Molecular covalent bonds across energy levels

[nomadreid]

TL;DR

In examples for molecular covalent bonds on the Internet (e.g., the site given in the full text), all components, with the exception of hydrogen, have the same energy level n. Yet there are bonds formed from orbitals of different energy levels, even though the bonding is more likely for identical n, no? So isn't it just whether the orbitals are s's, p's, an sp hybrid, or whatever? Why the n?

I am sure this is an elementary question; I'm just trying to clarify some points that were poorly explained to me years ago in secondary school. I know that a full answer would involve solving Schrödinger's equation etc., but keeping this on the level of valence electrons,...) I was confused by the sites, e.g. , https://chem.libretexts.org/Bookshe...1.7:_Molecular_Orbitals_and__Covalent_Bonding, using only components , besides H, that had the same n for all components. After all, isn't the whole idea of a group the similarities across peiods?

 

[DrJohn]

I think it is a case of giving you the simplest possible examples, using only the outermost electrons, where n, the principle quantum number, is the main contribution to the energy of the outer electrons, and l the azimuthal quantum number making a smaller contribution to the energy of the orbitals. They are deliberately choosing elements with only s and p orbitals to keep it simple but still show that predictions can be made.

If the full inner electrons were included, they would show that the number of bonding and antibonding orbitals would be the same, all would be full, and so make no contribution to the overall bonds as the bonding orbitals are canceled by the antibonding orbitals. It's only the outermost orbitals, when they are not full, that are likely in their examples to show any overall net bonding.

You could draw them all out for the sodium example and see this for yourself. Then repeat for potassium, and as the diagram becomes bigger you will see why they ignore the ones which don't contribute overall to the bonding.

And when it gets to elements with d orbitals, it gets even harder to draw.

 

[nomadreid]

Thanks, @DrJohn. The reason for not including the inner electrons is clear, but I thought it would be even simpler if, instead of saying for example, ns¹ and ns¹ give nσ, say that, among the valence electrons, ns¹ and ms¹ give σ, or something similar. But your explanation that that they are simply using the simplest examples makes sense, though. It just worried me to think that I was missing something...

 

[Frabjous]

The Caltech library provides an electronic copy of a nice book:
Gray, Harry B. (1994) Chemical Bonds: An Introduction to Atomic and Molecular Structure
https://authors.library.caltech.edu/105209/

 

[nomadreid]

caz, thanks. Looks good. downloaded!

 

[DrDu]

If the orbitals are of vastly different energy, you'd rather get an ionic bond.

 

[nomadreid]

Thanks, DrDu. I never noticed that. Very helpful!

 

[DrDu]

You are welcome!
This reasoning can be formalized. Pauling already introduced the electronegativity, which determines the ionicity of the bonds, in terms of the electron affinity and ionization energy.
According to Koopman's theorem, both are given basically in terms of the LUMO and HOMO orbital energies. https://en.wikipedia.org/wiki/Koopmans'_theorem

 

[nomadreid]

DrDu, thanks again; once again, your comments are helpful and the Wiki article is as well.