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Lecture 08. Introduction to NMR Spectroscopy

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Lecture 08. Introduction to NMR Spectroscopy
Concepts and Theory, Part 2
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Lecture 08. Introduction to NMR Spectroscopy, Part 2
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This is a graduate course in organic spectroscopy, focusing on modern methods used in structure determination of organic molecules. Topics include mass spectrometry; ultraviolet, chiroptical, infrared, and nuclear magnetic resonance spectroscopy.
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we Our but we're going to talk about stands today about that about 6 I want I want to continue our discussion of the concepts and theories behind in more spectroscopy and again this is not going to be about math anything anything to that extent but we're going to be thinking vary Mary qualitatively arts so when we last left things we had said that the choose spin states for dipole :colon nucleus like approach undersea 13 years been up and spend an hour if you've applied magnetic field there's a small energy difference between the spin upstate where were calling this the office and the spend down state what were calling the beta state and because then energy difference is so small unlike Iowa's spectroscopy or electronic spectroscopy UV Vis spectroscopy where the energy differences are very big and all of your molecules on the ground state here there is only a minuscule number of nuclei In the lower state more than the number in the upper state we said if there are if we take 2 million protons out of those 2 million protons depending on would be applied magnetic field it will be 50 EUR 80 year there about differences in population and it turns out that differences in population is going to be extremely important because it is only that differential population that's going to be able to get us all right so if we think about things in and xyz coordinate frame and I'll talk more about Metamora spectrometer in a 2nd and how it works but a mansion for a moment we have some coordinates to the X coordinate is coming out of the plane wide coordinators in the plane and Izzy coordinator is pointing up and we're going to have our applied magnetic field pointing upwards that kind of makes sense the superconducting magnets are always vertical because you've got this big part of liquid helium surrounded by a vacuum vessel surrounded by liquid nitrogen surrounded by a vacuum vessel and those small amounts of population that small differential of population with spin up is going to give rise to I that radicalization now in other words a way to think about this is for most of our cases we're going to have 1 nucleus pointing up 1 nucleus pointing down in the spin and there's no net vectors those vectors cancel each other out but for that small differential of excess vectors you're going to have some that mechanization along busy axis now the the way it works when you apply a magnetic field is you actually have those vectors the possessing around so in other words they are processing at that resonant frequency at Lamar frequency at 500 megahertz 417 thousand 500 gallons magnate so we actually can represent this by saying OK we've got spins sort of pointing in every which way and I'll just brought to directions they're all possessing around so remember remember and this is only the differential populations that were worried about because already for everyone we have 1 up and you have an opposing 1 spin down those vectors are going to cancel each other out now the other thing is they're not quite on access in other words they're not like this it's like a gyroscope if you've ever hung it from a strain the gyroscope doesn't lose 100 jobs strings the Giron physics the gyroscope doesn't hang vertically a kind of hangs off axis and goes around like this but if you think about it since those spins are not bunched up for everyone that's possessing like this there's another 1 that's obvious said it so in other words if it were just like this you'd say older Zdenek magnet is Asian along the z axis but also net magnet is ation along the Y axis but there are other spends that like this and they're all going around so everything's canceling out except the net mechanization along the z axis of blood I want you to imagine right now is that we're going to place a coiled along the x-axis and we're going to put energy into that Quayle were going to apply a magnetic force and I want you to think classically because the quantum mechanical thing is going to be will flip the spends I'll show you that the but you have your net mechanization along the z axis and think back classical physics if I apply a along the x-axis right hand rule and all that good stuff we rotate our vector downward so after we apply a pulse of the a upholstered fears are not mechanization when we apply an RAF policies are net mechanization moves along the Y axis and so I guess if I want to actually have 1 representative of just say Texas why Zaidi and I'll say Here's on a Magnus and as you'll see in a moment we're going to have continued processions and again if you're worried about the fact that all of our vectors are not lining up that they're all processing like this just think as I apply a policy and drive my magnet is Asian