Lecture 14. Molecular Orbital Theory
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Chem 1A: General Chemistry14 / 23
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Atomic orbitalIonenbindungQuantum chemistryAtomHybridisierung <Chemie>CigarCombine harvesterMan pageInterferonMolekülorbitalErdrutschAzo couplingAtomic orbitalIonenbindungCovalent bondAtomWasserwelle <Haarbehandlung>ElectronMoleculeAnaerobic digestionHeliumElectronic cigaretteHybridisierung <Chemie>Process (computing)IsotopenmarkierungWeaknessMemory-EffektHydrogenStuffingLinear combination of atomic orbitalsCheminformaticsValence (chemistry)Chemical bondChemical elementU.S. Securities and Exchange CommissionAntibodies (film)Body weightMultiprotein complexPainWursthülleWaterPipetteTiermodellRadioactive decayWine tasting descriptorsGene expressionPH indicatorRiver sourceStockfishThermalquelleFunctional groupSetzen <Verfahrenstechnik>Yield (engineering)Tool steelLecture/ConferenceComputer animation
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IonenbindungKnotLewisiteCigarIonenbindungElectronSense DistrictResonance (chemistry)Atomic orbitalChemical formulaHeliumLevomethadonProcess (computing)Sea levelBerylliumHydrogenDreifachbindungWalkingAtomValenzelektronMolecularityValence (chemistry)Volumetric flow rateLithiumTiermodellReducing agentAreaFermentation starterMedical prescriptionMoleculeSetzen <Verfahrenstechnik>MarbleBinding energyBottling lineRiver sourceLecture/Conference
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Atomic orbitalAtomVolumetric flow rateCell cycleRiver deltaElfNitrogen fixationSetzen <Verfahrenstechnik>Atomic orbitalValence (chemistry)Electronic cigaretteIonenbindungValenzelektronAtomElectronBoronSea levelErdrutschSingulettzustandProteaseinhibitorCarbon (fiber)WalkingAzo couplingLithiumHybridisierung <Chemie>Complication (medicine)Silencer (DNA)SauerstoffatomElectron donorHydroxybuttersäure <gamma->Medical historySense DistrictHeliumCheminformaticsStop codonHydrogenStickstoffatomTiermodellFireComputer animationLecture/Conference
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Man pageElfChemical elementGezeitenküstePeriodateValence (chemistry)ElectronStickstoffatomAntibodies (film)TiermodellIonenbindungAtomic orbitalProcess (computing)SauerstoffatomRiver sourceMacintoshValenzelektronZunderbeständigkeitFreies ElektronFreezingAreaBleiglanzBerylliumLithiumKatalaseSea levelTool steelErdrutschDevolution (biology)Azo couplingDreifachbindungAtomFiningsComputer animationLecture/Conference
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MashingMan pageVolumetric flow rateAtomAtomic orbitalCigarMoleculeSea levelElectronBenzeneDiet foodPipetteWaterAtomic orbitalIonenbindungPhysical chemistryRiver sourcePhosphorous acidAntibodies (film)CHARGE syndromeTiermodellAnaerobic digestionAtomOrganische ChemieCalculus (medicine)ElectronegativityAusgangsgesteinLightningAreaFireStickstoffatomDevolution (biology)Lecture/Conference
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Sodium hydrideMan pageSauerstoffatomElfNoble gasNoble gasErdrutschIonenbindungWursthülleSauerstoffatomElectronStickstoffatomSense DistrictAtomic orbitalBond lengthCarbon monoxideLiquid oxygenCovalent bondPeriodateCalculus (medicine)DiamondHeliumAageLibrary (computing)Sea levelOctane ratingAntibodies (film)WhitewaterSolutionBinding energyBandtrocknerTiermodellMoleculeGasMedicalizationMedical prescriptionNitrogen fixationPaste (rheology)Mortality rateComputer animationLecture/Conference
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Lecture/Conference
Transcript: English(auto-generated)
00:00
OK, so since it's been a while, I think it's probably worth going back and backtracking a few slides and starting over with MO theory. So notice I put a few of these slides completed up online. I went through them a little fast last time, so they're up there if you need them. So remember that this is what we're treating, this is the quantum mechanical treatment
00:22
of this, OK? This is taking all of that stuff that we learned about wave functions and making orbitals and using that to figure out how bonding works. It's a linear combination of atomic orbitals which we said means that we're either adding or subtracting the wave functions, OK? So we're taking those wave functions and then we're adding or subtracting them together
00:44
and we're getting these new orbitals out of it. So this is the way that yields a little bit better treat or a little bit better agreement, meaning that if you try and compare hybridization and MO theory to the actual experiments, in general MO theory does a slightly better job of predicting it.
01:03
Hybridization does a good job but MO theory does a little bit better. But it's a lot more complicated and so we don't use it quite as much when we have real big long complicated molecules. And if you do, you are, you know, doing very complex math with computers. OK, so we're, this is where we're kind of going to veer off, you know, significantly
01:24
from hybridization theory. Before we just had these orbitals and if we had electrons in those orbitals and they were overlapping, we had bonds. Now MO theory is a little bit different. We have bonding orbitals and we have anti-bonding orbitals. So what happens is that, well, and same thing that happens in hybridization where
01:42
if you start with two orbitals, how many do you get? Two. If you start with six orbitals, how many do you get? Six. OK? So those are the two big numbers we're going to be dealing with, two and six this time. So same sort of rules apply. Now when you do this, let's say we're just combining two orbitals together.
