygen gas.