from Lizzie access onto the Y axis the vector sum is right along the Y axis even know there's some matter like this I drive it down there countering each other there some like this and drive it down there countering each other and so our net mechanization ends up along the way that makes sense all right let's come back to to our suspicions to see what this meant so the way I was trying last time to represent this very small the difference between the Alpha space in the beta state was to show some vector sum stands pointing up in the and some stations pointing their loans In the biggest state and to try to represent this minuscule differences in population what I did for the purpose of my drawing was I drew 6 with spin up in the alpha state and for it's been down in the basis those representing exactly the spins of individual nuclei so in other words if we had a mole of more realistically if we had a newly of CHC L 3 polio core form in our animal or 2 what this would represent would be the difference in the nuclei of the hydrogen there and we would have out of that Millie of nuclei we would have on a small excess in the office there and they would all be Proceso alright so if we apply an RF pulse and going to be a little bit specific fearfully apply holes long enough that is what's called a 90 degree RF pulse or a over to that's just radiance and degrees your choice and they get used in interchangeably what that does is it equalizes the population of alpha and beta state
and so represent that 5 stand up and fight 5 spin down and this situation is exactly the situation that we have at the end of my little drawing over on the left him blackboard in other words here our net magnet is a ship and so the key is now we have no net maximization sped up knowing that maximization spin down but the very important point is we have the net mechanization focused along the line since it is not diffuse it is not pointing in all directions we actually have a net mechanization in the and if we apply a longer pulse a more powerful RF pulse so again I will represent our 6 little arrows and for little arrows representing our differential populations of the data state if we apply a more powerful RF pulse what we call upon RF pulse a 180 degree are pulse I can invert the population in other words I will represent that by 4 arrows pointing up in 6 arrows pointing down and if I want to drive that on my diagrams can anyone tell me what I do with my neck standardization on my little xyz diagram this fall it's going to point that exactly are and this is the damning thing while 1 of the many damning things about Anna Morris spectroscopy is no matter what you do With your pulses you are limited To the differences in population that occurs between the alpha and beta and later when we start to talk about 2 Deanna more spectroscopy were going to learn about 1 of the bomb common techniques now which is which is to go ahead and have polarization transfer now think about what I said before in the equation relating the Boltzmann distribution to the energy difference and remember how the Magneto generic ratio for carbon was escorted the Dujarric ratio for protons that means that roughly the Boltzmann distribution is going to be as quarter a quarter is bigger and differential population for carbon as it is for Proton so when we get into techniques like hm said which is a two-dimensional technique 1 of the tricks of this technique is to transfer the larger but still minuscule population difference from Proton to that of carbon but again what's damning is you never can get away from the fact that out of 200 million that out of 2 million protons at 500 megahertz there is no way to exceed that I think I said EU 1 out of 2 million population difference with the exception of some very specialized techniques that involve for example unpaired electrons and free radicals world were xenon atoms for that matter independent special optical techniques all right so we have a differential population and we know that if we apply a policy of the right length we can drive that population to have another mechanization in the ex-wife .period near let's take a look at how we get a signal out of the spectrum Our and again we have a coil and I'm going to represent that Quayle as being along the x-axis that's a little bit of an overseas location and now we have a net mechanization in the ex-wife .period and as I said it possesses and so trying of course it's hard in 3 dimensions I'm trying to represent this as recession in the ex-wife planning and trying to represent that with a curvy little arrow but what I'm really saying is you have your net magnet is Asian and it's moving around those vectors are moving around him will just take a single nuclear slight form its processing at the frequency "quotation mark calling the :colon so like at 500 megahertz sometimes it's called more frequencies so for example 500 megahertz for every 100 and 17 thousand 100 and are 500 just magic an animal or spectroscopy was actually discovered by the physicists and then rejected by the physicist because they figured that there would be this universal property of of a proton of how fast it possessed in any given and week when we come next time 2 the concept of chemical shift will see that the frequency the magnetic field that the Proton feels is modulated by the nature of the molecule by the environment and the