Molecular orbitals 2

MO diagram of HF:

Generally the more similar in energy two wavefunctions or orbitals are, the stronger they overlap. In MO diagrams, the closer the energy level of a molecular orbital with an atom's atomic orbital, the more likely the electron in that orbital is found on the parent atom. So from above we can predict that electrons in HF are far more likely to be found on the flourine atom - which agrees from what we would predict from knowing about electronegativity.

It also tells us that an electron promoted into the sigma antibonding orbital will be more likely to be found on the hydrogen atom.

The H1s orbital overlaps with the FP_z and F2s orbital. Three atomics orbitals of sigma symmetry therefore overlap to produce three molecular orbitals of sigma symmetry.

The 1s orbital on flourine also possesses sigma symmetry, but since it is not a valance orbital it is dismissed as negligible and not used in the calculation.

Flourine also has two p orbitals which produce two pi molecular orbitals. Hydrogen has no orbitals of the right symmetry to overlap with them. The two pi molecular orbitals are an example of "non-bonding orbitals".

The textbook writes that u and g notation are not used for molecular orbitals in heteronuclear diatomics, I don't have a good explanation for that because I don't know much about symmetry, I assume it's difficult to apply operations to a molecule when electron clouds are not evenly spread out between atoms as in homonuclear diatomics.

The bond order (b) is calculated by (1/2)(electrons in bonding orbitals - electrons in antibonding orbitals). Non-bonding orbitals are ignored. Applying that to the above diagram we get 1. This agrees with the single bond/one shared electron pair from lewis diagrams.

Here is the MO diagram of oxygen again:

This should give a bond order of two, giving the same prediction of a double bond that we would expect from lewis diagrams. You should also be able to tell that the O₂^- ion would have a bond order of 1.5, since the extra electron would only have an antibonding MO to slot into.

As a general rule, bond length decreases with bond order. So adding an extra electron to O₂ would make the molecule longer.