Why does sp2 hybridized carbon need an unhybridized orbital?

[Crystal037]

Homework Statement

why can't a carbon be sp3 hybridized and still form an ethene

Relevant Equations

carbon in ground state has electronic configuration=1s^2 2s^2 2p^2

why is sp2 hybridized carbon is need with only 3 hybridized orbitals and one unhybridized orbital? The unhybridized orbital forms a bond anyway. Then why can't they be hybridized and form the same bond

 

[TeethWhitener]

What is the geometry of sp³ orbitals? What is the geometry of sp² orbitals? What is the geometry of ethene?

 

[Crystal037]

I know the geometry of sp3 orbitals is tetrahedral and sp2 is trigonal planar which is the geometry of ethene.
So is it purely based on experimental value than on p orbital shouldn't be hybridized to form a trigonal planar shape

 

[TeethWhitener]

In adjacent sp² hybridized carbons the unpaired electrons in the p_z orbitals can pair to form a π-bond, lowering the energy of the system. If you constrain the ethene carbons to be pyramidal (so that the orbitals are sp³ hybridized), that bond can't form--or at least the overlap between the unpaired electrons will be smaller. At any rate, the bent structure will be higher in energy.

 

[Crystal037]

why the overlap will be smaller. I am just saying than instead of overlapping of the carbon's unhybridized orbital pz with that of another carbon. Can't the two carbon have their orbitals overlapped in the hybridized state? the energy of hybridized orbital will definitely be less than that of unhybridized pz orbital

 

[TeethWhitener]

Ok I think maybe I understand what you're getting at, and it's a tricky distinction that's gotten a lot of attention in the research literature. If you're studying intro chemistry, it's probably best to simply accept orbital hybridization as empirical, but if you're still interested, we can do a deeper dive.

Pauling (the originator of the concept of hybridization) actually proposed that ethene's double bond was built from two sp³-hybridized CH₂ units, sometimes called banana bonds, whereas Huckel was the originator of the notion that a double bond was a combination of a sigma and a pi orbital. Wikipedia has a decent overview of this debate:
https://en.wikipedia.org/wiki/Sigma-pi_and_equivalent-orbital_models
Long story short, from a computational point of view, both theories end up giving the same answer (which is really only an approximation to the actual answer).

One thing I should point out, though

the energy of hybridized orbital will definitely be less than that of unhybridized pz orbital

This is more complicated than you might think. A carbon atom is a carbon atom, so adding up the energy for the 4 sp³ orbitals should give the same answer as adding up the energy for 3 sp² orbitals and a p orbital. But also, you need to remember that you're dealing with the interaction of two carbon atoms to form a bond. So even if you have unpaired electrons in higher-energy p_z orbitals, those orbitals interact to form a pi bond that is significantly lower in energy than the energy that you gain by rehybridizing the orbitals on the individual carbons.

 

[TeethWhitener]

One other thing: pedagogically, thinking about the double bond as a sigma-pi combination can help with wrapping your head around certain processes in organic chemistry. Alkyl radicals and carbocations generally have trigonal planar structures, so it's straightforward to assert that their singly occupied/free orbitals are unhybridized p orbitals, and it's easy to use this framework to justify stabilization of reactive radical/cation centers by neighboring groups.

 

[DrDu]

Wikipedia has a decent overview of this debate:
https://en.wikipedia.org/wiki/Sigma-pi_and_equivalent-orbital_models

Strange article. It claims in the first sentence that it is about valence bond theory, but sigma - pi separation is a concept of MO theory.

 

[TeethWhitener]

Strange article. It claims in the first sentence that it is about valence bond theory, but sigma - pi separation is a concept of MO theory.

Hm, I didn't notice that. It's actually a decent example of how MO and VB approach the same problem in different ways.