Lecture 13. Coupling Analysis in First-Order and Near-First-Order Systems (continued)


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Lecture 13. Coupling Analysis in First-Order and Near-First-Order Systems (continued)
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Nowick, James
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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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I want to and I want to continue our discussion of first-order I'll analysis and the analysis of coupling and first-order in your memory systems and as I said the good news is that even know very few of the system that we deal with the truly first-order many of the systems we deal with can be analyzed as if they were first-order realizing that sometimes you will see some deviation so today we're going to look at multiplex and look and trying to to understand really understand them and to extract coupling constant from them and so we've already talked about multiple it's where you have all of the same type of coupling quartet story said Ted and no I wanna go and talk about multiple it's where of coupling where you have different coupling constants here 2 different types of press as I said if you have different types of protons but the coupling constants are the same so you have a proton that's coupled to a Mefin on 1 side of methylene on the other side and all 3 of those coupling constants are the same no big deal it's going to be a quartet you'll see it as a quartet you can analyze it is a quartet you can call it a quartet and that's great but now will look at some first-order coupling analysis were really have different coupling constants In I'll start with a simple example so remember last time we were talking about typical coupling constants I said well you know most of your visceral couplings most of your 3 bond couplings are about 7 hurts but there some that fall outside that range and said 1 of the categories that you have ah Al-Qaeda so let's take a moment to think about Al Keynes in will think about it church on I guess technically you'd call this 3 3 three-dimensional 1 view teams will talk about Turkey here so the Europe sister couplings are on the order of about 10 per cent think they gave you a range of numbers and I said If you want keep 1 number in your head 10 is a good number 2 to keep in your head so would say let's say we would expect about 10 hurts trains couplings are typically very different insists couplings I gave a range of numbers about 14 to 18 they said he won a key point number the head no let's keep let's keep 17 was as a typical coupling for traders and visceral couplings are all over the map I said for S P 3 assortment normal value might be 14 hurts as P to tends to be a lot smaller just a couple of efforts so if you want to keep 1 numbers and expert expectation I said 0 to let's say about 1 in let's take a look at how these resonances we would expect a lot so age is going to be swept by HBO and City and HC is going to splattered with about a 17 herds coupling constant and HP is going to support it with about 10 hurts coupling To put it another way in the different molecules eights is going to see some molecules where HB NHC are both spin up some molecules in which 1 is spent up and 1 is spin down some in which the other is spend up and the other is spin down and somebody rich bolsters spin down now in the case of a simple trip were you have the same coupling constant if 1 is spent up and 1 has been down the the others spend up to and beyond the swapped it doesn't make a difference but if your coupling constants are different then you're going to see different magnetic environments for those 2 molecules and the result is that you're going to 4 HA and indeed we will see for all of the others get a double of goblets where did you get we always name species by way of the 1st coupling constant gives the 1st name the big coupling constant gives the 1st name and the small coupling constant gives the last name In this case of course it's moot because its name is double that of doublets but as we see when we get to trip of doublets and double that of triplets it's going matter so 1 way to conceptualize the spin interactions is as sporting diagram and so we can say that age is going to be splattered with a big coupling of 17 herds and so well just remind us that this is 17 a each of those lines is going to be further splattered with the coupling of 10 herds and trying my best here the bid proportional and so we would expect we would expect a pattern somewhat like this were lines with them Lawrence online shape some and if I call these lines 1 2 and for and we see such a pattern we see a goblet of outlets are this is always going to be 1 minus 3 and that's going to be the same as to minus 4 are within the limits of experimental error because there is experimental error in key key positions because of things like digital resolution which says although Europe and a more spectrum is depicted as a series of smooth curves the curve is actually composed of a series of data points and the separation of those data points depends on your suite with a new acquisition time typically you have about 30 thousand to 40 thousand at 30 2002 say 50 thousand real data .period divided over the entire width of the spectrum so if your spectrum with it is 14 parts per million and your 500 megahertz so you're so your spectral with his 500 hertz per ppm of your sweep with a 7 thousand hertz and if you have a 30 hurt as 30 thousand .period spectrum that means each of your points is going to be separated by a few tenths of a hurts right by 7 thousand divided by the number of points by what's 832 thousand real points that would be called the a 64 K dataset because in the 48 transform you collect 64 thousand real and
