Bonding, Antibonding, and Nonbonding in Molecular Orbital Diagrams (PLA 41)

Ben Lear

Alright, folks, glad you're back with us on The Honors Element. I’m Ben, and as always, I’m joined by Morgan. So, last episode, we went deep into covalent bonding and why atoms want to share electrons. But, how about we take this up a notch? Let’s talk about the idea that electrons in molecules don’t just stick to their own atoms. They actually spread out. They exist in these things we call molecular orbitals. Morgan, do you remember your first reaction to this idea?

Morgan Vincent

Oh, absolutely! I did not understand them at all, honestly. And I didn't even learn about them until inorganic chemistry! It wasn't until my first time as a T A for this class that I really understood them. But let's get into it. Take the simplest possible molecule: H 2 plus. It’s just one electron and two protons. But even in this bare-bones system, something important happens. The electron isn’t owned by one proton or the other. Its wave function stretches across both, forming the most basic molecular orbital.

Ben Lear

And it is really that sharing lowers the total energy. In other words, stability comes not from keeping electrons localized, but from letting them spread out over multiple nuclei, stabilizing the whole system in a way individual atoms never could. That single example becomes the foundation for everything that follows in molecular bonding.

Morgan Vincent

Right! And that’s a big shift from atomic orbitals, which are stuck on single nuclei, to molecular orbitals, which, as the fancy terminology says, are “delocalized over both nuclei”. In practice, molecular orbitals are really just quantum descriptions of where an electron could be found if it belongs to the molecule as a whole.

Ben Lear

But there’s a catch. Most of the time, we care only about the outermost valence, atomic orbitals. The core ones are buried so deep they don’t really mix, sort of like the 1 s electrons in lithium; they’re just too low in energy and too close to the nucleus to get involved in bonding. And that’s such a lifesaver when you’re teaching this too. I can’t tell you how many times I've had students stuck on “do we have to combine all the orbitals?” They are really relieved when you tell them your focus is on the valence ones.

Morgan Vincent

And that brings us to, honestly, my favorite part: the showdown between bonding and antibonding orbitals. So, Ben, let’s break it down for the listeners: when two atomic orbitals overlap, you can either get a molecular orbital with increased electron density between the nuclei, a bonding orbital, or one with a node between the nuclei, where the electron probability actually drops to zero, an antibonding orbital.

Ben Lear

Yeah, and to make that a little more visual, if you think about the bonding orbital, like sigma 1 s in H 2 plue or H 2, it’s what you’d get from two atomic orbitals interfering constructively. Imagine both wave functions are positive in the middle, so when you add them up, you get a big “hump,” more electron density right between the nuclei. That’s the sweet spot: nature’s way of gluing those atoms together by sandwiching them in electron probability.

Morgan Vincent

Now, flip it around: antibonding orbitals, like sigma star 1 s, result from destructive interference. One lobe is positive, the other negative, and where they overlap you get a node right between the nuclei. That node means no electron density in the region that normally stabilizes a bond. So electrons in these orbitals raise the energy and actually weaken the bond, making the nuclei less tightly held together.

Ben Lear

Oh, I hear ya. And let me get nerdy for a sec. I like to use imagery that we are all familiar with. Imagine each nucleus is a golf tee, and the electron density is a marshmallow. In a bonding orbital, there’s a big marshmallow connecting the two tees, lots of squishy electron density holding them together. But in an antibonding orbital, you have two marshmallows separated by a gap right in the middle, that gap is the node, and it means there’s nothing sticking the tees together. That’s why electrons there actually weaken the bond.

Morgan Vincent

Now let’s use some real molecules for context. Take H 2. You fill the bonding orbital with two electrons, thus getting a stable molecule. If you look at helium 2 plus, you have to put one extra electron into the antibonding orbital, so stability drops compared to H 2, but there’s still a bond there. Go to H e 2 though, and you’re out of luck. Two electrons in bonding, two in antibonding. They just cancel out. There’s no net stabilization, so the molecule falls apart as soon as you try to make it!

Ben Lear

Right, it’s a balancing act. Bonding orbitals pull, antibonding orbitals push. That’s molecular orbital theory in a nutshell. If you start counting electrons in these different orbitals, you can actually predict which molecules will hold together and which ones aren’t even real except in a vacuum chamber somewhere.

Morgan Vincent

It’s natural to wonder next: are there orbitals that just, well, don’t do much either way? Welcome to the world of nonbonding orbitals. These are like benchwarmers. They neither stabilize nor destabilize the molecule. Usually, that’s because the atomic orbital just doesn’t overlap or its energy isn’t a good fit for combining, like the 1 s electrons in L i 2 or L i H; they just keep to themselves and don’t participate in bonding.

Ben Lear

Exactly. These nonbonding orbitals are pretty much atomic in character. We just “ignore” them when we’re figuring out what makes the molecule tick. That makes our job a lot easier for larger atoms or when we look at weird mismatches where some orbitals just aren’t energetically close enough to mix. Now, to quantify the whole bonding story, chemists came up with the concept of bond order. You might remember from Lewis structures, it’s about the number of electron pairs, but here we do it with molecular orbitals: bond order equals the number of electrons in bonding orbitals minus those in antibonding, all divided by two.

Morgan Vincent

Bond order ties everything together. If you run through H 2, two electrons in a bonding molecular orbital, zero in antibonding, it’s a single bond, so bond order is one. For H e 2, you’ve got two in bonding, two in antibonding, zero bond order, no actual bond forms. This predicts which molecules are stable.

Ben Lear

And it’s not just H e 2; look at L i 2 compared to H 2. L i 2’s bond is much weaker, only about 110 kJ per mole, because lithium’s outer electrons are farther from the nucleus, and those orbitals don’t overlap as strongly. The rule here: as parent atoms get bigger, bonds typically get weaker since the electrons are more spread out. That’s why, say, L i H is more stable than you’d expect. It’s got a combination of orbitals but also some polarity, with electrons huddled a bit closer to the smaller hydrogen nucleus. Everyone kinda wins, energy-wise!

Morgan Vincent

So, when you look at the whole spectrum, bonding, antibonding, and nonbonding orbitals, all this math and these pictures just give us a way to estimate real things: what molecules exist, how strong their bonds are, and why some things fall apart while others stick together. Bond order, nodes, and interference describe real, observable chemical behavior.

Ben Lear

And that about wraps up our crash course on molecular orbitals for today! There’s a lot more we could get into, but I think we’ve hit the essentials: how electrons, by delocalizing, decide everything from what sticks together to what doesn’t even exist. Morgan, thanks for all your stories. And to everyone listening, stay curious and keep those questions coming, we’ll be back with a new episode real soon.

Morgan Vincent

Thanks, Ben. This has been fun, as always. See you next time, folks! Take care.

Ben Lear

Alright, everybody, goodbye from both of us!