Spin-Spin Splitting in Proton NMR Spectroscopy Explained

[00:00:02]- [Voiceover] If we look at this molecule, we would expect three signals on an NMR spectrum.

[00:00:06]So this proton has a chemical shift of 7.25 parts per million.

[00:00:11]This proton is in a slightly different environment and so we get a slightly different chemical shift at 6.7.

[00:00:17]This three protons are equivalent and therefore, they give us one signal at a chemical shift of 3.9 parts per million.

[00:00:25]So based on what we know so far, we would expect the top NMR spectrum.

[00:00:30]So these three protons give us a signal at a shift of 3.9.

[00:00:34]So that would be this signal right here.

[00:00:36]Let's make the next proton red.

[00:00:39]So this proton right here in red has a shift of 6.7 so we would expect this signal.

[00:00:45]And then the last proton here I'll make it blue.

[00:00:48]This one is at 7.25.

[00:00:51]So this is the expected NMR spectrum based on what we know so far but this is not the actual NMR spectrum.

[00:00:57]So the actual NMR spectrum is this one down here.

[00:01:03]We still see this one signal with one peak for the protons in green.

[00:01:09]But if we look at the signal for the red proton, so on the top version we had one signal with one peak.

[00:01:16]In the bottom version here, that one signal has been split into two peaks.

[00:01:20]Let me go ahead and highlight those.

[00:01:21]So there's one peak and then there's the other peak.

[00:01:25]So the signal was split into two peaks.

[00:01:28]The exact same thing happened for the proton in blue.

[00:01:31]So we had one signal with one peak in the top version and down here that signal for the blue proton was split into two peaks.

[00:01:40]So we call this spin-spin splitting or spin-spin coupling and let's look in more detail about what's happening with that red and the blue proton.

[00:01:51]So let me go down here.

[00:01:52]We have some more room.

[00:01:54]Let's go ahead and draw in the spectrum with no interaction between the proton.

[00:02:01]So the first version that we talked about we expected one signal with one peak at 6.7 parts per million.

[00:02:08]That was the proton in red.

[00:02:11]And then we expected one signal with one peak at 7.25 parts per million and that was the proton in blue.

[00:02:18]So this top version here is the spectrum with no interaction between our two protons.

[00:02:25]But in reality there is an interaction because remember the red proton, the magnetic moment of the red proton can be up or down.

[00:02:35]It can be aligned with the external magnetic field or it can be aligned against the external magnetic field.

[00:02:40]So the red proton has a magnetic moment or a magnetic field that's going up or it's going down.

[00:02:46]Let's think about the example where the magnetic moment or the red proton is aligned with the external field first.

[00:02:53]We have our red proton and let's say the magnetic moment is aligned with the external magnetic field.

[00:03:00]Let me go ahead and draw in the external magnetic field like that.

[00:03:04]We called this B knot.

[00:03:06]And these two vectors are going in the same direction.

[00:03:09]So the magnetic field, the red proton adds to the external magnetic field and let me go ahead and draw in a larger vector here because now the effective magnetic field felt by the blue proton has increased.

[00:03:23]So the effective magnetic field is larger than the applied magnetic field because the red proton's magnetic field is adding to it.

[00:03:32]And so the proton in blue feels a larger effective magnetic field.

[00:03:37]And remember what that does, the energy difference between the alpha and the beta spins states.

[00:03:42]If you increase the magnetic field you increase the difference in energy between the alpha and the beta spin states.

[00:03:48]Therefore, you get a higher frequency signal and a higher chemical shift than expected.

[00:03:54]So this has the effect of increasing the shift, the chemical shift for the blue proton.

[00:04:00]We can draw in the blue proton at a higher chemical shift than expected.

[00:04:06]All right, let's do the same sort of thing except this time let's think about the red proton's magnetic moment aligned against the applied magnetic field.

[00:04:15]So this is the situation where the magnetic field of the red proton is going down.

[00:04:20]That's in the opposite direction of the applied magnetic field.

[00:04:24]So I draw in the applied magnetic field here.

[00:04:27]And so, the red proton's magnetic field is going to cancel out some of that external magnetic field and the proton in blue feels a smaller effective magnetic field.

[00:04:36]So I'm exaggerating here just to get the point across.

[00:04:40]But the proton in blue feels a smaller effective magnetic field that decreases the energy difference between the alpha and the beta spin states.

[00:04:50]Therefore, you get a lower frequency signal and a lower value for the chemical shift than expected.

[00:04:56]So a lower value for the chemical shift for the blue proton.

[00:05:00]So I go ahead and draw in the signal for the blue proton at a lower value for the chemical shift.

[00:05:06]And so, the end result is the signal for the blue proton is split into two.

[00:05:12]The signal for the blue proton is split into two because of the two different magnetic fields of the red proton.

[00:05:20]The blue proton also has a magnetic field pointing up or down and so the blue proton splits the signal for the red proton in the same way.

[00:05:31]So we can go ahead and draw, we can go ahead and draw the red proton being split in the same way.

[00:05:37]This down here represents the spectrum of where both protons are coupled to each other.

[00:05:45]We call this coupling.

[00:05:47]And so we end up seeing the signal split into two different peaks which we call a doublet.

[00:05:53]Let me go over here and let's look at our protons again.

[00:05:57]The proton in red is split into two peaks.

[00:06:02]The signal is split into two peaks like we talked about here.

[00:06:05]And the proton in blue, the signal is split into two peaks like this which we talked about right here.

