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Lecture 19. Spin Rotations T1 & T2


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Title Lecture 19. Spin Rotations T1 & T2
Title of Series Chem 131B: Molecular Structure & Statistical Mechanics
Part Number 19
Number of Parts 26
Author Martin, Rachel
License CC Attribution - ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/18928
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

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Subject Area Chemistry
Abstract UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 19. Molecular Structure & Statistical Mechanics -- Spin Rotations T1 & T2. Instructor: Rachel Martin, Ph.D. Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules. Index of Topics: 0:03:49 Inversion Recovery (T1) 0:04:59 Relaxation Along the Z-Axis 0:09:20 Spin-Spin Relaxation (T2) 0:12:29 Spin Echo (T2) 0:14:04 H NMR Spectroscopy: Spin-Spin Splitting 0:23:49 J-Coupling Product Basis 0:37:21 Sample Spectrum 0:39:14 The Difference Between a Quartet and a Doublet of Doublets 0:42:24 General 2D Pulse Sequence 0:45:56 H-N HSQC
the morning everybody OK so couple announcements before we get started on 1 is there were still some extra credit things that I'm working on it but I think I have done all the mid-term 1 grades if I mysterious sorry it was an accident please reminder I don't think so that I think about all of our as Everybody is no doubt aware of determines Friday so what we're going to do is it's time to finish up these sort of new material that we need to don't come for the mid-term today and if everything goes well hopefully next time will just be a little bit of review sort of recapping what's going to be on this exam and does applications of an so what's try to get through this Saturday I think we have any questions about last nite before we go on article yes the the end of the day well so the only term symbols late rambling going to explicitly ask you write down on this exam or for diatonic molecules so that's so that's about it so we reviewed it in the atomic case just because I want to make sure everyone remembers from last quarter because it's it's really analogous to that by where and spend a lot of time and that takes the for the atomic ones it takes a lot of time rate down and down we you know it's just not the main emphasis so for the you know the diatonic molecules you should be able to do stuff like that USA general chemistry knowledge and right molecular orbital diagram and then you use that to to generate these things and be able to to use the information contained in those terms symbols and make conclusions about it the yes but start just that's right so there's going to be a whole bunch of selection rules and Frank common factors in deciding here which transitions happen and what the intensities of different transitions are and how to interpret spectra so 1 thing that showed up on the practice the term that we didn't see the 1st time is spectacular looking at spectrum being able to learn to read things off of them and wants information about the molecule and the fact that that didn't show up last time should tell you something that you probably and again so we did you know sort of so rotational vibrational spectroscopy especially I are enrollment we did sort of leave off talking about that year before last in terms that stuff will be on there again lots of selection rules and also some some anymore and again the anymore questions will be sort of 2 types 1 is using the matrix representations of different things that we've been warning about you know at a basic level continuing super advanced on the and also being able to predict spectra of molecules and explain what they look like I'm not going to give you a structure of some extremely I'm not going to give you a really complex spectrum expected generator structure of some organic molecules can be the other wearing a look at the molecule and predict what the spectrum looks like because that's really be emphasis is on I want you to understand that spectroscopy OK so
last time we left off talking about T-1 and somebody asked a really good question at the end of last last time about does this relaxation time effect language and it doesn't that's the relaxation in the ex-wife plane which is called T 2 so what's review a little bit what's going on with 1 and then we'll talk about the difference between 92 a peso the 1 is a longitudinal relaxation time this is the time that it takes after you flip here been down the ex-wife plane this is how long it takes on the comeback along the and return equilibrium and so we ended up last time talking about the inversion recovery experiments is the experiment that we used to measure 1 so we flip stands down and then we do in a raid experiment where we wait a little bit of time at the beginning and 0 and then we pulls back into the ex-wife playing and attacked and then the 2nd time we do the experiment we wait a little bit longer so the man's vision has a little bit more time to relax and so the amplitude is smaller and again what we see what we do this as a function of time with with longer and longer delays in there is that we start with all the main musician negative and then it comes back up and goes through 0 and then levels off to the equilibrium value and this is different for differently if we had pending on their local chemical environment and the reason for this is that in order to come back to equilibrium the nuclei have to experience local changes in the magnetic field you know that they have to give back some energy to their environment somehow and that's why I T 1 is also sometimes called spin lattice relaxation so you know we're giving back some energy to the back and coming back to equilibrium OK so here's