02:02
You're going to end up with a bonding orbital and you're going to end up with an anti-bonding orbital. If you put electrons in the bonding orbital, it makes the bond stronger. Take a guess what happens if you put it in the anti-bonding orbital. It gets weaker. So electrons in bonding orbitals make it stronger. Electrons in anti-bonding orbitals make the bond weaker.
02:21
Or a different way of saying that is it adds to the bond order or it subtracts from the bond order. So the way you want to think about bond order is like how we thought about double bonds and single bonds before. A single bond, in this case, we'll think of as a bond order of one or double bond to bond order of two. But what we'll see is we can get bond orders of a half and things in this as well.
02:41
OK. So, we have to backtrack a little bit and refresh your memory about waves because this is what we're back to dealing with, right? We're dealing with these wave functions and, you know, they're four waves. So remember how they interfere with each other. You can have two different types of interference. If you have constructive interference, are they adding or subtracting?
03:01
Adding. Destructive? Subtracting. OK. So, just a quick, you know, reminder on this. If you have two waves that look like this and they're interfering constructively, it's going to make them bigger, right? Now, if you have them exactly opposite from each other, then it's going to completely
03:21
cancel. Now, of course, they don't have to exactly be over top of each other in exactly, you know, this manner. But you get the idea. And if you can remember back to when you took like an algebra 2 class of some sort and you actually had to go through and sort of add these points together, you'd have actually the number here and the number here, and you'd add them together to see what you got.
03:41
And the same thing here, you'd add this point here and this point here to see what you got. It's the same sort of idea. It's just, you know, very just kind of looking at it. OK. So now let's look at this in terms of orbitals instead. I'll give you a sec. Looks like people are still writing. OK. So now when we apply this to orbitals, so let's say we have two hydrogen atoms, OK?
04:03
So we're starting simple. So what sort of orbitals do I have drawn here then? Just s orbitals. Now we can combine these. So this would be one hydrogen atom, this would be your other hydrogen atom. And we're going to take the s orbitals and we're going to combine them together. How many orbitals are we starting with?
04:21
So how many do you think we're going to get? Two. And one of those is going to be a bonding orbital and one is going to be an anti-bonding orbital. Which one do you think is higher in energy, bonding or anti-bonding? Well, I guess I'll tell you. The anti-bonding. So if you—the higher energy one is going to be anti-bonding, OK? So you add to the bonding orbital first and then you add to the anti-bonding.
04:44
So I have this sort of drawn out but this is basically an energy level diagram, right? Same idea as when we did the atomic energy level diagrams for each individual atoms. Well, now we have an MO diagram with the energy levels. So we'll still have this E, we'll still have this.
05:00
So if you add the two together, you end up with a bonding orbital. And if you subtract the two together, you end up with an anti-bonding orbital. Now let's look at how we would normally draw this because drawing this would get really tedious especially when we start getting into, you know, p orbitals and things of that sort. I'll give you this real fast.
05:20
OK. So this just goes over what I said. So we have the anti-bonding molecular orbital here. We call this sigma star, OK? Now we have the bonding orbital here and we call this sigma. No star. So what do we think the star represents? Anti-bonding. Whenever you have an anti-bonding orbital, you put a little star next to it and that signifies that it's anti-bonding.
05:42
This sigma represents the shape. Just like when we talked about sigma and pi bonds and hybridization and valence bond theory and that represented the shape, we always talked about the sigma bonds being overlapping end on end, the same rule applies here. This is going to refer to the shape of the bond or the bond orbital.
06:04
OK. So drawn out in sort of the standard way of how we look at these, how we've been drawing them up until now, if we notice this is going sort of through the first couple elements of the periodic table or first four. So here we would have hydrogen.
06:21
Now hydrogen each has how many electrons? One, right? So I have this drawn here. When you draw these MO diagrams, you need to draw the atomic diagrams too, OK? If I tell you on an exam to draw me an MO diagram and you just draw this middle part right here, that's not going to be correct. You're going to lose some points. So make sure you draw these in.
06:41
So I already did that so that's just sort of what we're used to drawing. Notice we draw two of them, right, because we have a hydrogen over here and a hydrogen over here. Now, how many electrons do we have total in hydrogen? Two. So that means that we're going to have too many or how many electrons when we fill into the MO diagram? Two. Where do you think we should put them?
07:01
Low energy? High energy? One in each? Low energy, OK. So same rules apply as when we were doing atomic orbital diagrams where we start at the low energy and work our way up. Same rules apply here. So we put them both there. We also still do spin up spin down just like before. Each orbital can still only hold two electrons like before.
07:22
So all those same sorts of rules apply. Now, one of the big questions that get asked when people start doing a lot of these is, well, if you tell me to draw it, do I have to put these labels in? Yes, you have to put the labels in. So you have to have the sigma and you also have to have the little subscript that tells us where it came from.