[00:06:13]That's the idea of spin-spin splitting.

[00:06:16]Next we're gonna look at another example which is just a little bit more complicated but uses this exact same idea.

[00:06:25]Let's look at this molecule.

[00:06:27]So this proton has a chemical shift of 5.77 parts per million.

[00:06:31]And the protons here in red are equivalent and we would expect a signal at 3.95 parts per million.

[00:06:39]So we expect a signal due to two protons at 3.95.

[00:06:43]This represents two protons here and we expect a signal for one proton at 5.77.

[00:06:51]This signal isn't as intense because it's only representing one proton.

[00:06:56]If the red and blue protons did not interact with each other, we would expect that this for the proton NMR spectrum but they do interact with each other.

[00:07:06]And so we need to think about the magnetic moments of the two red protons.

[00:07:11]I could think about the first red proton having a magnetic moment that's pointing up and the second red proton having a magnetic moment that's also pointing up.

[00:07:19]So this is one possible combination of magnetic moments.

[00:07:24]Another possible combination, I could have the first red proton having a magnetic moment pointing up and the second red proton having a magnetic moment pointing down.

[00:07:33]Or the first proton can be pointing down and the second proton pointing up.

[00:07:37]That's two more possible spin combinations.

[00:07:40]The last possible spin combination would of course be the first protons magnetic moment is down and so is the second protons.

[00:07:46]This represents the possible combinations of magnetic moments or magnetic fields for the two protons in red.

[00:07:54]Let's take the first possible combination.

[00:07:57]Let's think about both protons having magnetic moments pointing up.

[00:08:02]Let's say our applied magnetic field, our external magnetic field points in the same direction.

[00:08:09]When you think about the magnetic field experienced by the proton in blue, we would add the magnetic fields for the protons in red.

[00:08:17]And so the effective magnetic field is increased, it's higher than the applied magnetic field.

[00:08:24]So we've increased the magnetic field experienced by the proton in blue.

[00:08:30]Therefore, increasing the energy difference between your alpha and your beta spin states increasing your frequency, and we get a higher chemical shift.

[00:08:38]So we get a higher value for the chemical shift.

[00:08:42]We could think about the chemical shift being higher.

[00:08:46]Let me go ahead and draw that in like that.

[00:08:48]So past 5.77.

[00:08:51]Let's look at the next two possible combinations.

[00:08:53]So this one and this one.

[00:08:55]We had magnetic moment up for the first proton, magnetic moment down for the second proton, and then down for the first and up for the second.

[00:09:03]What effect do those magnetic fields have on the effective magnetic fields felt by the proton in blue?

[00:09:13]Well, let's think about the first combination.

[00:09:14]So this combination right here.

[00:09:16]We have one, one magnetic field up, one magnetic field down, they would cancel.

[00:09:22]Same thing with this combination, one down and one up.

[00:09:24]Those magnetic fields cancel.

[00:09:25]And so, the effective magnetic field felt by the proton in blue is equal to the external magnetic field because the magnetic fields of the protons cancel each other out.

[00:09:37]And so we would expect, we would expect a signal at the proper, at the correct chemical shift.

[00:09:43]We would expect a signal at the correct chemical shift at 5.77 and this signal is actually going to be more intense than this signal and that's because of probability.

[00:09:53]There's a greater probability of having one of these combinations of magnetic fields than having this combination.

[00:10:00]So twice the probability gives you a doubly intense signal at the correct chemical shift.

[00:10:06]Finally, let's look at the last combination.

[00:10:08]So both magnetic fields pointing down.

[00:10:10]Both magnetic fields for the protons in red pointing down and we have our applied magnetic field pointing up.

[00:10:19]The effective magnetic field felt by the proton in blue is smaller.

[00:10:25]So we have a smaller value for the effective magnetic field.

[00:10:29]So we've decreased the magnetic field felt by the proton in blue.

[00:10:33]Decrease in the energy difference, decrease in the frequency, decreasing the chemical shift, right?

[00:10:38]So we'd expect a lower chemical shift.

[00:10:41]So we can go ahead and draw in a lower chemical shift so like that.

[00:10:47]Let's think about this signal up here.

[00:10:50]We said we'd expect one signal for the proton in blue but that one signal is affected by the magnetic fields of the different protons in red.

[00:11:00]And the possible combinations of the magnetic moments of the red protons take the signal for the proton in blue and give you three peaks.

[00:11:09]So we have one peak at a higher chemical shift, one peak of double intensity at the correct chemical shift, and one peak of lower intensity.

[00:11:18]And so, if we look at the NMR spectrum, so this is the signal for the proton in blue.

[00:11:24]The signal is split into three peaks, one, two and three and we call this a triplet.

[00:11:30]This is a triplet.

[00:11:33]What about the protons in red?

[00:11:36]The protons in red are affected by the magnetic field of the proton in blue.

[00:11:40]And the magnetic field of the proton in blue can be aligned either with the external magnetic field or against the external magnetic field.

[00:11:48]It's like the previous example we saw.

[00:11:51]Two possible magnetic fields for the proton in blue therefore, the signal for the protons in red is split into two.

[00:12:00]So we get a signal for the protons in red split into two, I'm attempting to draw that here.

[00:12:07]The signal is split into two peaks.

[00:12:09]The signal for the protons in red is split into two peaks and we call this a doublet.

[00:12:15]All right.

[00:12:16]More about spin-spin splitting in the next video.