you collect 64 thousand points in the time domain and when you do a 48 transformed that converts due to 32 thousand real points in the frequency domain and 32 thousand imaginary points in frequency domain so that spectrum is going to have 7 thousand divided by 30 thousand is what about at a quarter about . 2 5 per soul hurts right would be about 20 . 2 5 .period forfeits digital resolution which means your point sir separated by a few tenths of a Hertz now for that very reason when we report our spectral observations you don't wanna reporter coupling constants to better then a 10th of a Hertz because by the time you're at a hundredth of a hurts your numbers are insignificant I think about your rates in line with his on the order of profits due to the uncertainty principle and errors and shimmying about 1 . 2 yards you have a digital resolution of about 22 current so that means you can determine the peak position just a a couple of tenths of a so what I typically do to get the best accuracy is I take the position 1 and position 3 and I subtract them and I take position to except for and I subtract those and then I averaged 7 this case here let's say I get 17 . 0 Hearts and I report this as a D 17 . 0 10 . 0 parts from all some showing to be 1 minus 2 and 3 minus 4 and I would take those an an average family get about 10 you will find on many of the homework problems as you go along and we get to the more advanced part course I include a peak print out if you want the PDF you can simply highlight that people bring down pasted into XL Split your data from 2 using the text to columns command and then simply in your XL spreadsheet just take 1 minus 3 to minus 4 1 minus 2 and 3 months for an average of 4 of ways and get your coupling constant out without having to resort to pencil and paper calculation are right so this is a J let's take a look at what we'd expect for each fate so H should be is going to be split by HA with the coupling constant of 10 hurts and it's going to be swayed by a city with a coupling constant of 1 of her so it too will be a doubling of doublets and I will try to draw everything proportionately on my black words here and so here we have 10 hurt and here we have our 1 hurts and we get a pattern that looks I think so an see we also expect to be a double that of doublets and here we'd expect it to be have coupling constants of about 17 herds and 1 herds so again I will draw my lungs splitting diagram and that would be something would have bullets that we'd observed how's that sound since this it is this long OK the distance from 1 to to 4 so look we've moved apart 17 hurts and then I've moved 5 hertz out here In 5 hertz out here well what would you call about it would be I'm MCI 1 . 5 to 3 . 4 from 1 to 4 so wonderful aura is going to be 17 plus 10 Harris which is 27 and actually you hit upon something that's a super the .period the difference between the 1st line in a multiplied and the last line is the sum of all Of the juries no by all of the Jays I'm even with all of their multiplicity is built then and this is what came up when we were talking about that problem in discussion section we were trying to figure out how many hurts the spectrometer was and so I said Well let's assume you have the typical Triplette let's assume a typical coupling is 3 her member the problems the question was what was the field strength of the spectrometer we got 200 and something 350 and we had 1 peak that looked like this and another peak that was as a sex that looked like that and so 1 way to do this problem was to measure this distance and say Oh well that's about 7 hearts but they're measuring it with a ruler and it's not so accurate so another way to do this is to say will measure this distance that's going to be 14 her why because a triplet is a proton that's led by 2 7 hurts couplings the two-time 7 is 14 and then I said well the way I did it which should just gobble more accuracy was to look at the SEC's tact and since I said all of the Jays are about 7 herds this distance From Outer aligned to out of line corresponds to the sum of the 5 Jay's all of which are the same better coupling it so this corresponds to 35 and what's important about this then is that the distance between the outer alliance becomes a check what a Y me I mean that if you will have analyzed a multiplex correctly and you understand it correctly and you've extracted all the Jays correctly then you can go ahead add up all those Jason of course if 1 of the Jays corresponding to trip you added and twice and that's going to correspond to the distance between the 1st and the last and if you haven't
