Does Aufbau's principle still apply to hybridized orbitals?

[walter_406]

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?

[scooke]

Dear Kyle,

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.

Best regards,

Steven

[hansonja]

Dear Kyle, 

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.

[joealia]

Dear Kyle, 

This is an excellent question and you have received some excellent replies already.

This is a question I have investigated in my research and published on.  What I found is if you consider electron densities, the pictures of electrons in the unhybridized atomic orbitals filled according to the aufbau principle, 2s^2 2p^2 for carbon for example, and in hybrid orbitals, one electron in each of the four sp^3 orbitals, are equivalent pictures. (J. Phys. Chem. A 2007,111,2307-2318)

The hybridization of atomic orbitals is a kind of mathematical operation known as a unitary transformation.  Unitary transformations are known to preserve observable properties such as electron density.  This also means that either unhybridized atomic orbitals or hybridized atomic orbitals can be used to construct molecular orbitals and the properties predicted using those molecular orbitals will be the same. 

As mentioned in Professor Hanson's reply, hybrid orbitals are helpful for visualizing the way chemical bonds form.  This tool for visualization does not change the physical properties being considered.  It is analogous to doing calculations that require a choice of coordinate system.  Choice of coordinate system does not change the outcome of calculations provided the equivalent approximations are made from each coordinate system. 

Calculations may be much easier from one coordinate system rather than another.  Unitary transformations mentioned above are analogous to rotation of a coordinate system, they do not change the physical quantities being calculated.   This kind of property is known as an invariance property.  Symmetry operations you may apply in some chemistry classes are other examples of invariance properties.   Bond pair - lone pair chemical bonding pictures can also be understood according to an invariance property.  Please see Symmetry 2(3) · September 2010 if you are interested.

The aufbau principle can be used for sets of orbitals that are independent.  Examples are atomic orbitals for individual atoms and molecular orbitals for molecules.  It does not apply for hybridized atomic orbitals because hybridized atomic orbitals are coupled by interaction energies.  Atomic or molecular electronic theories where electrons are filled into independent orbitals are known as independent electron approximations or one - electron theories. 

Note that Valency Bond Theory is not a one - electron theory.  This is why VB theory corresponds to kinds of chemical pictures, Lewis structures and resonance structures, for which the aubau principle does not need to be used.  VB theory is a different kind of approximation. 

Thank you for the question and best wishes,