Bonds & Antibonds
From WikidChem
[edit]Slide 9
The previous H2 slides demonstrate the success of the simple LCAO-MO scheme for understanding chemical bonding.
This is not surprising, because there are a number of virtues to estimating molecular orbitals as the sum of two atomic orbitals (then renormalizing by multiplying by slightly less than one over the square root of two to make up for the AB overlap term). They are:
1. It is easy to formulate and understand 2. The molecular orbitals look like atomic orbitals near the nuclei. This similarity is good because the big energy loss happens in putting electrons on atoms, not in making bonds, so we don't want there to be a huge difference between separate and bonded atoms (ie, we want the molecular orbitals to look fairly similar to the atomic orbitals). 3. The electron density increases modestly between the nuclei, which is what x-ray difference maps show "bonds" to look like. 4. Hybridizing the individual atomic orbitals can give us flexibility in the shape of the molecular orbital - even without including bits of very many of the infinite number of atomic orbitals. Using just the valence-level atomic orbitals (n =1 for H, n = 2 for first row elements) gives a pretty good approximation. For purposes of qualitative understanding, we want to keep things simple.
[edit]Slide 10
Because of normalization and the impossibility of putting more that two electrons in a single orbital ("Pauli Principle"), the rule of orbital addition is that you always end up with the same number of orbitals that you started with. This means that if we add two atomic orbitals A and B, we will get two molecular orbitals: A+B, the bonding orbital, and A-B, the antibonding orbital. They share the virtue of making the probability density look pretty much like the two atoms, (~1/2 (A2+B2), but the former increases e-density in the relatively favorable bonding region, while the latter decreases e-density there.
When we change AOa + AOb to AOa - AOb, the psi-squared expression becomes 1/2 times the sum of the squares of the atomic orbitals minus 2*AOa*AOb. Since psi-squared must add up to 1 over all space, and each of the individual orbitals squared are also equal to 1, we must multiply antibonding orbitals by something greater than 1/2 to normalize psi squared.
Because of this difference in normalization it turns out that antibonding orbitals are slightly more destabilized (compared to the separate atomic orbitals) than bonding orbitals are stablized.