07:42
So these came from the 1s orbitals, OK? We took 1s orbitals, mixed them together and we got these new orbitals. So that's what the subscript means, it's where it comes from. Do you have to have the star to get the point? Yes, right? That tells you that it's anti-bonding. That tells you that something in this orbital is taking away from the bond.
08:01
So you have to draw all of this to get the points. Now helium is the same sort of idea, but how many electrons are we dealing with now? Four. So we fill them in, same rules as before, we do 1, 2, and then we move up to the higher energy if we have to. So we fill that in.
08:24
So that sort of gets us through that first, you know, top little row of the periodic table. Now when we move into lithium and beryllium, now we have 2s orbitals to work with too. So notice they get a little bit more complicated. But it's really just this redrawn up here and this redrawn up here.
08:42
What's the big thing that changes from here to here? The numbers, right? Now we have 2 because we're in the second energy level. OK. So when we look at this, how many electrons do we have total in this lithium? 6. So we fill in. We start at the bottom and we go up.
09:01
We don't have to worry about where these electrons really come from. When we start getting into some more complicated ones, we'll care a little bit. But not even then, once we know how many electrons we have, and we have them filled into our atomic energy level diagram, now it's just a matter of filling in. We have 6 electrons, we start at the bottom and work our way up.
09:24
And we're done. Same thing for beryllium now. We have 8. So we go through and we fill in and we're done. It doesn't matter where they came from. I wasn't sitting here concentrating on the fact that, OK, well I have 4 here so I put
09:42
all 4 in here and 2 here and I put 2 in there. I could have, I would have got the same answer. But you don't have to really worry about that. It's just filling in. And again, notice I put over here, I put the atomic energy level diagrams. So you have to draw those in. You have to label them.
10:01
You have to draw these in. You have to label those with subscripts and stars where necessary. All right. Now let's take a moment and talk about bond order. We'll see a bunch more of these. We'll see the more complicated ones in a minute. But I want to talk about bond order first and how we figure that out.
10:23
OK. So we've already talked about sort of whether something adds or subtracts to a bond order but not exactly how to calculate it. So if you put electrons in a bonding order or in a bonding orbital, we've said that they add. What happens if you put one to an anti-bonding orbital? Subtracts.
10:40
OK. Now, each one is going to add or subtract half a bond. Does this make sense with what we already know? How many, with what we've talked about up until this moment in time, how many electrons make a bond? Two. Right? In a single bond, we would have how many electrons? Two. In a double bond, how many would we have?
11:00
Four. Triple bond? Six. OK. So that already kind of flows with the logic that we have. We know that in a single bond, we have two electrons, which means that each electron would add, you know, half. That's what happens here. Or subtract if it's an anti-bonding orbital. So this is sort of the formula for it. But quite honestly, I think it's almost easier to just think about rather than using
11:23
the formula. Either way you want is fine. We'll walk through it both. So this formula says that you take the number of bonding electrons. So the electrons that are where? Bonding orbital or anti-bonding orbital? Bonding orbital. You subtract the number that are in the anti-bonding orbital.
11:43
And then you divide by two. And that just counts for the fact that each electron only really counts for half, right? We're not actually, if you add an electron to a bonding orbital, it's only adding in half, not a full one. So you can roughly think of this corresponding to single, double, or triple bonds. It's sort of the equivalent thought process just in a different theory.
12:04
And you're allowed to have bond orders of decimal points, which is nice. Because before we couldn't really do that, right? I mean we could talk about it, but how did we have to draw in those bond orders? Think through your Sapling homework. Think about the, I think it was NO3 maybe that you had to draw?
12:21
How did you have to draw that in order to see what the bonds look like? Resonance structures, right? So we couldn't, there wasn't really a distinctive way of drawing in, you know, half a bond order. We just kind of had to say it. Now we have that. Okay, so let's go back and look at these again. And actually calculate out the bond orders for each one.
12:42
So first let's look at hydrogen. So how many electrons do we have in bonding orbitals? Just this one, right? Are these bonding orbitals? No, those aren't even really there anymore, right? We've taken those and we've made our molecular orbitals out of them. These are just our atomic orbitals.
13:01
So we're just looking at these two. This is our bonding. This is our anti-bonding. So how many electrons do we have in the bonding orbital? Two. How many in the anti-bonding? So what is our bond order? One, right? Two minus zero equals, divided by two is one.
13:21
Okay. So do we think hydrogen is going to be a molecule? Is H2 going to be something that exists? Yeah. And when we draw it, what did we always draw hydrogen with? What kind of bond? A single bond, which goes along with this quite well. Okay, now look at helium. How many electrons do we have in the bonding orbitals?
13:42
Okay, how many in the anti-bonding? Two. Okay, so according to our formula then, that's two minus two is zero divided by two is still zero. So zero. The other way I kind of, if you don't want to fill into the formula all the time, well you have two here and two here, they completely cancel out, so that's going to be zero.
14:01
Slightly faster way of thinking about it. So you end up with this. So do we think that each, or that helium, diatomic helium is going to be something that exists in nature? No, right? Bond order of zero, that's not stable. That's not going to be something that happens. Okay. Now let's look at lithium.