a here's an application about that was done as a collaboration between my Lavin Professor shock as well so if you have an organic molecule
were some of the carbons have were have a really long T-1 because they're not attaching protons so you know here we only have 1 None non-operated carbon that's a that's number 1 here we can see that it takes a lot longer to relax than the other ones it's that the little tiny 1 that that's labeled C 1 In both the structure and spectrum where we do if we have a sample we really 1 get the structure of it and it has a lot of winery carbon is there the hard today to see the signals of it's really hard to overestimate how much this waste your time because when we do another Merkel sequence the whole pulse sequence that were doing takes you know Ms it's not it's not really that long but then we have to wait several seconds to maybe minutes or even longer in the case of these these problems that have a long relaxation time so were wasting most of our instrument time just sitting around in their different ways to deal with that here's 1 that we came up with
so in this case we have instead of are normal 5 millimeter in March to that's about this line it has the same diameter everything but it's more like 5 feet 1 and there's a lot of Central incident inside the probe there's a stepper motor that moves the sample up-and-down and it's all filled with the same sample but in between the pulses as were as were signal averaging we move the sample up down so that each poll's happens on a different part of the sample so in other words were beating the relaxation time by not all saying on the same physical sample for different experiment so you know we pulse on some region the simpleton Rockwell and then we go to take next scan the sample gets moved up and Repulse on a different part of it and it gets moved up again repulsed under different per and by the time it comes back down the the long relaxing the 13th have hopefully already relaxed so that's so that's 1 way that we can make use of building different probe technology to To be some MR parameters the otherwise problematic and so here's what that
looks like so we get for this molecule we can see I'm here for the stationary too we have recycled is that the delay in between scans so like I poles down to the XY plane and then wait in the top case a quarter of a 2nd before pulsing back and then 1 2nd in the middle ones and 4 seconds in the bottom 1 and you can see that the signal was very strong in these cases because even if I wait for seconds the signal has a relaxed always back to equilibrium before added up as in the case of moving to the very bottom 1 were pulsing on different sample every time and so stuff has plenty of time to relax yeah so hopefully that illustrates the the idea if you can see you know how we can try to manipulate the stuff then you understand our work comes from OK so now Woodstock about T 2 so this is a different phenomenon so T 1 has to do with the modernization being in the ex-wife plan and relaxes back to equilibrium by giving some energy to the environment T 2 happens in the XY plane it's D phasing so are her spin states get out of phase in the ex-wife plane but there's no energy transfer involved in T 2 and this is what determines the language and so here's a here's a good illustration of this 1 we give our 90 degree polls all the spins in the sample or aligned along z at least a 1st approximation warning when were looking at this in terms of the ball mechanization Becker and then we Paulson the DXY White Plains but they have different resonant frequencies because they have different chemical shifts and so they're going to fan out so they don't stay here as they process they don't stay together they're going to possess at different rates and and spread out this can happen for a number of reasons so 1 is is chemical shift as I said another 1 could be local in homogeneity is in the sample so that he can see things that that look like differences in chemical shift but they're actually due to just differences in local magnetic environment due to you know your sample is a funny shape it's filled with little granules that are not uniform and things like that can really affect the measure language with and so often it's important to determine the OK what's the real T to what's the fundamental line with of the sample separate from things like what kind of an environment is again innocent made up of a bunch of little granules that have different magnetic susceptibilities you at boundaries and so here's what the the functional form Of this thing looks like it's it's also just an exponential decay but this is the defacing that occurs in the XY plane and that tells us aligned with OK so now how do we measure t to see you might think from me I just said that it's the it's the exponential decay parameter that determines that the line with the B "quotation mark Fourier Transform signalman time domain seem I think a good way to measure it is to just in a measure the FIT and then fitted and find that the decay constant that exponential or you can imagine that we just 40 transformed spectrum and get aligned with and measure that line within that would tell us to to and if experimentally everything was perfect that would work really well but it doesn't because as I said they're all sorts of other effects like maybe you're magnetic field isn't as homogeneous as you think it is or maybe your sample is in a whole bunch of all granules that that gives some new kind of differences in local