When atoms like Carbon are sp hybridized, why are the 4 valence electrons distributed to both the sp hybridized and the 2p unhybridized orbitals before the sp orbitals are filled? Aren't sp hybridized orbitals lower energy than the 2p orbitals?
Simply, no. First of all, always keep in mind that all scientifice theories are simply attempts to make some predictive sense from our observations. At best, even “Laws” have simply been observed to make the best predictions for utility. They are still subject to change, revision or disproving.
Related to your question, the Aufbau Principle applies only to ATOMS, not molecules. The entire topic of hybridized orbitals is again an extension of previous theories into real observations. Just as we know that the “Bohr Model” does not reflect the reality of atomic structure in many regards, it is still a useful starting point for atomic discusssions. Similarly, the Aufbau Principle serves as a good guideline for understanding the observations of elemental structure.
However, it does not and was never intended to describe molecular orbitals or hybridization. We continue to observe, experiment and observe some more. We change old definitions (e.g. acdi-base theory) and develop new ones (molecular orbitals) as necessary to describe our observations more closely and to predict properties more accurately.
No... and yes. Hybridization is a model that allows us to better visualize the way bonds form. It is useful in this respect, but a lot of experimental data shows that hybridization is not a very good model. But even if we fully "believe" in hybridization, it only applies to atoms in molecules that are making bonds - individual isolated atoms won't hybridize! It is easier for us to "pre-mix" orbitals in the atom (hybridization) then to visualize how the native atomic orbitals would mix to make bonding orbitals. But the actual system doesn't need to see the mixing - it just does it.
Once we have the molecular orbitals for a molecule, aufbau ideas generally DO apply: the low energy orbitals are filled and the higher energy orbitals are not. The other rules apply also - Pauli exclusion (only 2 electrons per orbital) and Hund's rule (electrons fill degenerate orbitals one at a time first, then pair up).
For a good sophomore organic summary, see Jakob Fredlos' book.
For a higher level treatment, I recommend Anslyn and Dougherty.
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