got it right it won't come out right and what's also important is let's say your multiplex is a little bit brought me this came up with somebody in the whirlpool research group was looking at confirmations of boxer occur Bingham of sigh quick cuts occur being in my hands and couldn't exactly see sighs of multiple it but he darn well could see whether the multiplex was roughly 7 hurts wide or whether the multiplex was roughly 15 twice and that was able to tell me whether it's Proton was axial were equatorial on a cycle hexane type bring on a yacht part Pyron ring and hence history chemistry in the current issue so this is why this is extremely important so far thoughts your questions Art I handed down before but I realize not everyone brings the paper and handed out of work a two-sided spectrum to thinks if you have a handout from last time that had the on the um uh the phenylalanine on it you don't need to grab a new 1 but I decided to make extra because I realize not everybody is prepared actually if we can sweep the this week the extras over to this side of the room that that'll take care of a lot of stuff Our everyone everyone have 1 or the other sort of co-opting so let's go ahead let's take a look so this is a real spectrum of 3 3 died Mathilde 1 beauty that I pulled out of the SIA website and then just using illustrated just expanded the multiple and put them on top of a you may hurt scale itself based on this right now we should very easily the able to see which Proton corresponds with soul this multiplex here just expanded over here and further expanded on top of our hearts they'll hear these 2 multiplex here and here Our expanded over here and then extended onto 2 show which 1 is this so that which 1 is best 8 C and this is then alright let's let's take a moment to actually read off the scale yes reader ruler think catalog and see how actual coupling constants compared to the difficult 1 so let's analyze the HA figure out what the 2 chase really we will be the same forbade the NHC the city is improving the icy Romania's prepared as a MII with my head the head the ruler from the bookstore really is good to have a scientific ruler here for this are right so who wants to love to tell me what you got the 2 Jason HA sounds sounds about right OK so age is a With 18 and 11 hurts here would be a good example of where I weep right couldn't report to us more accurately than nearest hurts because we simply don't have the resolution if I were measuring this on an actual spectrometry and I was able to read with with accuracy or people print out I would report for example this as 5 . 8 3 )right parenthesis J equals whatever I read with accuracy here I can only say would be like 18 and 11 . 0 Hearts and assuming the interval worked out I would write it as 1 age and you would report so this is how you tabulate how you tabulate and more data alright what about aides said 17 and 2 what you get 18 and true 18 and 2 of about 18 into it doesn't surprise me that the 2 were coupling constants are the same because coupling constants should be the same mind you if I get different values for example in Agadez digital error there's experimental error if I got 17 . 4 4 1 and 17 . 6 for the other I would report what I observed the data that I would observe I would report for the 117 . 4 for the other 17 . 6 and that's perfectly reasonable what about for this 1 to
11 and we always reported as the big big coupling constant 1st and a small gathering constant I thought certain questions on this fall these days the what if you're reporting a whole series so so great question the question is do you report dealt the 5 . 8 3 said Delta means chemical shift in ppm so yeah from reporting in individual number I would prior reported from tabulating data these days what people typically do when JOC chemicals short shifts reported in hurts relatives with respect to TMS would respect the solvent peaks of people typically don't it's kind of falling out of fashion but Delta was used specifically remember I mention this obscure town scale from the sixties Delta we use specifically to to indicate its on the Delta scale nailed the town scale is so much forgotten that people tend not to not to put as much emphasis and using delta by letter trying let's try some more multiplex and what I'm going to do and I'll show you another another thing that's useful in just a 2nd but what I'm going to do is give you a handout that has some simulated multiplexes show you where I got them in just a 2nd but we analyze them so the best way to really really get an understanding of something is too is to work through it and we've already kind of beating to death a double of doublets I'm going to I'm going to step back and go on but now we have another patterns and how would we describe this pattern tripling of double Letson and I wanna come come to this all right so for the purposes of this class were always going to name it as big coupling constant dictates the 1st name small const coupling constant dignity dictates the last we're going to work through both of them and see the differences now the reason it is important to have agreement on this nomenclature is that if we don't have agreement then you will have different interpretations of the pattern and turn many couplings of different types you have and when it comes to actually understanding during chemical relationships you will get it wrong now the only problem is there's a heck of a lot of confusion in the literature I will make a case for this system of nomenclature This is what we're going to use in the class I can show you at least 1 example where a different system of nomenclature is used I can also show you an article that analyzes everything in terms of doubling of double of doublets and for example we call this a D D D with the Sanger I take issue with that because people invariably erroneously extract coupling constants by that method and get meaningless numbers for example they will measure 1 distance and call it 1 J and another distance and quality other adjacent measures 7 . 