magnetic field that had nothing to do with the chemical composition of the sample and so in order to do that we need to use a pulse sequence called the spin echo so the spin echo refocuses everything in the ex-wife .period and so you can imagine that I you know you have Boston's Paul Stanley BFI and they spread out and there going all around in different directions and then we wait some amount of time here it's called Tower virtuoso they fan out and then we give 180 degree pulse so that reverses the fast ones in the slow ones and so then we weigh the same amount of time and they come back and at that point everything is refocused we can measure the signal and if we repeat that a bunch times that tells us the actual T 2 of the samples so anything you can think about this is like is like a racing the starting gun goes off and the runners take off and the ones that are really fast get way out in front and then ones that are kind of slow you're in the middle and then you know the lazy ones are just kind walking along and then if you have another starting gun and everybody has to turn around and come back if they go the same case they're all going to get to the finish line at the same time you know someone farther than others spin echo does exactly that and it enables us to seperate effects of local you know the issues with the homogeneity of the sample or homogeneity the magnetic field from the actual spin spin relaxation there is a need to use it for me 1 well it's it's a totally different from and right so so the spin lattice relaxation goes this way and the spin spin relaxation is in the ex-wife plane so they're very different things so the spinnaker doesn't really tell you but that's about the way we measure that is with the inversion recovery so we put the signaled the magnification Asian down and then doing a raid experiment with for it to come back up so the the T 1 that the longitudinal relaxation is an energy transfer process so that's how you leave said that OK in Articles 10 Mar experiment the system doesn't spew out folk it has to but it has to release the energy in other ways that Howard doesn't it's bumping into things and in interacting with little Bibles locally and releasing energy as the transverse relaxation or T 2 is just the phasing these these things get out of phase with each other and it's not an energy transfer process where they're quite different phenomena OK so let's get back to are a sort of practical picture of Anwar we're tied into the quantum mechanics again at the end so we talked about different properties in an hour spectrum that can tell something about your molecule so we had to the number of animosity Ingalls and spectrum so the number of inoperable protons of it's a spectrum we also talked about the different intensities of them which again you have to be careful if you're talking about something other than protons it might not be perfectly quantitative but if it creates pretty good in the case of protons now we have another couple of parameters that we didn't know about before they can tell us something about the sample T 1 and T 2 and in fact those do get used pretty often to us to tell us things about not only molecular motion but also molecular structure so let's say move on to the the last major private we can use to get something about the perspective at least in the case of a spin one-half nucleus and that is the spin spin splitting so here's an example of a spectrum that has since splitting going on and here the residents has a pattern that tells you something about what's going on with its neighbors and so let's just review the rules about this in kind of a qualitative way before we get and how it works OK so if you have equivalent protons they don't
splinter the signals so if you have a say in methyl group and it's not near any other protons it's just isolated then use that 1 piece they don't support each other if you have some set of n not equivalent protons that skin splits its neighbor into endless 1 peaks and for protons we see the splitting if they're not equivalent and they're on the same carbon adjacent province if they're further away from that usually the coupling is too weak to see OK so now imagine that I have a C 13 labeled samples so all my carbons see 13 labeled C 13 is a spin one-half protons been one-half In all the spectra that you look at an organic chemistry we talk about the splitting between the plan that the protons and nearby protons but we also know that see 13 is a reasonable 1 of our nucleus and it's 1 per cent natural abundance but that is enough you should be able see some of it so why don't you see Sporting's between the Proton in the car and they know yeah that's not exactly right see you can you can see so that the quantity as well like you have see 13 at natural abundance of 1 % it turns out that for most small molecules that is plenty you should be able to see it the recent you don't see the splitting is is that the carbon is actually decoupled from the Proton as part of the whole sequence we do the experiment and I think it's really important to point this out because nobody tells you this when you worry about these things in in sort of a the practical context so if you don't wanna see splitting from see 39 year proton spectrum what you do is instead of just having that simple experiment where you apply a pulse 2 protons and then wait and detect signal while you're detecting on the proton you apply the high-power RF fields To the carbon to just scramble it's 9 musicians so instead of being able to interact with the protons during that acquisition period the carbon is just moving around this that the signals