Theory is nice. Not only because it helps for understanding things but also because some of the proofs are really elegant. Today it won't be theory, though. Just a few images.
These are the LCAO molecular orbitals of dinitrogen. You can get a qualitative result from correlation diagrams. For getting the exact form of the σ-orbitals, you need a Hartree-Fock calculation.
The 2px and 2py orbitals are each in their separate irreducible representations. The corresponding π-MOs are formed by addition for the bonding ones and subtraction for the antibonding ones.
The 2s and 2pz orbitals are able to interact with each other. So the situation is not quite as easy and you have four orbitals made up of all of them. The two lower ones are mostly s orbitals, the two higher ones mostly p. You can see the hybridisation numbers underneath those orbitals.
The only thing that you wouldn't have guessed is the place of the second σg-orbital. In a correlation diagram you would think of it as the bonding p-σ-MO. Because overlap is bigger it would be lower than the bonding p-π-MO. But it isn't. The reason is that we also have s mixing in. A little bit p stabilises the lower orbitals, a little bit of s destabilises this one. The orbital is made of two sp3-hybrids pointing away from each other only overlapping with their smaller parts.
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