4 and 7 . 0 and say those 2 different shades and they're not it's simply the limits of the 2 digital resolutions experimental error so for the purposes of this class for the purposes of what makes sense we will always follow this nominee which are it's so let's take a look at Wall when this we I know that our big coupling constant is I'm sorry doubling of triplets the 2 are now now we're on the same page so a doubling of triplets can be thought of as a pair of triplets we slept with the big into the government and families fled with a small into a trip now tell you a secret for absolutely every multiplied out there for every every every multiplied out there the smallest is the difference between the 1st and 2nd lines and the last and next-to-last line every every multiple new can work yourself work your way through convinces so if we call these speaks 1 2 4 5 6 and we look at them in a peak print out and I just number them 1 2 3 4 5 6 9 of a caveat for you I've simulated this and my simulation happens to run from lower top-flight ppm typically when you see a real specter of it's going to run from high Tolosa typically 1 would be at the top 2 3 4 5 6 0 OK so small J is always going to be the 1st and the 2nd or the last in the next election this is simulated data so the numbers according exactly but if I were dealing with real data what I would do is take an average this so for example we have that's 459 so this is a column for herds this is a column 4 ppm that's the height that's what you'll see in a typical print out for 59 . 5 7 miners 455 . 3 0 that number happens to be 10 points 4 . 2 7 and because this data is synthetic because it is simulated I would take the last 2 and I find that it is exactly the same number for let's see 444 . 70 -minus 440 . 4 3 and not surprisingly because it is simulated it is the exact same number so within reporting two-tenths of a this is 4 . 3 with real data I would take that too and Everett said sorry for a doubling of triplets the distance between the 2 tall lines between lines to win 5 is always going to be your binge depending on the small ratio of a small J to the Big Jake these 2 lines may swap so big Jane maybe 1 to 4 or it may be 1 2 3 if they swapped so if you know exactly what it is you can take that but you can always be safe taking to defy you can always be safe taking the 2 victims so here I
get that it's 455 . 3 0 0 -minus 444 . 7 0 in that's 10 . 6 so if I was reporting this I would report the data in the order J small J 10 . 6 4 . 3 per cent of the he's just like any other it would still be considered a doublet of triplets and I will show you we can do that pattern In the 2nd are so what I want us to do is work through induced splitting diagram for this and I have this graph paper here and we'll do it just the sake of ease will do it as 1 boxes a Hertz and what I'll do is a DTD of attended and for it's just to make it easy stuff I do my splitting diagram I go ahead and I'm going to splayed out into for the double at some going to go 5 each way a 1 2 3 4 5 1 2 3 4 5 this happens to be the boxes to the huge graph paper and then if I continue my splitting diagram I'm going to splitting into a triplet with 4 parts and so I'm going to go out each way for a and have a line in the center so I can go out 1 2 3 4 out 1 2 3 4 then on this 1 I can go out 1 2 really was no salt do I go to into note because remember a trip is a splinter with 2 Hertz coupling constant so sold a triple-A is identical To a doubling of double With have for hearts so doing a little short cut here OK so what I'm saying is a true good for birds is there and that's the same as a that's the same as a DDD with 2 identical coupling constants and so we can take a look at that and see what we get so if I go out like this I'll try to make it fit is exactly on scale not drawing on graft safer and if this is for and now we slept 4 In 4 we go online with intensity of 1 In line with the intensity of 2 flying with intensity of 1 and so a Triple-A you're going to with the 4 hurts coupling constant is going to move out for Hertz in each direction that makes sense because remember I said that if the total J is 8 hurts because you have to forfeit coupling then those outer to alliance arrayed hurts apart that makes sense and so I can grant this and autograph it with the relative intensities of 1 did you 2 0 1 1 2 children using not to go out to hurt Sunday its size so I I said we're going out for her it's because the triplet is for and for it's too for Hertz coupling constants of Triplett with 4 hertz coupling is conceptually the same as a DVD with is indistinguishable From a D D With for forfeits and for her so so what I'm sorry if if you want you can drive us what still named this as a triple-A 0 are so let us let us compare this now 2 these Triplett of double its couple coupling pattern so of course a triplet of doublets is something where you have 1 big couples you have to big couplings and 1 small powerful and you can think of it so this is a privilege of doublets and you can think of this as a you can think of it as 3 double-edged sword trio "quotation mark and so Europe Jiang is going to be 1 might and again we can think of this 4 5 6 5 6 In our big J it's going to be 1 minus 3 which is the same as to minus 4 which is the same as 3 minus 5 which is the same as before 1 intersect so this facing this facing this spacing and the facing all correspond to the triple and if I want the best thing would be to take an average them for maximum accuracy in this case with simulated data I could just say alright that's equal to 464 . 