moving around spin space in a randomized way and you're not seeing it there are a lot lots and lots of different ways you that's what I've described as continuous wave the coupling to supply a pretty high field to the decarbonization scrambling there are lots and lots of symmetry based methods that smarter than that that enable you to get better decoupling for lower power we don't have time to talk about but I do want to to remember that we do that we have to have the coupling in order to get reasonable spectra Of these things here without seeing all kinds of splitting it's also a useful tool at times to be able to you know say turn off the decoupling during a situation that where you would actually find some utility and seeing the coupling between the sea between the proton and you can do that you can control all these things experimentally at the time OK so if we're back to talking about protons here again J. coupling is is through bond we don't usually see sees splitting between pro consider separated by more than 3 signal once and that's just because the Vijay coupling here is very weak so that's why we get to rule that the splitting his time between protons and same carbon that and on adjacent apartments N we again they have to be not equivalent so it's it's relatively rare that we have not equivalent protons on the same carbon but it can happen if you have a rigid structure where things are not moving around in a flexible way like if you have a ring structure for instance in their 2 protons litter that have different chemical environments he would have none equivalent comes on the same program OK so now let's look at the the splitting patterns here so if we have a proton and has 1 neighbor that's not equivalent it's going to be splitting 2 a Dublin why because if I'm sitting at that Proton and it has 1 neighbor it can either be up or down and depending on whether it's whether the neighbors upper down it's going to be adding to or subtracting from the main magnetic field and that gives me a little bit of a difference in the at the frequency if we have to not equivalent neighbors there's so that it could split into 3 peaks and also the intensities are not equal anymore we have a triplet that has intensity 1 2 2 1 wife again it has now it has to neighbors making either both be out or both be down and those little peaks on either side and then in the middle you can have 1 up 1 down but you can do it in 2 ways so it adds up constructively in the middle and that's why that peak is larger so then moving on if we have 3 neighbors these signal that we're looking at is going to be Split into a quartet and again same argument you can have all 3 down all 3 up and then there are various ways to have you know 2 down and 1 up and so that explains the the widest patterns look that way In these specter that use looking at in organic chemistry OK so 1 more thing to Titus together you may have also seen these things were the peaks leaned toward the group that it so that it's adjacent to have you have you heard that sort of as a heuristic to to use look to interpret the spectra where you have no differences in intensity and they're not they're not you know they're not exactly 1 two-to-one rural or whatever you would expect the reason for that is that the Spalding's or not quite equivalent you get things with them signed cited it's not that the splitting the article those Oracle won the energy of these different states is not exactly problem so you know all of is a little bit more energy than all down and so that's why you see these differences and intensities OK so we have hopefully title of this practical stuff into you're thinking about what the actual spin states are doing and how that's affecting the local environment of the of protons will circulate that looks like OK so this is called the product basis so now we have instead of just here we talked about looking at individual spins and Aragones states there are Alphand Bader now let's talk about the case where we have to coupled spins and so are overall wave function is going to be a linear combination of these couple spends we can have alfalfa beta beta alpha beta and Beta Alpha and the notation we'll see is if he's been really far apart in chemical shifts Bill be called a acts and if they're closer together and chemical shift that we called a and B. that's just notation but we will see it so it's important to recognize a Case of You have no field then all of the state's all on top of each other they have the same energy and then if we add a magnetic field we
have to take into account the splitting for the Zaman interaction of I won so the 1st then and then there's also the Zaman interaction for right to so these things get full again and then you again as I mentioned these levels get shifted up and down according to J. coupling and as I said they're not exactly equal which is white we see some differences in this clients so this is the same thing that we've already said with the kind of conceptual picture pointing fingers up and down this is how we write it down mechanical terms but exactly the same concept OK so now we write this in terms of the hell Tony and it has a day coupling term so Our This is our Zaman Hambletonian again so we have I know maker not for I want and I too times the respected by disease operator for each 1 so those are just the the Independent Zaman Hambletonian is for spins you also see called I and literature instead of I 1 and I too and then we have this J. coupling terms that's also in terms of a product of 2 I operators breaches Spencer and so if we apply the Hambletonian To these couples spin states we get essentially