Spin-spin splitting (coupling)

if we look at this molecule we would expect three signals on an NMR spectrum so this proton has a chemical shift of seven point two five parts per million this proton is in a slightly different environment and so we get a slightly different chemical shift at six point seven these three protons are equivalent and therefore they give us one signal at a chemical shift of three point nine parts per million so based on what we know so far we would expect the top NMR spectrum so these three protons give us a signal at a shift of three point nine so that would be this signal right here let's make the next proton red so this proton right here in red has a shift of six point seven so we would expect this signal and then the last proton here I'll make it blue this one is at seven point two five so this is the expected NMR spectrum based on what we know so far but this is not the actual NMR spectrum so the actual NMR spectrum is this one down here alright so we still see we still see this one signal with one peak for the protons in green but if we look at the signal for the red proton right so in the top version we had one signal with one peak and the bottom version here that one signal has been split into two peaks I'm going to highlight those so there's one peak and then there's the other peak so the signal was split into two peaks the exact same thing happened for the proton in blue 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 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 so let me go down here we have some more room and let's go ahead and draw in the spectrum with no interaction between the protons to the first version that we talked about we expected one signal with one peak at 6.7 parts per million and that was the that was the proton in red and then we expected one signal with one peak 7.25 parts per million and that was the proton and blue so this top version here is the is the spectrum with no interaction between our two protons but in reality there is an interaction because remember the red proton right the magnetic moment of the red proton can be can be up or down it can be aligned with the external magnetic field or it can be aligned against the external magnetic field so the red proton has a magnetic moment or a magnetic field that's going up or it's going down and so let's think about let's think about the example where the magnetic moment of the red proton is aligned with the external field first so we have our our red proton and let's say the magnetic moment is aligned with the external magnetic fields let me go ahead and draw in the external magnetic field like that so we call this B naught and these two vectors are going in the same direction right 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 alright so the effective magnetic field is larger than the applied magnetic field because the red protons magnetic field is adding to it and so the proton in blue feels a larger effective magnetic field and remember what that does the energy difference between the Alpha and the beta spin States right if you increase the magnetic field you increase the difference in energy between the Alpha and the beta spin States therefore you get a higher frequency signal and a higher chemical shift than expected so this has the effect of increasing the shift the chemical shift for the blue proton so we can draw in the blue proton at a higher chemical shift than expected all right let's do the the same sort of thing except this time let's think about the red protons magnetic moment aligned against the applied magnetic field so this is the situation right where the magnetic field of the red proton is going down that's in the opposite direction of the applied magnetic field right so I drawn the applied magnetic field here and so the red protons magnetic field is going to cancel out some of that external magnetic field and the proton in blue feels a smaller effective magnetic field so I'm exaggerating here right just to get the point across but the proton in blue feels a smaller effective magnetic field that decreases the energy difference between the Alpha and the beta spin States therefore we get a lower frequency signal and a lower value for the chemical shift than expected so a lower value for the chemical shift for the blue proton so I go ahead and draw in the signal for the blue proton at a lower at a lower value for the chemical shift and so the end result is the signal for the blue proton is split into two so the signal for the blue proton is split into two because of the two different magnetic fields of the red proton and the blue proton also has has a magnetic field pointing up or down and so the blue proton splits the signal for the red proton in the same way so we can go ahead and draw we can go ahead and draw the red proton being split in the same way and so this down here represents the spectrum of what where both protons are coupled to each other all right so we call this coupling and so we end up seeing the signal split into two different Peaks which we call a doublet all right so let me go over here and let's look at our protons again all right so the proton in red right is split into two peaks the signal is split into two peaks like we talked about here and the proton in blue right the signal is split into two peaks like this which we talked about right here so that's the idea of spin-spin splitting and next we're going to look at another example which is just a little bit more complicated but uses this exact same idea let's look at this molecule so this proton has a chemical shift of five point seven seven parts per million and the protons here in red are equivalent and we would expect a signal at three point nine five parts per million so we expect a signal due to two protons at 3.95 so this represents two protons here and we expect a signal for one proton so at five point seven seven so this signal isn't as intense because it's only representing one proton so if the red and blue protons did not interact with each other we would expect this for the proton NMR spectrum but they do interact with each other and so we need to think about the magnetic moments of the two red protons so 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 so this is one possible combination of magnetic moments another possible combination I could have the first red proton having having a magnetic moment pointing up and the second red proton having a magnetic moment pointing down or the first proton could be pointing down in the second proton pointing up so that's two more possible spin combinations the last possible spin combination would of course be the first protons magnetic moment is down and so is the second protons so this represents the possible combinations of magnetic moments or magnetic fields for the two protons in red so let's take the first possible combination so let's think about both protons having magnetic moments pointing up we let's say our applied magnetic fields right our external magnetic field points in the same direction so when you think about the magnetic field experienced by the proton in blue right we would add the magnetic fields for the protons in red and so the effective magnetic field is increased right is higher than the applied magnetic field so we've increased the magnetic field experienced by the proton in blue therefore increasing the energy difference between your alpha and your beta spin States increasing your frequency and we get a higher chemical shift alright so we get a higher value for the chemical shift so we can think about the the chemical shift being higher let me go ahead and draw that in like that so past five point seven seven let's look at the next two possible combination so this one and one so we had a 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 so what effect what effect those magnetic fields have on the effective magnetic field felt by the proton in blue well let's think about the first combination so this combination right here alright so we have a one one magnetic field up one magnetic field down they would cancel alright same thing with this combination one down and one up those magnetic fields cancel 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 and so we would expect we would expect a signal at the proper at the correct chemical shift right 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 right there's a greater probability of having one of these combinations of magnetic fields than having this combination so twice the probability gives you a doubly intense signal at the correct chemical shift finally let's look at the last combination so both magnetic fields pointing down so both magnetic fields for the protons in red pointing down and we have our applied magnetic field pointing up so the effective magnetic field felt by the proton in blue right is smaller right so we have a smaller value for the effective magnetic fields we've decreased the magnetic field felt by the proton in blue decreasing the energy difference decreasing the frequency decreasing the chemical shift right so we expect a lower chemical shift so we can go ahead and draw in a lower chemical shift so so like that so let's think about let's think about this signal up here 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 and the possible combinations of the magnetic moments of the red protons take the approach take the signal for the proton in blue and give you three peaks right 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 and so if we look at the NMR spectrum alright so this is the signal for the for the proton in blue the signal is split into three peaks one two and three and we call this a triplet so this is a triplet what about the protons in red the protons in red are affected by the magnetic field of the proton in blue and the magnetic field of the proton and blue can be aligned either with the external magnetic field or against the external magnetic field so it's like the the previous example we saw two possible magnetic fields for the proton in blue therefore the signal for the protons in red is split into two right so we get a signal for the protons in red split into two I'm attempting to draw that here so the signal split into two peaks right so the signal for the protons in red is split into two peaks and we call this a doublet alright more about spin-spin splitting in the next video