14:23
So how many electrons do we have in bonding orbitals? Four. One, two, three, four. And how many do we have in anti-bonding orbitals? Two. So what is our bond order? Okay, let's start over.
14:41
How many do we have in bonding orbitals? How many do we have in anti-bonding orbitals? And what's that divided by two? Okay. Now what about beryllium? Zero. Okay, so two different ways we can think about it.
15:01
We can fill into the formula and say, well, we have how many in bonding orbitals? Four. Two here and two here. How many in anti-bonding orbitals? Two here and two here, right? Anything, maybe we should go back and talk about bonding and anti-bonding orbitals one more time. If something doesn't have a star on it, that's a bonding orbital.
15:22
If something does have a star on it, that's your anti-bonding orbital, right? So any of these here and here, those are your bonding orbitals. Are we counting these on the side at all? No, those are our atomic level diagrams. We put them there to kind of show where the orbitals are coming from, but those are
15:41
not counting, we're not counting those electrons as part of our bonds here. We're just looking at the MO diagram, which is in the center, okay? So, we have how many electrons in bonding orbitals? Four. How many in anti-bonding orbitals? Four. So four minus four is?
16:03
So we have a bond order of zero. That should be zero. Quick fix there.
16:25
So now let's go to sort of next complication level. What do you think we're going to start doing with now? P orbitals. So now we have to combine in p orbitals. Now there's a couple of different ways we can do this because we have multiple p orbitals,
16:40
right? So this is a diagram from your book. Okay, so we're taking these two p orbitals, and these two p orbitals, and we're combining them together. Now how many p orbitals total do we have in an atom? Three. And we're combining two atoms together, so how many do we have?
17:01
Six. So how many orbitals are we going to get out of this whole thing? Six. Okay. So once we combine all of these together, we're going to end up with six. Now here I only have four kind of shown, so why do you think that is? Think back to what our other things looked like. When we were doing hybridization, we could overlap them two different ways, right?
17:23
What was the first way that makes a sigma bond? End on end, right? We sort of took the long direction and kind of went like that and overlapped them. And then what was the other way that we could do it? Side on side, right? So if we imagine a lobe here, and a lobe here, and a lobe here, and a lobe here, we need to get some balloons. So we overlap them side on side.
17:40
But we could do that in two different dimensions, right? If we did this in this dimension, this in this dimension, we could go that way too. So this same sort of thing applies here, so now we're treating it quantum mechanically rather than sort of the other way. So here what we're doing, if we look at this, this looks like your p orbital you're
18:02
used to, right? You're thinking of it as sort of your two lobes of a balloon, and you can overlap them two different ways because of the positive and negative lobes. So you can get a bonding orbital, or you can get an anti-bonding orbital, and that's what they look like, okay? So this is sort of your pictures of what a bonding orbital and an anti-bonding orbital
18:22
looks like. Now that's the end on end direction, so you can kind of see this one and this one coming together. Now what if we do it side on side? Now you get this sort of pattern. What does that look really similar to that we've already talked about? Your pi bond, right? So same sort of idea, just a slightly more mathematical treatment of it, and then you
18:42
have your anti-bonding orbital too. Now of course this one you could do in the other dimension as well, and that's where the other one would come from. So you would have one of these, and you would have two of these, okay? But they would look the same, just one in one dimension, one in the other.
19:02
Okay. So when we go through and we make these, so I've already shown you a few of the simpler ones, but this is sort of my way of stepping out all of the steps for you before we move on to the more complicated ones. First step is you're going to draw your atomic diagrams, okay? So the same things that we drew on the last midterm material, you're going to need
19:23
to be able to do that again. So you're going to draw your atomic orbital diagrams off to the sides, alright? You're going to fill in the electrons that you normally would. So you know something like carbon, you would put your electrons in your S orbital and your electrons in your P orbitals, just like before.
19:42
Now this is the part that's going to be a little weird until we actually look at it. I say decide on which order the energy diagram would follow. We're going to just leave that one alone for a moment. And then I'll show you when we actually, I have pictures of them. Okay, so then you're going to add up all the valence electrons. In your book sometimes they'll draw in the 1S all the way up above.
20:02
All I really care for the MO diagrams is that you draw the valence shell, right? So if we're talking about hydrogen and helium, just draw the 1S. If we're talking about all of the second rows, just draw the 2, the 2S and 2Ps. So once we draw those in, you're going to take the valence electrons from your atomic
20:23
diagrams, you're going to add up all of those electrons, which is what we did for lithium and beryllium, right? We said, okay, well there's this many electrons, we added them all up and we filled them in. Same thing here. Now, this next part, poly-exclusion principle, Hund's and Aufbau's principle still apply. What does all that mean?
20:40
Those were the principles that I sort of told you about and said, you know, make sure you know the basic ideas and you can follow it, but I don't care if you match them up. These were the ones that said, can I have two electrons going up in an orbital? No. One has to be spin up, one has to be spin down. They were the ones that said, how do you fill across a P orbital?
21:02
Do you fill two in the first one and then one by itself or would you go one, two, three across? One, two, three across. Those are all of those rules. You're going to treat those exactly the same. It hasn't come up yet because we've just been dealing with S orbitals. Same rules apply. So now let's actually do these so the rules make sense.
