What Does Molecular Orbital Theory Say About the Overlap of Atomic Orbitals?

[jdawg]

Hey! So I'm a little fuzzy on my understanding of MO theory. One question I had on my study guide said that according to MO theory, overlap of two s atomic orbitals produces _________. I know the answer is one bonding molecular orbitals and one antibonding molecular orbital. Why is this?

Also I would like to know how many bonding and antibonding molecular orbitals would be produced from various combinations of s and p orbitals. If someone could provide me with a few examples I would really appreciate it!

 

[Astudious]

Hey! So I'm a little fuzzy on my understanding of MO theory. One question I had on my study guide said that according to MO theory, overlap of two s atomic orbitals produces _________. I know the answer is one bonding molecular orbitals and one antibonding molecular orbital. Why is this?

Also I would like to know how many bonding and antibonding molecular orbitals would be produced from various combinations of s and p orbitals. If someone could provide me with a few examples I would really appreciate it!

Hmmm. I don't find that to be a very reasonable answer to the question. Overlap of two atomic orbitals in general always produces one "bonding" molecular orbital and one "anti-bonding" orbital. They do not need to be s-orbitals. I would have been confident of writing "sigma and sigma* MOs" as the answer if I saw that question on a test.

In general, if you combine n atomic orbitals (or n molecular orbitals to see what the new ones will look like), you will get n molecular orbitals out. "Bonding" and "anti-bonding" classifications are approximate and only definitive when used with respect to the overlap of 2 orbitals (2 s orbitals or 2 p_z orbitals gives sigma and sigma*, where z is the internuclear axis by convention; 2 p_y or p_x orbitals gives pi and pi*). The reasoning requires a little quantitative knowledge of MO theory (though not the background behind that). You could look into LCAO for that: http://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals

Note that the method is far more powerful than just the use you have suggested (combining atomic orbitals in diatomics). Wikipedia gives an example for water, for instance. For larger molecules, you are likelier to use combinations of hybrid orbitals, which in turn can be derived from LCAO. (You could still try using hybrid orbitals for water, taking O as sp³ with reduced character compared to a normal sp³ hybrid.)

 

[DrDu]

For larger molecules, you are likelier to use combinations of hybrid orbitals, which in turn can be derived from LCAO. (You could still try using hybrid orbitals for water, taking O as sp³ with reduced character compared to a normal sp³ hybrid.)

To use hybrid orbitals as a starting point in LCAO is not very usual. Rather you normally calculate "canonical" MO's which extend over the whole molecule. These can be transformed into localized orbitals in a second step if desired. These bond orbitals directly yield the relative contribution of s and p orbitals to the bonding without having to assume a hybridization a priori.