an energy we referring obviously it's any idea value of it is going to be an energy because it's a it's a Hambletonian but we can look at it in frequency terms that's what we're going measuring in March back from just have to remember that equals each new and then convert to a bank at the angular frequency we're going to have these 4 different frequencies that we see in where the peaks show up that result in there that result from whether you're adding or subtracting the 2 different resonant frequencies of the original nuclei that we're looking at and the day coupling at the time and so we have all kinds of different combinations of adding and subtracting OK so I don't expect you to memorize this at this point you know as far as keeping all the signs straight I do expect you to understand it and be able to to tie this back together to you know what what this means is a physical picture so you know for instance if I gave you this I might want you to a broad spectrum of these 2 couples spins and point to where the different peaks are for instance that saw that something that might be reasonable thing to know how to do it so it's so it's important to be able to to make a connection between the practical stuff that we already know and how we write it down on mechanical terms OK so let's go back to work stuff looks like In the product basis so we are looked at this in terms of the spin states but would stick up the specter again OK so we have if we have a proton that has no coupled hydrogen it's going to have a single unless of course I turned 13 the coupling often it's going to be a doubly so here's another of fact about this stuff the J. coupling between the carbon in the proton we are going to be a little weaker than between the protons and so you know we won't see necessarily as many couplings to 2 carbons like "quotation mark will usually just see the directly bonded carbon if we have a 90 coupled spectrum focusing on the next picture we have 1 couple hydrogen so that gives us in Dublin and again if we turn up to see 13 the coupling we would get a Dublin about what we would have a splitting for the the 2 protons and each 1 would be slowed by the value for the macabre Silver to couple hydrogen is we get the Triplett with the pattern of intensities there that we talked about and etc. so 1 of the important things as far as figuring out what the spectra telling you is being able to interpret the pattern of intensities in terms of the different spin states so yes this is the that's a really good question so then the question is if your see 13 is isn't the coupled with would you take that into account before or after the other 1 the answer is if you're trying to broadly spectrum you would have to know the values of the J. couplings to draw them any broader 1 that's bigger 1st and then splits the the little 1 based on that so would depend on the actual values yeah you have to do and land the OK which which cases had about when the world yeah but well so that the one-year detecting the 1 hydrogen and it has 1 neighbor right in its neighbor can either be upper down and so it has 1 peak for the for interacting with the other state of neighboring 1 peak for interacting with the downstairs neighbor you what groups of rights that's what I was saying we have the peaks leaning toward so that's why because you have some a very small differences in energy you can't always see if they're really really small like all of these things have small energy differences anyway so so you can't always see it that something to OK so let's look at some equivalent spends in some cases where you as as we just talked about what happens when you have 2 different J. couplings which when you apply 1st OK so here's a molecule that's kind a rigid and it has been equivalent it has the possibility to have equivalent hydrogen is on the same carbon a case in the 1st case there aren't any couple hydrogen so so that a single that's easy the 2nd 1 it is a double it again that's easy you only have 1 in equivalent per ton on adjacent carbon but then if we look at the 3rd 1 we have the blue 1 in the red wine and hear that so it looks like that's the the larger coupling but then we also have this interaction with the green 1 and so we splits we support the signal into the larger double under the doubled its further apart and then the smaller coupling comes in as a little splitting on top of each of those and so it's important to be able to tell the difference between a doubling of doublets which is what this says and the quartet at cost you tell the difference by looking at the intensities secured all the same size and for quartet you have this 1 2 2 2 2 1 intensity ratio and so that's something that gives you an important clue when you're trying to figure out what kind of molecule you're looking at buying using in more spectrum OK so we can take this 1 step further if we have you know 1 more Proton that splits these things and is an equivalent then