21:22
Okay. So these are your second row diatomics. So not counting the first two that we already did. These are the ones that you have to be able to replicate if I handed you a piece of paper and said, do this. As your book goes on, it will get super complicated and I'll tell you exactly what
21:43
you do need to know. But for your reference right now, you should be able to replicate the slide like on your own with a blank sheet of paper. I'm not going to actually do that and hand you a blank sheet of paper and say, you know, make this. But you should be able to if I wanted you to. Okay, so boron. So first step is make the atomic level diagram.
22:03
So I've already drawn this in for you just for the sake of time, but I don't have to draw this in for you, right? On an exam, I can just say, make me the MO diagram of boron. Make me the MO diagram of carbon. But for the sake of time, I've drawn it in for you. So if we write in the valence electrons for boron, it looks like that.
22:23
Three electrons. So I did this for each side. I've done this for boron here. Now, now comes the next part if you look at your slide where I say, decide on the order of the diagram. Look at these, boron, carbon, and nitrogen, and now look at oxygen, fluorine, and neon.
22:44
What's different about the ordering? It's pi sigma. So right here, we have sigma is higher than pi, sigma is higher than pi, sigma is higher than pi, pi is higher than sigma. Now, what are these pi's and sigma's referring to?
23:01
These, right? The types of bonds. So the ways that we overlap them. So we overlap them one way and we get this. Is that sigma or pi? Same rules apply as with hybridization for this one. It's a sigma, right? End on end. It's a sigma. And then these were pi. That's why we have two pi orbitals, right?
23:21
We have two different versions of this. We could overlap them in one dimension or the other dimension. So back to this then. So that's how we get this pi and this sigma. Now, for each one of those we have a bonding and an anti-bonding. So these are our bonding orbitals.
23:41
These are our anti-bonding orbitals. So what I mean by decide on the order is, basically for this slide, is it boron, carbon, or nitrogen? You're going to do this ordering. Is it oxygen, fluorine, or neon? You're going to do this ordering. Now, a question that may be running through your mind is, where in the world did I
24:00
get this from? I just put up this whole picture and I have not really completely explained how I got this. Basically, people plugged in all these equations into computers, just like when I showed you the pictures of the orbitals and I said, hey, this is what the probability densities look like when they're all mapped out. So, same rules here. People plugged this into a computer and they calculated these and they see what they
24:21
look like and then they match up really well with experiment. So that's where these come from. So that's why we know that this is a different order here than here. Now, if you look at this in your book, you'll notice I made my own diagram up. This is based off my AP Chem book, not your book. In your book they have them all at the exact same energy levels. They didn't
24:42
really draw it as an energy level diagram. They didn't sort of designate that out for you. So it looks like it just flip-flops here, like there's some magical thing that flip-flops. If we look at mine, what do we notice about this flip-flop here? Is it really just a flip-flop or what's happening here? It's a slow gradient, right?
25:00
It's that here this happens to be quite a bit higher and then it goes lower and lower and lower. I don't care that you know exactly these orderings here. This isn't to scale or anything of that sort. I just wanted to get across the idea that this isn't just this magical point where it flip-flops. It is a gradient, and that these are levels that someone calculated, that the computer will calculate for you.
25:23
So when that's middle bulletin point on the last slide, when I say decide on the ordering, for these you have to know that for this grouping the sigma is higher than the pi, and for this grouping this pi is higher than the sigma. Does that happen up here with these?
25:43
No, those are the same, right? So it's just these bottom two of the pi that you have to worry about. Now, if you've maybe flipped a head in your slides or glanced a head, you notice I don't put any of the other diatomics from the periodic table on there. What do you think that means? Do you have to memorize all the diatomics for all the periodic table?
26:01
No. As far as we're going to go for what you have to like know the ordering for is here. We're not going to go on and I'm not going to make you memorize like any more than this. So this is the sort of thing that you need to know and you need to know how this flip-flops. So let's actually make these diagrams now.
26:20
So we have this, we've decided that the order is pi is lower than sigma because I've drawn it out. So how many electrons do we have total to work with? Six. So we just fill them in. Notice what I did with the p. Did I put spin up, spin down here in one orbital? No, you filled them across, right?
26:42
Just like you did with your p orbitals when we were drawing the atomic level diagrams, we do the exact same thing here. We spread them out. What's the word for this? We have two orbitals that are at the same energy level. You remember? Yeah, degenerate. Good. A couple of people remembered.
27:01
So remember that phrasing too, right? If I were to say why do, or if I were to say, you know, what does it mean if the two energy orbitals, or the two orbitals, excuse me, are at the same energy level, you would say that's degenerate. So make sure you know that terminology. Okay, let's move on to carbon. How many valence electrons? Four.
27:23
So we fill them in. You have to fill that in in order to get all your points. You can't just leave it with just the MO diagram. You have to, again, remember all of these subscripts. So notice what changes here. Our subscripts here is 2s, right? Where does that come from?
27:41
Well here, we took them from the 2s orbital. What do these come from? 2p, good. Okay, so how many electrons? Oh yeah. So you can fill in the 1s for these, and I think in your book they do.
