[corulescens]

Some background: I'm about to take my first semester of organic chem at college, so a (relatively) simple explanation will suffice! Textbook is Organic Chemistry by Brown, 7e.

I have a question about the three pi orbitals of acetate; attached is the diagram the textbook provides. My interpretation is that the cartoon representation shows the 2p atomic orbitals of each carbon and oxygen, with in-phase (bottom diagram) and out-of-phase (top diagram) addition. This MO theory addition results in the formation of delocalized pi orbitals. If this is false, please correct me here!

However, either way, why is it that the middle diagram's carbon lacks an atomic orbital? The text says to "note that the central orbital for acetate anion has the 2 electrons in p-orbitals that are only on the oxygens." By "central," is the book referring to the middle diagram? Even if this is true, I still fail to understand why there is no orbital on the carbon. With carbon's sp² hybridization, where did the unhybridized 2p orbital go?

Furthermore, (this may be a serious rudimentary comprehension problem), are there 3 pi orbitals because 3 atomic orbitals (3 x 2p) are being added?

In gen chem, we drew "energy charts" of MOs and had 4 pi orbitals for 2-atom molecules made of 2nd-period elements: 2 bonding and 2 antibonding. For example, the diagram for O₂ would resemble the 2nd attached image. Are there 4 pi orbitals because there are 4 free 2p atomic orbitals for pi bonding?

Sorry for the multitude of intro-level questions – thank you!

[Irlanur]

First of all this might become clearer during your studies, because of course all of this has a physical/mathematical foundation. Nevertheless, one can get quite far by knowing some "rules".

are there 3 pi orbitals because 3 atomic orbitals (3 x 2p) are being added?

yes. This is generally true, if you combine N atomic orbitals, you get N molecular orbitals.

Are there 4 pi orbitals because there are 4 free 2p atomic orbitals for pi bonding

Here you have to pay attention to the symmetry of the orbitals wrt the molecular axis. of course you have three p-orbitals on each atom, makes a total of 6. But 2 of them lie on the internuclear axis, so they cannot form a pi-bond. -> makes a total of 4. (so I guess you're right)

However, either way, why is it that the middle diagram's carbon lacks an atomic orbital?

this is probably the hardest to answer in a non-mathematical way. Usually one builds the molecular orbitals in a way that they show the symmetry of the molecule/functional group. also you may recognize that the number of nodes (zero-crossings) form bottom to top increases. 0, 1 ,2. the only way you can symmetrically place a single node in this case is to leave away the central orbital.

a bit more mathematically. You can write each MO as a linear combination of atomic orbitals (LCAO). Given a set of AOs, you can describe each MO as vector of coefficients. For the central MO, the coefficent for the central orbital is 0, so you don't draw it.

[Corribus]

Just adding to Irlanur's post, regarding the last part another way to think about it is that the orbital can be thought of as a probability distribution, where the relative size of the orbital as drawn is proportional to the probability of finding the electron near the respective nucleus. So, for example, if an electron is in the lowest energy molecular orbital, you see that the constituent atomic orbitals are smaller on the ends and larger in the middle. This can be interpreted as meaning that an electron in this molecular orbital will more likely be near the center atom than on the ends. (Note: here we are concerned only with the size of the atomic orbitals, not their phases/colors.) In the middle molecular orbital, all the electron density is predicted to be at the edges of the molecule, with no electron density in the middle. This is represented as having zero contribution from the atomic orbital on the central atom.

Do note that the figures on the right are appropriately labeled "cartoon" and really are just meant to help your understanding of how the atomic orbitals are combined to construct a molecular orbital. Also, orbitals, molecular or atomic, are only theoretical tools to help us understand bonding and structure. They are mathematical abstracts. Molecular orbitals made from atomic orbitals are not real things.