that 1 near here it's it's clear that the coupling is going to be smaller because it's it's another bond away and so that's each of these things further so you just keep you know ply the largest coupling 1st and keep going with this branching pattern and again the relative intensities of the lines tell you a lot about how things are connected so here's a here's again a pictorial representation of that if we have the methyl group question all I I don't know it just that's how it works for this molecule you would have to I'm if you have if you have it as a situation where it's further away than you can definitely predicted it's going to be smaller otherwise some their eventual rules that that can help you predict what which couplings are going to be smaller than what for purposes of this class right now I would you probably just tell you the coupling values we some of armor are larger than others and in it's not you know predicting which ones are which from looking at the structure is kind of beyond the scope of what we're doing right now the other than if it's further away obviously going be smaller coupling OK so again here's a here's a good pictorial representation of the case where we just have 1 neighbor and this year this tiny little arrow pointing out I'm with and against the main magnetic field is that little that you're seeing the neighbor as a spin-off or stand down and Addington subtracted from it other things that that we should mention this is we've covered most of those but I stuck here because I want to make sure the point out that coupled spins always have the same coupling constant so if we have 2 sets of signals likes to say we have that that 1 proton that's next to the methyl group the year that the 1 proton is going to be Split into a quartet and methyl group is going to explode into a Dublin but the spacing between those is going to be this exactly the same value because of those things are coupled to each other they have the same coupling constant so that's also and a nice clue when you're using these spectra to interpret it and find out the signal molecule to find out the structural molecule things the couple to each other always going to have the same coupling value and you know coming back to your question of how do you know which which J. coupling is which here is a table of sort of some standard values of what these coupling constants might be but there are some theoretical treatments of this Gallician is pretty good for calculating parameters and you you can calculate these things the physics is pretty well understood I'm also serve in parallel with calculating its people have just measured vast tables of information you organic chemists over many years have compiled just a bunch of tables of different compounds and whether couplings are and so we have both of these sources of information drawn about what coupling constants again for us but for purposes of can I will give you values of J. couplings that I wanted to do something with it so it's kind of beyond the scope of what we're doing OK so you should be able to to look at spectra and yeah tell me why they look the way they do you should be able to take a molecule and dried cinema spectrum including you know if I say what happens if we turn the carbon the coupling off then what is a lot like should be able to deal with that to you might see nuclei for things other than we better things other than Proton carbon so should be able to to be prepared for that and you saw some examples of the homework were the different types of nuclei 11 tons and carbon the principles are the same so Panama is pretty versatile we can do this with about anything that has a nuclear spin other things that are staying one-half nuclei are no and 15 pounds phosphorus 31 there are lots of these things around also quarter applauded I'd have more spin states you know more than just a plus and minus one-half and we may have to deal with those OK so here's a more complicated splitting patterns so if we look at something like nitrobenzene you know here H H B H C just have 1 set of neighbors were as Is Split by To equivalent to an equivalent sets of protons and so you should be able to look at something like this and be able to generate the correct splitting patterns and I In explained why they look the way they do you should also be able to to use symmetry determine that you know the protons on either side of the the benzene ring if we take a plane to here this way through the molecule or the same and again don't forget the difference between a quartet double the woods they mean very different things in terms of what the the is adjacent to and you can tell by looking at the intensities so the quartet has different intensities that's 1 way the it's that's different about it but if you look closely also has the difference splitting so in the quartet the splitting between the peaks is the same in every case because it's it's based on a single J. coupling as a double of the double of doublets has 2 different values here's another example of example of a double develops so protons see there has 2 different coupling values so you should be able to 2 generate things like this for molecules of about this complexity may be a little bit harder and you should be able to get the year the splitting patents right OK and again so that's and that's what I wanna say about proton and it does apply to all kinds of other nuclei that we might wanna look at again you will also see see 13 spectrum the main difference here is that for 1 thing the chemical shift ranges much larger so for protons everything happens about In a range of about 0 12 ppm for it's more like 0 to 200 there are other things that have much larger differences in chemical shift so why what makes protons have a tiny chemical shift stringency 13 has a much larger 1 it's polarize ability of the electron out so a proton just has to to electrons around it at most and it doesn't have much opportunity to have chemical shift anisotropy your differences in the local magnetic field whereas the 13 has a lot more electrons around it it's electrified is more Izabel we get a larger chemical range from that you would expect that something like the non which is also a good thing one-half nucleus would have a huge chemical shift range because it has a really big of electron out and you'd be right it does and not so that's something people take advantage of some applications particularly in imaging things like lung tissue and void space where it would otherwise be hard to OK so now let's talk about some applications of Denmark so what we've gotten so far covers pretty much what I expect you deal with 1st this exam and willing to talk about some applications OK so in the context of measuring T 1 and T 2 we talked about a raid