28:01
Personally, I don't care if you do or don't for an exam because they're all going to be the same. And so it gets a little redundant. All I really care is valence electrons because that's where you're going to be filling into. Your valence electrons are the ones actually doing the bonding. So if you just do your valence ones, you're fine. And honestly, for lithium and beryllium, if you just do 2s, I'm fine with that too.
28:20
You don't have to draw in the 1s if you don't want. For bonding, like bond order purposes, it doesn't actually make a difference because when you fill in the electrons, they cancel, right? How many would you have in the bonding orbital of 1s? Two. And how many would you have in the anti-bonding orbital? Two. So they would cancel out anyways. So it's drawn both ways.
28:44
Okay, so now we have eight electrons. So we can draw them all in. Now, for nitrogen, we have five valence. Hopefully you're kind of getting the pattern here, so we'll go a little quicker.
29:02
So how many electrons total? Ten. So we have this.
29:23
Next one. We end up with twelve total. Yeah, six each, so twelve total. Good. So we end up with that. Are you catching the pattern hopefully here? Any questions as we're doing this? This slide kind of gets redundant if I talk too much on it.
29:42
Okay. So this is sort of the max that you're going to have to replicate from scratch without some information from me. Any of these are free game for me to say, draw the MO diagram of nitrogen without any other information. Now let's go through and calculate the bond order since it's a little bit more complicated. Exact same rules apply though, right?
30:01
Are there any questions? It looks like maybe there's a few. Oh, good catch. That's a 2p. That should say 2p. Thank you. And I will fix that on the slides and post it too.
30:24
Okay. Alright, so now to go through and calculate bond order. So how many do we have in bonding orbitals here? Four, right? One, two, and then these, four.
30:42
How many in anti-bonding orbitals? Two. So our bond order then is one. You'll sort of catch also the pattern that these just all cancel out. And so if you're doing this sort of on the fly in your head, which some of you like to do, then that's perfectly fine,
31:02
you can actually sort of ignore these and notice that they cancel out. If you're calculating it, same sort of thing, but it doesn't make a difference either way. So next one. We have how many orbital, or how many electrons in bonding orbitals? We have four here, but then don't forget these. So six. And how many here?
31:23
Two. So two total. And two. So we look at this and we say, well, how many do we have in bonding orbitals?
31:42
Well we have six here and then two here, so eight. And then how many here? So we get a triple bond. Okay. Next one. Oxygen. So how many in bonding orbitals?
32:01
Six. Two is eight. And then how many in antibonding? Two and four. So we end up with a bond order of two. Go through this a little bit slower at home, too. And make sure that you can do this kind of all from scratch. Okay, now fluorine.
32:21
So, same rules. So we have two in bonding orbitals here, six in bonding orbitals here, two in antibonding here, four in antibonding here, so we get eight minus six. So you're counting everything that's not in an orbital that's a bonding orbital, so it doesn't have a star next to it.
32:41
We're counting those as our bonding electrons, and anything in the orbitals that have the star on it, the antibonding orbitals, we're putting those as a subtract. And the neon, of course, is zero, because it's completely filled. Okay? So, well, as far as the practical significance,
33:09
it'll change some of your bond orders around a little bit on the lower levels. Well, actually, it doesn't even do that. It'll change whether it's paramagnetic or diamagnetic in some cases, though. As far as how it comes about, it's because of the calculations.
33:22
It's because when you actually plug these into a computer and you actually get the energy values out, the sigma happens to be a little bit lower than the pi. And you don't really have to worry too much about why that is, other than that, it is. And then your second?
33:44
You mean as far as... I'm not sure what you mean. Okay, so her question was, is there any way to know... You mean for calculating the bond order and such. Her question was, is there any way to figure out how many electrons are bonding
34:00
in the bonding orbitals or the antibonding orbitals without making the MO diagram? Not really. I mean, if you get really good at it, you can think about it in your head, you could do that, but you're still creating the MO diagram. And honestly, these are a little tough to do that with. You can get kind of quicker at it, because if I don't ask you to draw it, you can just sort of draw out the lines
34:21
without having to draw out the pis and the sigmas and labeling them, but you really kind of have to create them to see it. Yeah? Yes? So, okay, her question was, do you use these charts for anything other than diatomic molecules? And the answer is yes.
34:42
And for your own sort of entertainment and knowledge, skim through your book over the section that has, and you can see that they do it for water, and you can see that they do it for benzene. That goes a little bit beyond the scope of this class, so we're going to leave that be. You'll talk about it a little bit in organic chemistry to describe some things like how benzene works,
35:02
and then if you take physical chemistry, you'll talk about it a lot, but in this class we're kind of going to let it go at diatomics. Now, something that we will cover is heteronuclear diatomics. You won't have to know the ordering, like, for instance, whether pi and sigma are flip-flopped, like this or like this, but I'll tell you that and you can create them,
35:21
and we'll do that in a minute. You can use them for much more complicated molecules. It just, there's this point where, in this class, there's a level of memorization to it that loses a little bit of value. There's another hand up.