molecule hence different types of protons processed at different frequencies chloroform process is at a different frequency than TMS CH 2 groups of ethyl alcohol protests at a slightly different frequency than the CH 3 groups these differences in frequency of very very small but they were upsetting to physicists because physicists figure this has to be universal property of protons and when they saw varied by magnetic environment in the molecule they gave it the contemptuous term chemical shifts anyway so OK so what happens if you have a coil and you have a magnet rotating in that Quayle think back to your physics well eventually have will get to relaxation but right now let's just mansion it this the anyone ever done this again as a kid where you take a magnet and you spend it coil great the thing electorate they would you and forehead yeah but here we get a current in the coil and this is this is the basis for all of this stuff so while the nuclear generators are working hard and Sandeno no frame making steam what they're basically doing is turning a magnet inside coil in practice it's done with armature wires but is the exact reverse of a motor and the simplest motor you can make involves taking a of quail and taking a magnet on an excellent putting an alternating current and reverse will you spin a magnetic inside a coiled you get an alternating current and so the current looks something like this on the x-axis going to plot voltage and on the Y axis I'm going to plot time and an AC current is simple and the voltage vacillates in a sign is so it'll fashion so we get this it goes on to call the
sine wave if you if you want and technical and yes I should be at the peak of my of my way right here but what that saying is as the magnet as the the veterans like this in relation to the coil your current comes to wait your voltage comes to a peak and then as it gets along the negative x-axis you come down and it gets to the negative Y axis it comes up and for your 115 that 117 thousand 500 doused magnets were going ahead and having this this discourse of this frequency being perhaps 500 million cycles per 2nd it has to be in the ex-wife line that's that comes from the polls that we apply so remember we have a net magnet is Asian along access we apply a calls that polls drives the magnetic magnet is isation into the XY along the Y axis and we get procession that pulse is equalizing the population of alpha and beta states and in doing that is basically making same numbers spin upstate same number spin down but is directing them together In 1 way and in practice when you apply pulses they actually come in force for those of you run a spectrometer how many of you run and more spectrometer and you do number stance is equal before ages 16 that's no access speak but no accidents because we're actually doing what's calling called face cycling which means in order to cancel out artifacts we 1st do we do a set of 4 experiments or 8 experiments you 1st do a positive X falls for example than you do in negative X than a positive why polls than negative light poles and 8 and then the average them altogether and that reduces article to the big problem with all of this is we're dealing with ,comma really minuscule 6 and so the killer in spectroscopy we've got very few nuclei that are available we've got very small magnetic vectors we get very small signals and the whole key is held again enough signal out of their over all the noise that's coming so that you don't need an entire NMR fault samples in a march fall of pure simple and you can take just a few milligrams or less of compound in your animal or 2 so if I want to give my very very simple diagram on an animal or spectrometry so you have a solenoid the solenoid adjusted coil in which you have electricity it's a superconducting coil superconducting so that you have the electricity flow forever and you don't have to keep putting more electricity and to do this you haven't cooled in liquid helium In order to minimize the evaporation of the liquid helium you have a vacuum around that'd you were vessel any of you who has a vacuum thermosphere coffee has that but in order to further minimize the loss you have that you were contained in liquid nitrogen and a 2nd you were around there was liquid helium is expensive and all places at that all offer so you have your solenoid and then you have your a more simple more to and then you can think of it as your oil so your goes to an amplifier so this is just like a radio at this point you coil goes to an amplifier because you're getting a minuscule signal was never opened in America radio side so the 1st thing you see is some sort of metal Quayle ride on an armature that oil 1 of them is to forward the ATM frequencies and a different 1 tuned for the FM frequencies or if you have a stereo and you have 1 coil that your FM antenna and 1 Quayle material to obviously none of this is Inter's radio so anyway you have 2 different oils that comes back to what I was saying before about having a member I mentioned broadband detection and the proton coil so in general different coils shapes work well for different frequencies and so 1 coils on the inside and so if we are doing Proton and Mark it's best to have your Proton Quayle the inside if you're trying to get the best carbon and Amara in general it's best to have a talk to 2 carbons frequency remember differ by for work on the inside OK so then for modern Panama what you do is you go from an amplifier were going to go Digital so after you get a signal was signal is analog after you go to the signal in word processors were going to digitize that simply means converted the bits and bytes so in other words instead of having a voltage here that's you know 1 . 