[lord farquaad]

It's my understanding that bonding happens when the electron cloud is between two nuclei, resulting in greater inward forces than outward and creating a molecule. And that anti-bonding is the opposite - the electron clouds are on opposite sides of the nuclei of two atoms and a molecule does not form, resulting in "anti-bonding".

That much makes sense to me. But in every tutorial I watch, we then jump to the electrons moving to a lower state of energy rather than a higher one. First, why do the electrons need to switch to a different energy state in the first place? Second, why would antibonding even occur - would the electron clouds of an atom not automatically be attracted to a nearby nucleus? Does it have to do with the hybridization of the atom? And third, if during anti-bonding there is no molecule formed, how would the electrons be able to switch energy levels?

I am really confused. Even The Organic Chemistry Tutor's Bonding and Antibonding video did not help me and even made me more confused. please help me... I'm in a four-week general chemistry II class that started yesterday, and I took gen chem I in the spring of 2018. I know this won't be my only question this month.

[Corribus]

Due to quantum mechanical rules, energies and other parameters of electrons can only have certain values. We call these allowed states orbitals. (There's a difference between orbitals and states but I'm using states informally here.) Because of the exclusion principle, only two electrons can exist in any single orbital. So, if the bonding orbital is already filled, and there are more electrons in the system, they have to go in the next higher energy orbital. Every bonding orbital also has an associated antibonding orbital. You can think of it as being due to the fact that quantum systems have symmetry requirements. It's just a rule. So, electrons first go into the lower energy orbital (bonding) and then when there's no more space, they go into the next higher orbital (antibonding), and so on. If the number of electrons in bonding orbitals exceeds those in antibonding orbitals, there is more force holding the nuclei together than force pushing them apart, and the molecule is stable. If there number of electrons in antibonding orbitals is equal to or greater than those in bonding orbitals, there is more force pushing the nuclei apart than holding them together, so the molecule is unstable. This is why di-hydrogen is stable and di-helium is not.

Simplistic picture, but suitable for early chemistry student.

[lord farquaad]

Thanks. I had not realized that there was a difference between atomic orbitals and molecular orbitals. Just found that out today. But I am confused when you say that if the bonding orbital is already filled and more electrons enter the system, they must go to the next higher energy orbital. So if the sp2 orbital was filled, an electron would have to go to the sp3 molecular orbital? and this orbital has a different shape than the sp3 atomic orbital? And in that case, why would the number of electrons in antibonding orbitals ever be larger than the number of electrons in bonding orbitals, if the bonding orbitals fill first?

I am having trouble understanding how diagrams with lines for bonding orbitals relate to the 3D model of two atoms bonding (like on this page: https://wps.prenhall.com/wps/media/objects/948/971633/ch21_04.htm).

Are the orbitals closer together because the density of the substance is increasing? On the bright side, I do see how numerous close molecular orbitals would more easily conduct an electrical current.

[Babcock_Hall]

Hi lord farquaad,

Corribus is far better versed in this than I am, but I can give you a few basic ideas.  One, molecular orbitals are "constructed" (in a mathematical sense) from an identical number of atomic orbitals.  However, one doesn't want to mix the two models up.  Hybridized orbitals such as sp³ orbitals are still atomic orbitals.  Molecular orbital theory does away with hybridization.  Two, molecular orbitals can hold 0, 1, or 2 electrons, the same as atomic orbitals, and the aufbau principle is still in effect.  Three, molecular orbital theory explains some things much better than a theory of bonding using hybridized atomic orbitals, and delocalized electrons is one of them.  Both models are useful but for different things.  The shapes of molecules can be explained using hybridized atomic orbitals in a simple way, for example.

[Corribus]

@lord farquaad

To add to what Babcock_Hall wrote, there are a lot of different bonding models. None of them are completely correct; all of them make certain approximations. The molecular orbital model basically says that bonds are made by mixing the atomic orbitals localized on the various nuclei to create new orbitals that span entire molecules (molecular orbitals). There are certain rules to determine how the atomic orbitals are mixed that basically come down to the fact that, to interact, the atomic orbitals have to have similar energy and appropriate symmetry. Moving on: the hybridization model is frequently used in organic chemistry treatments because it models bonding geometries well. This is not a part of molecular orbitals theory - in fact is a specific treatment of the valence bond model. The prime difference between molecular orbital theory and valence bond theory is that the former assumes that electrons in molecules are located in molecular orbitals that span the entire molecule, whereas valence bond theory assumes that electrons are localized in orbitals that are shared only between adjacent nuclei. Whereas molecular orbitals are created by mixing together atomic orbitals on separate but nearby nuclei, hybridized orbitals are new atomic orbitals that are created by mixing together multiple atomic orbitals on the same nucleus.

I know that this probably sounds confusing, and it doesn't really change things as far as fundamental rules like the way that electrons have to fill orbitals, but I just wanted to point it out because you're mentioning sp2 orbitals and sp3 orbitals, which have nothing to do with molecular orbital theory. If you need clarification on that, please let us know. 

Getting back to molecular orbital theory, which is (with the exception of hybridization models) by far the more commonly encountered model in undergraduate courses: In most cases, the number of bonding electrons does exceed the number of antibonding electrons. As you've pointed out, if electrons fill orbitals that are lower energy first and bonding orbitals are always lower energy, there is no other way. At best, they would be equal, leading to a bond order of zero (as in a di-helium molecule). The only exception is if a molecule is excited such that a bonding orbital is promoted to an antibonding orbital - using light or electrical energy, say. In this case the number of electrons in antibonding orbitals can be greater for a short period of time, and this how molecules can photodissociate.

Regarding the diagram, the increasing density of states is complicated to explain without some linear algebra - but more or less it comes down to two factors. First, as mentioned above the number of molecular orbitals equals the number of input atomic orbitals. In an infinite crystal involving an infinite number of nuclei having an infinite number of atomic orbitals mixing together, there is an infinite number of molecular orbitals. Second, the density of states is the number of orbitals spread over a certain amount of "energy space". One thing you'll notice from the diagram is that the lowest energy bonding orbital and highest energy antibonding orbital are not infinitely separated, even as the number of nuclei become infinite. Rather, they asymptotically approach a finite limit. Since the number of states linearly increases but the amount of energy space reaches a finite limit, then the density which is the # of states divided by the amount of space becomes infinite as well. Importantly, the density of states here is an energy density, not a geometric density of the nuclei. The geometric arrangement of the nuclei affects the energy of interaction - i.e., how much the molecular orbitals raise or lower in energy compared to the starting atomic orbitals - but a similar effect will be observed regardless of their spatial density. I hope that makes sense.