35:43
Okay, so her question was, So, for the atomic orbitals diagrams on the side, do you have to draw everything in, or specifically the electrons? Yeah, you have to draw in the electrons and make sure you label them, too. On exams, this one tends to be one where people forget to label them and they forget to fill in the electrons because they're so busy concentrating on this part of it,
36:02
but you really need to have both. Now, let's do this for ions. So, same sort of rules apply as all of the things we've been doing before, but now we're going to do them on the MO diagrams.
36:21
So, we add or subtract electrons as we need. So, if something is a negative ion, are you going to add electrons or subtract them? Negative ion. Add or subtract electrons? You're going to add, right? You have a negative ion, so you need an extra negative charge, so you add in an electron. What if I make it a positive ion?
36:40
Take an electron away. So, same rules as always apply here. Make sure you take them away, you know, properly. You're not going to take two from the same orbital if you're in the π bonds. And same rules apply as before, you're going to start low and build high. You start with the low energy electrons, or low energy orbitals,
37:01
and go up to the higher energy orbitals. Now, what I mean here, this doesn't apply to homonuclear diatomics. Now, homonuclear, that means same nucleus, right? So, heteronuclear would mean different nucleus. So, keep that in mind when you're thinking about things. So far, we've only done the homonuclear ones,
37:22
and that's just because they're a little bit simpler to deal with, and so we're starting there. But, when we get to where we're doing heteronuclear ones, you're always going to give the electrons to the electronegative atoms. Where are you going to take the electrons away from? The non-electronegative or the electronegative? What does electronegative mean?
37:42
Think about that for a sec. How much it wants to pull electron density toward it? So, if we have to add in an electron, are we going to want to give it to the thing that wants a lot of electron density, or the thing that says, nah, I don't want that electron density? Yeah, the thing that wants it, right? So, if you're adding in electrons, give it to the electronegative atom.
38:01
If you're taking away electrons, give it to the more electronegative, or, excuse me, take away from the more electronegative, or take away from the less electronegative. Less, right? It doesn't want a lot of electron density, so take it away from there. Now, does that play any real, does that matter when we get to the MO part of it, the middle part of it? No, we're still just counting electrons and filling them in from low to high.
38:25
So, let's do this real fast. So, we'll start with nitrogen. So, this is straight from your other diagram that we drew. I put it here just so that it matches with the charges.
38:40
So, this is a homonuclear one, so it doesn't really matter where we add or subtract from. We should do it symmetrically once we get to a charge of two. Okay. So, let's do the N2 plus first. So, if we have a plus ion, are we going to take away an electron or add an electron? Take away. Does it matter where we take away from over here?
39:01
Nope. So, we fill in, I took away from the one on the left, it doesn't really matter. Now, we count how many electrons we have, which is? Nine. And we fill in. Alright, next one.
39:23
So, let's do this one. So, we have a negatively charged ion. So, what are we going to do? Add or subtract an electron? Good, we're going to add an electron. Does it matter where we add it to? Nope. So, again, I added it to the left, but it doesn't really matter. And when we fill in, now we have 11 electrons.
39:45
So, we get this. Okay. So, negative two. So, we've now added in two electrons, or one more from here. Now, does it really matter where we add it into?
40:00
We should keep it symmetrical. So, we should add one to each side. So, I've added one to this side and one to this side. So, when we go to fill in, we have this. Now, notice here, same rules apply with the ions that apply with the regular atoms,
40:21
or molecules, that I fill in one here and then one here. I don't put two of them in one, right? When you have degenerate orbitals, or orbitals of the same energy level, you fill across first, and then you double up if you need to. Okay. So, now let's look at the bond orders for each of these. So, what was the bond order for nitrogen?
40:46
Well, let's recalculate this. You're right, but we'll recalculate it since we didn't seem to have a large agreement. So, how many are in bonding orbitals? We have six here and two here. And how many are in antibonding orbitals? Two.
41:01
So, we have a bond order of eight minus two divided by three. Or, I like to just kind of think of canceling these out and then taking the six and dividing it by two. Either way. So, we get a bond order of three for nitrogen. Okay. Now, what do we think is going to happen when we add or subtract electrons?
41:21
So, let's look at the adding, or the subtracting of an electron. What do we think is going to happen here? Is the bond order going to go up or down? It's going to go down. Why? Where did we take away an electron from? Yeah, we took one away from the bonding orbital, right? This one right here, that's a bonding orbital and we took an electron away from that.
41:41
So, do electrons in bonding orbitals add to a bond or subtract from a bond? They add to a bond and we took one of those away. So, this one should be lower. Now, let's look at this one. Where did we add an electron to? A bonding orbital or an antibonding orbital? Antibonding. So, is that one going to be lower or higher?
42:03
Let's think about it again. If you add an electron to an antibonding orbital, does that add or subtract from the bond order? Subtracts, right? Antibonding. Think antibonding. It keeps it from bonding. It subtracts from the bond, okay? So, antibonding takes away from the bond.
42:22
Bonding adds to the bond. So, now we added an electron to an antibonding orbital, an orbital that keeps it from bonding. So, is it going to have a lower bond order or a higher bond order? Lower. Is this one going to be even lower or is it going to go back or is it going to be higher?