0 0 7 8 2 3 Miller vaults you're basically going to convert your voltage to 2 binary and say That's 1 1 1 0 0 1 1 etc. so we go to an agency or analog-to-digital converter and anachronistic computer and printer and for those of you who run an enema spectrometer you probably know the command or J. receiver Dane whose heard that was what you're doing there is basically saying OK we want to have we want to fill up as have as big a number of we had 8 bit analog-to-digital converter in other words the digits of 0 or 1 you want your biggest signal to fill up that thing to be as close as possible to 1 1 1 1 1 1 1 whatever it once it is but if it's bigger you're going to saturated and then you're going to get all sorts of artifacts and clipping but if it's too small if you're representing a maximum signal by 0 0 0 0 0 1 1 1 and then by the time you're down to very small signals you just don't have the digital capacity for them so that's what you're doing when you were just adjusting the OK so that's my pigeons diagram of an animal spectrometry and what's happening and as I've said it's more complicated because we have coils in all 4 directions and you're going positive externalities about and so far as the being the advance which of course is accepted it is ubiquitous in an unmarked is the Fourier transform and I can guarantee all of you are going to be able to intuit what this is with 0 mathematics I have nothing against but there's incredible power to being able to actually understand stuff rather than calculated extras needed back here however I give it a simplified version and all that our explaining a few details but let's start this far so this is a
"quotation mark way a corresponding to a procession at 1 cycle for 2nd I want to In other words every 2nd we go around once if we take this function and 48 transform it we end up having
an amplitude axis and time axis and what the 48 transformed does is converts the time axis To a frequency axis so we still have an amplitude and now we've gone from time 2 frequency and so far I write 80 will graft 0 1 2 the I can represent God that's lousy and uneven I can represent the 48 transform as key at 1 1 sign of person and to a first-order approximation that's all there is to a 48 transform it is taking that oscillation and
saying What's the Frequency Of the oscillations so if I take this 2nd graf here and we 48 transformed what's the 48 transformed that 2nd grand a peek into hurts now you've ever looked at your free induction decay will come to wanted FID but you've collected Matamoros spectrum you see that we're going it that legally thing is the free induction decay that's what's going into Europe Quayle at each cycle if you've ever looked at it it's not a simple sign what it is a simple sine wave if you only have 1 type of protons if we do it and pure CDC L-3 that has all CHC 3 and not a lot of water in a lot of TMS you just that the case will tell you about 2nd but normally what you see is something that has more complications and so here what I did literally this was just done an XL as an example I took our 1 cycle per 2nd graf and I took her to cycle per 2nd graf and I added them together To get this red and so if we take the 48 transformed all this red curve again we get frequency just represent that is 0 1 2 3 etc. but now the 48 transform is going to be a peek
at 2 herds of peak at 2 and a peek at once In other words basically what that saying is this is just the superposition all of 81 cycles per 2nd current and 2 cycles per 2nd at and obviously animal spectrum in winter ethanol they have peaks for the CH 2 grouped in 3 peaks for the CH 3 group it's going to be a heck of a lot more complicated parts per million is like cycles per 2nd and more specifically if you have 500 megahertz procession then you're
going to have 500 hertz is 1 ppm a thousand hertz is 2 ppm 15 1500 hertz it's 3 people and if you have
300 megahertz procession if you have that 70 thousand doused mag I talked about last time you're going to have 300 Hertz's is 1 ppm 600 Hertz is 2 ppm 900 hertz peace the now are not exactly playing honest with you because if you have a frequency at a certain member this is amplitude In time the 48 transform transforms the time axis deer frequency access if this goes on for ever then you end up with a line of infinite sharpness what actually gives rise To distorted peach hearsay is something at this frequency but then dies lost where the next financial and so on when renewed 48 transform 8 co-signed wave dying off with an exponential decay you actually get something that looks flies and then a martini and I'm not a great artist but I will try my best to represent the shape of this piece you have little wings coming out and this is what you call a low-rent line shape Lawrence is just a mathematical function that corresponds it's equals 1 0 4 1 over X squared plus plus 1 annual later on CNN after simulation programs that actually incorporates this you'll get to play with however the main point is peaks are not infinitely sharp and this doesn't go on