Why HF is said to be formed from H-1s and F-2pz overlap?

Question

According to Wikipedia, HF is formed by the interaction between hydrogen's $1\mathrm{s}$ orbital and fluoride’s $2\mathrm{p}_z$ orbital:

In hydrogen fluoride HF overlap between the H 1s and F 2s orbitals is allowed by symmetry but the difference in energy between the two atomic orbitals prevents them from interacting to create a molecular orbital. Overlap between the H 1s and F 2pz orbitals is also symmetry allowed, and these two atomic orbitals have a small energy separation. Thus, they interact, leading to creation of σ and σ* MOs and a molecule with a bond order of 1.

So:

1. If there is a too large energy separation between H-1s and F-2s, isn't the energy separation between H-1s and F-2p even larger?
2. Can it be experimentally verified that the bonding is indeed via the F-2p and not the F-2s?

Answer 1

You fell into a wrong analogy with the picture of energetically far apart. Let me break down your picture into something visible:

Imagine the orbitals of fluorine at different heights of a mountain (I’ll use the Zugspitze, because it feels like home). 1s is at the very peak of the mountain (yeah, I’m turning this around just for simplicity). The Eibsee (c. $1000~\mathrm{m}$ over sea level) would correspond to the 2s-orbital. Garmisch-Partenkirchen, the town in the valley before the mountain, ($700~\mathrm{m}$) would be the 2p orbital.

We need to place the 1s-orbital of hydrogen somewhere so that the height difference to the Eibsee is too large for an interaction. One possibility would be the Höllentalanger hut at around $1300~\mathrm{m}$. That would render the energy difference to both fluorine’s 2s and 2p too large. But in fact, hydrogen’s 1s is better placed at the height of Oberau, $650~\mathrm{m}$. That is way too far away from the 2s but rather close to the 2p.

This is confirmed by energy diagrams of $\ce{HF}$ like that presented in this lecture (in German). (Just search for HF on the page, it’s not far down. Ignore the text around it and look at the scheme.)

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Now you may be asking yourself why the hydrogen’s 1s energy is so high compared to fluorine’s orbitals. Compare ionisation energies, which are typically understood as the energy difference of the highest orbital to ‘an electron in vacuum’. For hydrogen, this energy is $1312~\mathrm{kJ/mol}$ while for fluorine this is $1681~\mathrm{kJ/mol}$. The reasoning behind it is fluorine’s very high electronegativity, attracting the electrons towards its nucleus. Fluorine’s nucleus has a $+9$ charge which is much better at drawing electrons in than hydrogen’s $+1$ (even though it needs to draw nine electrons in rather than one). This stabilises all of fluorine’s orbitals; and those which are ‘closer to the nucleus’ (s-orbitals) most.

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I am not well-educated in modern physical chemistry methods, but I heard that orbitals were visualised. If that is the case, it won’t be long until we can visualise the $\ce{HF}$ orbitals, and indeed show that the bonding orbital (highest energy σ type) will have a nodal plane through fluorine.

Answer 2

1. No, there is larger energy separation between H$_{1s}$ and F$_{2s}$. To see this lets lie a lot and say that orbital energies are proper energies. So thinking classically, the energy is due to coulomb interaction between the nuclei and the electron, electrons always have the same charge, but fluorine nuclei have much more charge than hydrogen. That means that (in this picture) the electron in a H$_{1s}$ would have greater energy than one in F$_{1s}$ (the second one much greater in absolute value). An F$_{2p}$ electron "feels" like there is not as much charge in the nuclei (because the coulumb repulsion with inner electrons), so its energy is closer to the H$_{1s}$ energy.

By the way, I have to say it, I do not find much sense in the argument about the closeness of orbital energy to assert about the overlaps.

2. No, it can't be measured because orbitals does not exist. All we can do is perform molecular calculations to get an approximation to the wave function. Then force the separation of this function in hydrogen like orbitals (other functions with whom we are familiar or obsessed) through projections to make this kind of interpretations.

Answer 3

Wrong way round- search "orbital potential energy" and you'll know what I mean.

Hydrogen 1s is much higher in energy than F 2s and slightly higher then F 2p; that's why the bonding MO is centred mostly on fluorine and the unfilled LUMO is mostly on hydrogen.