4 3 minus 453 . 5 . 2 6 and that number happens to be the 11 . 1 7 small and as I said before any multiply it you can always take the 1st minus secondary next to the last minus next last miners last the small J is 1 minus 2 3 minus 4 5 minus 65 1 2 since this is simulated data I'll just take 464 . 4 3 -minus 457 . knowing too and I get that that's 6 . 5 so I would report this as 11 . 2 6 . 5 per that's the maximum resolution of the of the instrument and carbon mob your sweep with his nail about 20 times as large typical late your digital resolution is on the order of 1 her because you might have 32 thousand data points but sweep with now might be for example to 20 thousand hertz and so you did your resolutions about 1 typically people report Jason carbon to just alright so let's go ahead and it will stimulate this as a 11 6 and so I will make my Triplette and I will go down and I will go out 11 and I'll go 1 2 3 In and Out 11 and
then also let each of those into 6 hurts double at so I go out 1 2 3 1 2 3 allowed 1 2 3 1 2 3 and helped 1 2 3 1 2 3 and I get lying well I am the latest will "quotation mark well you know all the digital resolution great question so the digital resolution of an 800 megahertz spectrum there isn't any higher than the digital resolution of the 300 megahertz spectrum ,comma which means your lines isn't any sharper so since no matter whether you measure on a big spectrometer a little spectrometer this distance is still exactly the same the separation of lines in Hertz is the same it'll look pretty similar it's just a few have tainting to non first-order effects AB type of effect you'll see last of different now I want to show you to other things this 1 here can anybody name real quickly you see the pattern it's a double-edged of triplets is safe pair of triplets and books and if you go ahead and you take this lying to this line to the 5 is revenge 1 2 2 1 and 3 to 4 is your small Jr and I'll give you the name of it this 1 happens to be 7 . 8 In 5 . during her yeah I want to show you a couple of tools and I want to show you 1 last time alright so this is this is why generated all these peaks this is downloadable on the Web site and so for example if I wanted to make a double of triplets with 10 . 6 and 4 . 3 What I do is simply enter 10 . 6 and cost since we have to couplings of 4 . 3 making up a Triplette I simply enter 4 . 3 twice and there's the pattern that we just saw this just simulates the line with if the lines are a little fatter a little thinner back into Arendse line shapes the 1 that I call aligned with the 1 that we just saw which was 7 . 8 and 5 . 9 Is that 1 and the 1 that we saw before that which was your triplet of doublets with 11 . 2 0 In the 6 . 5 that was the same type of tool exists in
doodle so I can go ahead and simulate a system for example with 11 . 2 all Tuesday ends 6 . 5 and they're
even little convenient convenient slider tools that can take us In 2 Our doublet of triplets that we just saw alright last thing I
want to show you as this will prepare you to tackle just about anything yeah this pattern over here
here we have 3 distinct coupling constants so this
pattern it is a program the right right she'd here actually which was the next 1 on your page was this 1 war was in it this this was so I will grant you this notice that it was the other 1 hour or so I will grab this 1 ends with all that is 1 where you have 2 of the other 2 are not in the form of people are itself are we will do we will do this 1 here which is the last 1 we sweat With 3 distinct coupling constant so it is a double layer of double of Dublin and if we think about our lines here 1 2 3 4 5 6 7 8 remember normally in number from the top all right we name about Big Jack medium J a small small Jr is always the 1st minus the 2nd which is 1 minus 2 where the net last in the next-to-last which is 7 to 10 8 that's 8 point 1 nite I will do the math the medium J is always for a double of double of double it's 1 minus 3 war 6 months and 6 minus 8 always always always that up that standpoint 7 6 the Lawrence J. is being there 1 minus 4 war 1 minus 5 and turn there 5 minus war the 4 minus 8 rather than deal those vagaries remember what I said before that 1 miner safety is always the sum of the Jason and if you have like a triple their to those dates so that is always J. small plus J. medium plus large and in this case that is 31 . 9 1 which means J large is equal to 31 . 9 1 minus 10 . 7 6 minus 8 . 1 9 is equal to 12 . 9 6 and so if I report this it's 13 . 0 0 10 . 8 and a morning and I will leave it to you to work through the splitting tree on this you will get plenty of this in a handout that I've assigned for next week although given where at you could do for for this homework said I'd encourage you to to at least work through it it's a workbook handout that goes with today's lecture anyway OK that's what I think I want to say right now you have all the tools to tackle complex first-order and your first-order multiplexes the was


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