forever reason this doesn't go on forever is what's called a relaxation so there are 2 types of relaxation there's longitudinal relaxation sometimes called spin has sometimes also referred to see it referred to as team won relaxation and what this involves is really equilibration of the alpha and beta stage I transfer of energy from motions in the sample that is the way to think about this is when we applied our pulse we drove a mechanization down into the ex-wife playing in other words what that means is we took the alpha and beta states that were the Boltzmann distribution the natural distribution to begin a magnet and we force them to an unnatural distribution but eventually Due to spin lattice relaxation new nuclei foot their stand back today is too busy axis the flip their the population returns and now you see why you have an exponential decay it's a half-life process any given nucleus has and finite probability of having it spin flip back to the natural populations states and so that's like radioactive decay that occurs with a half-life call the relaxation time or more specifically the team 1 relaxation the top so that gives rise to our acknowledgment of the day that gives rise to a exponential fall now there's a 2nd tied the 1 relaxation is a little more important In small-molecule anymore spectroscopy but there is a 2nd type of relaxation it's also for transverse relaxation sometimes called spin spin relaxation sometimes called T 2 relaxation and what transverse relaxation does is involves the interaction of Spain's with other spins in the sample leading to an uninvited she explains in the ex-wife .period up on
bunching of students in the ex-wife was so interaction with spins of other nuclei we've stuck on bunching of spins in the ex-wife .period what is that means will remember I said when we applied our pipe calls all of our net magnet is station was along the x y plane and all the suspense of the same type are processing together but if they on bunch if duty getting tickled by other nuclei some possess a little faster and Sampras Cecil on talking now for 1 type of nuclear like the hydrogen chloroform what happens to the net mechanization From that vectors look at where we look at the vectors is starting to cancel each other out were still in the XY .period in other words are population of alpha and beta states hasn't been butter we still have that non Boltzmann population from the initial polls where it's in this case for pipe polls 50 % up 50 per cent down but now we're losing our focus in the ex-wife plane as they on bunch are mechanization gets smaller and smaller and the signal falls off and so through these relaxation processes through T-1 relaxation and Trudy to relaxation we have a falloff in you know and so we get a line that has a with to it are there 2 concepts that are closely related to 1 concept we saw as the whole idea of the 48 transformed gives rise to a peak with a with a 2 it but the other thing is that lying with is related to the uncertainty principle so we can always go ahead and blamed quantum mechanics just the uncertainty principle as you've probably heard it is that you cannot know with exact accuracy both the position and the velocity of an object To put it in other terms the longer you can make a measurement the more accurately you can know the velocity Laura the longer you make a measurement Phil more accurately you can know the angular velocity that's the same ideas and infinitely sharp lines if I have something possessing and we can watch it forever we can know that this is possessing at 500 . 0 0 0 3 2 1 5 cycles per 2nd however if you only get to look at it for a little bit you say what was moving fast it wasn't moving at 100 cycles per 2nd it wasn't moving at a thousand cycles per 2nd it was somewhere around 500 cycles per 2nd and expressed mathematically what we get is that Delta Nu times Tower is equal to 1 over route to hide what this is is the I'll call this the hair of wine with meals you was in a 2nd and this is towers the half-life of despair and so let's come back to our Lawrence line shape and let's come to some hypothetical ideal so remember we're talking frequencies so our hypothetical ideal is this is the hypothetical exact frequency but the point is if we can measure the frequency exactly because we're not measuring it for infinitely long because the frequencies from the line is relaxing we can only tell where only thing somewhere around here and so you get a pity that has some West to and this is our Delta Nu and from your point of view but you often think of and when I think of when I look is this is what I like to call the lined with In other words it's sort of that have height In other words it's it's too Delta Nu this here resigned Wyoming it said within plus or minus the open to all this center value but we can't tell exactly here I look and I say OK this line is this fact alright so what does that mean if we have a town 0 equals 2 seconds that leads to Delta Nu is equal to 1 over route 2 route to piety is equal to . 1 1 that's