42:41
Even lower, right? Because we've added another one. And if we made it another minus, if we made it minus three, it would be even lower. So, now let's calculate them all out and prove this. So, if we take this and we calculate all of our electrons that are in our bonding orbitals, So, that's two, four, six, eight. And all of them in our antibonding orbitals, we get two.
43:06
Now, if we do it for this one, we get two and a half. And we know what nitrogen is already, we've done that one. It's three. And we do N2 plus, so now we have two, four, six, seven minus two.
43:25
We get two and a half. Does that make sense with what we just talked about? Well, we started with a bond order of three and we took away one that was in a bonding orbital. Would we expect it to go down by a half? Yeah, right? Because electrons add or subtract how much of a bond?
43:44
Half. And if you forget about that, you can think about the fact that we have always talked about a single bond having two electrons, right? So, each one's half. Now, over here we added one and we added it to an antibonding orbital. So, that went ahead and subtracted a half as well.
44:02
Here we subtracted a whole one, but that's because we've added in two electrons and both went to an antibonding orbital. Okay? So, this is how you do ions. We'll eventually get to one where you have to worry about electronegatives and stuff, but this one we don't need to. Okay, so now I want to take a minute and look at a case that I think is fairly interesting.
44:24
And that's molecular oxygen. So, this is the MO diagram for molecular oxygen. I took it straight from the other slide where we started with oxygen. Now, there's some things to notice about this.
44:41
First of all, what's the bond order? It's two, right? And I got that because how many are in bonding orbitals? Two, four, six, eight. How many are in antibonding orbitals? Two, four. So, we get a bond order of two. Now, is it paramagnetic or is it diamagnetic?
45:03
Maybe we should have a refresher on what paramagnetic and diamagnetic means. Okay, paramagnetic. Does that mean unpaired or paired electrons? Unpaired. Diamagnetic, paired or unpaired? Paired. Okay, so now we have paramagnetic equals unpaired, diamagnetic equals paired. Is this paramagnetic or diamagnetic?
45:22
Paramagnetic. Paramagnetic, good. Okay, we can agree upon this, right? Now, draw the Lewis structure for oxygen. No, really, draw it. Just take a few seconds and draw the Lewis structure.
45:41
Forget about MO diagrams for a second and just draw the Lewis structure for me. Not everyone is writing. Okay, what does it look like?
46:01
Is that what you got? Okay, so does that have a bond order of two? In this way of thinking about it, is it a double bond or a single bond? It's a double bond, so that's a bond order of two. Is it paramagnetic? No. Okay, well let's draw it paramagnetic.
46:21
I can make it paramagnetic, right? I'll take one of these bonds and I'll just draw it like that. Okay, now I have it paramagnetic. But what did I screw up when I did that? The bond order. Now I have a bond order of effectively one there. Okay, well how do I draw this then to make it so that it has a bond order of two and that it's paramagnetic?
46:41
You don't. You don't. You can't really do it. So it's one of those situations. So then what does experiment say, right? That's always what we should go to. We should say, well, which one's right? Is the most theory in this case right or is it going to be this Lewis structure model? Well, let's go to the experiment. If I were to take and I were to, you know, pour some liquid oxygen over a magnet, you would see that it really is paramagnetic.
47:02
So that's true. It is definitely paramagnetic. And the thing is that when you measure the bond lengths, we have ways of doing that. The bond lengths come out to be two. So we can't actually accurately represent it like this. One or the other is sort of not represented properly.
47:21
But with M-O diagram, we can actually represent exactly what M-O theory or exactly what experiment says. So when I originally had said that, hey, M-O theory is a little bit more complicated, but it's a little bit better at explaining things, it's cases like this that come up. There's not a ton of them, but it does come up.
47:46
So next one. Let's do carbon monoxide. So this is the first time I've shown you a heteronuclear diatomic. Now, rules for these, for what I can test you on, I can tell you to draw me the M-O diagram of something like CO or NO or something of that sort,
48:02
but I have to give you some hints. I have to tell you the order, okay? So you'll notice Sapling will do this too. They'll tell you to draw a diatomic and then they'll tell you the ordering of the energy levels. This is what they're getting at. So in this case, I've just drawn this out for you. On an exam, I wouldn't have to draw it, but I would have to say, well, we have sigma 2S, sigma 2S*,
48:23
pi 2P, pi 2P*, and then sigma 2P. There is a copy-paste glitch, so make sure you change all of these to Ps, and I'll fix that, but it's a glitch. It's a systematic copy-paste glitch. Okay, so let's look at this.
48:45
First of all, we're going to do some other things other than CO. So why don't noble gases form diatomic molecules? And use a Mo diagram to prove it to me. So this one doesn't actually have to do with CO. Look at your helium, look at your neon.
49:02
What is your bond order on all of those? Zero, right? So what happens is that if you were to form a bond, you would have the exact same number of electrons in the bonding orbitals as the anti-bonding orbitals, and so it's going to be pulled apart. You're going to have a bond order of zero. There's nothing that's going to be holding it together.
49:22
So a Mo diagram, if you draw it out, would show a bond order of zero. Okay, we have two more examples to do. I'll do it next time. Notice your Sapling homework deadline did get moved back. We didn't make it quite as far as I hoped, not a big deal. So your Sapling deadline got moved back a little bit.