experiments and so we've already seen the concept we have an experiment and we have some time delay that would in increments and make it longer and longer and longer it shall we do the experiment In an unmarked turns out that we can do this in a more coordinated way and Fourier transform the results and get a two-dimensional more spectrum Sony explain what I mean by that so here is the very simplest two-dimensional and marks experiments called cozy correlation spectroscopy and if we look at the last polls here the blue ones and the free induction decay that's our normal 1 pulse and marks Berman so if we just did that part of the sequence we would see just a 1 the spectrum and so each 1 of these free induction occasion this picture represents just that currently experiment a case now what happens if I put another poll delay in front of it so if we look at the pink ones if I have a 90 degree polls and then I don't wait any time I do another 90 degree polls I'm just going to put the mechanization a 1 0 1 democracy anything for the 1st point 1 I detected right but then if we step through this and wait a little bit more time organize signal and this is going to grow in and if we look at the the free induction decay that we see we have also you as as we are a that delay we seem that the gap that that starting amplitude of the FIT that we get in what's called the director mentioned that's the part that were directly measuring with last fall's that's going to be modulated in periodic fashion as a result of the delay because we're going we're going to have you anything from you do a 90 degree Paulson and another 1 and see no signal all the way to you know we let it relax and then and then on to a point where it's going to be an optimal .period for detection and Albion a solitary in the indirect mention and so that we can do is Fourier transform these things in 2 dimensions and we get information about what's been the correlated to each other in a typical year thing that we might use to correlate them would be Jacob likes and now we've learned about how the the coupled by J. coupling here's some of what something like that might look like on this particular 1 is correlated through die poor coupling but because it's a it's a solid spectrum but we see the same kind of thing so in this case be the blue spectrum is 13 and the green 1 and 15 so notice that we only see the sea 13 the coupled to an and 15 and vice-versa and you can think about this as a topological maps so we have the FIT in both dimensions the Fourier transform and get peak so we took a slice through the dimension we would see our normal Our Wendy and more spectrum you coming up this fire going off to the side and we're looking down on this thing that looks like a mountain range because we have these peaks in 2 dimensions and now this looks like a topological maps so everywhere there's a dot that means that there's a C 13 coupled to an and 15 here's what that looks like for protein so this is a proton nitrogen Hsu so everywhere there's a peak there's a proton coupled to a nitrogen and all these little annotations on it annotations indicating which amino acid residue in the protein they belong to and we can't actually figure that out just by looking at this experiment it's too complicated we need to do a lot of three-dimensional experiments were read we look at interactions among protons and nitrogen and carbon and walk through the protein backbone to assign them but this is something that's very useful when you're studying proteins and going about trying to get the structures so what this looks like so it so we have to overlaid spectra here so the black 1 is the crystal it's approaching the mix-up that's that's 1 of the structural proteins of our islands as this is something that that we work on and my group and there's also a mutant of this protein which is 1880 that means that b glycine position 18 it's mutated Bailey and were interested in this in my lab because this is a point mutation that causes the disease if you're born with this mutation you get cataracts at age 6 and so were interested in learning about how is the new protein different from the wild type and so multidimensional and spectra really tells a lot about that so
here are some annotations indicating where different peaks corresponding to different residues in the wild type move around in protein and by doing a lot of these different kinds of multidimensional spectra and we can build up a picture of the whole proteins so the 1st step is we have to assign it weekend you know we have to get an address for every Proton carbon and nitrogen in the protein by following along the back home through various multidimensional experiments
so you to the experiments don't do it we need three-dimensional experiments so for instance we could have like proton carbon nitrogen as the 3rd dimension that we get a few that has these spheres of intensity in it and we can use that to to map out where things are and then in the end we can use that to get the structure and I'm going to tell you a little bit more about that next time and were also gained a little bit every year for the exams seal on Wednesday
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