. 2 2 herds lying with if I have a towel and this is of course seconds if I have to to how we equals 1 then Delta Nu is equal to 1 over clout the the equation here it's equal the . 2 2 hurts easy and that's . 4 4 kurds lined with now the relaxation of protons typically occurs on the order of 1 or 2 seconds so there is a real theoretical limit tell howl shop year peaks can be because that theoretical limit is going to be determined by the relaxation carbons are funny because they relaxed more slowly and there is the reason that you end up not having on big peaks for quarts you know that your quarks always quarter carbon sir carbon heels and problems with 4 things connected are always very short is because between pulses you don't go ahead and have a full return back the stage know you you don't have control of it you have a little bit of control if you remove that if you enter her magnetic impurities van which we actually doing experiments like the inadequate experiment then you can increase you can decrease the life if you remove power magnetic impurities for example if you buy freeze palm thought the gassing remove dissolved oxygen which is paramedic from your sample you can decrease the T-1 relaxation because remember it's the interaction with nuclei that flips the standard so you have oxygen it's permanent are so the point is exponential decay leads to line broadening and if you have a little bit of exponential decay like soul then you get a sharp lying if you have a lot of exponential decay you get a broader this evolved from Portland transport yet you reduce the effect of the disease by aligning you can do various tricks so in the case of molecules that have very restricted Mogens like salads T 2 relaxation becomes critical and in the case of salads to get good spectra you have to spin the sample at what's called the magic angle to reduce relaxation T 2 relaxation to their old tricks but for the most part relaxation isn't a problem proton NMR it's a good thing because it allows you to repeat your experiments and that brings us brings us to the next and I think perhaps the last thing time will talk about it as a said carbon and marking the pain because it's the relaxation is so slow that it makes Europe makes Europe keep small aren't so the last thing I'll talk about a signal language no I've already hinted that you have this notion of phase cycling that you really have to do experiments in sets of 4 world or a with the exception of certain pulsed field gradient experiments that all talk about later that reduces face cycling this becomes important thing to do but you got all the trouble the synthesizer compound make up an animal sample you collect the spectrum it's no big deal to collect data for a minute instead of 4 5 seconds so that's not a big deal but the big problem that we have as I said an awards Avery and sensitive technique you have a very low signal not finding the low signal what you're fighting is the noise and we talked about the choir probe the choir probe the other day doesn't increase the amount of signal but it does decrease the amount of noise electronic noise think of noise and static you tune to an FM radio station that's far away you hear a lot of static doesn't occur in Internet British radio because it's all digital but you tune to a state station it's far away There's a lot of static so what can you do the static is random so if you go ahead and collect refuted 6 repeated signal you can average it out the signal-to-noise varies and as is the square root of the number of stance in other words if I collect more data I get more signal-to-noise but the noise is going up as well it's just going up randomly so in other words if I go from 16 stands which is a very reasonable number 264 stands I don't quadruple my signal-to-noise I double the signal-to-noise and so if you're collecting 13 and a more spectrum and you've got a lot of noise you say Oh well if I go ahead and I want make my spectrum twice as good I've got to collect data for times as lot if it's midnight and you've been collecting since 10 PM know that your Spectrum's only going to get a little bit better only 1 . 4 times better if you wait till 2 in the morning if you wait till 6 in the morning it's going to get twice as good if I double the concentration also doubled the signal-to-noise state to acts so again I'm sitting there at midnight and thinking My God I don't want to be sitting here till 6 AM I run up to the laboratory adopts a more simple and my animal or 2 and now by 2 in the morning I have places to inspectors so
that's that's the general gist there are a number of other aspect I think I give us a reading in Claridge that I'd like you to look over there a number of other aspects of 48 Aymara spectroscopy including digital resolutions but suffice it to say right now we collect data for a few seconds the data is becoming as your signals falling off like so we have more noise here relative to signal so we don't want to collect data forever so in the end we strike a compromise we collector for a few seconds we average the data we perform a few mathematical operations to smooth it out because the 48 transformed of a truncated signal if I just from carried my signal the 48 transforms actually looks more like this where we have a couple of wiggly things around the peak so we applied weighting functions that's called the exponential multiplication we apply weighting functions so you don't just promptly you actually drive the signal down so that you get a better 1 shape and you can read a little bit more about the flowers are I will pick up next time talking about chemical chefs and at that point will start to talk about differences between different types of evidence within the molecule