Lecture 27. Using HMQC-TOCSY or HSQC-TOCSY to Deal with Overlap

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Lecture 27. Using HMQC-TOCSY or HSQC-TOCSY to Deal with Overlap
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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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there is clear single quantum correlation for all intents and purposes they give you the same information the HS QC technique requires facing remember what you did on year you face the a knows inspector right on the 2 d on the refrigerator you faced on the no ceded to the facing work my then led the mouse you you get the boxing need to 1 side the other PHS QC technique requires that the HA QC technique doesn't require that fills done a great job in the Spektr lab of making most of the experiments really easy to runs you don't have to be super expert technically implement these the ones we you have facing require a little more skill to implement as it turns out we tried to implement both H QC and QC and QC taxi ends up being a little better for this and in fact right now alliance working working up an example of this for the final exam so well so I do think what we're talking about a quarter of all that we've gotten to a point I mean taxi when I 1st introduced just plain old Toxey as part of our service we go for correlation experiments remember I said we're going to take our core of correlation experiments as cozy Toxey QC HMV state and then I said I don't want to get overwhelmed and information anachronism so I said Let's start with cozy an ancient QC and use those as R B 6 for addressing to spectra and then we brought in HMV and we saw how each NBC can be really useful for putting the pieces together and they talked about toxicity and then we had for example the they program for problem will we saw how taxi could be really powerful for elucidating spin systems Chris toxic and be like a super cozy either you can get the whole spin system at once not member that's been locked mixing time parameter if you start and begin with a really small spin Mark mixing time you can go like 1 more jump beyond cozy and if you go and have a longer parameter you can go Gold 2 jumps 3 jobs you can use a series of talks spectra like a super cozy spectrum and is long as you have some regions that don't overlap during good shape so just diagram what I'm in other words in cozy right we're going from 1 proton to the next and then the next this is cozy in Toxey we get those same correlations as cozy but mail you go beyond you hop through the spin system and so what ancient fears toxicity and QC Toxey do Is there basically like taxi but with the advantage of the dispersion of the sea 13 which some say White proxy applied with dispersion of seafarers team dimension and in terms of what they're going for us saying good we were overlap you and basically so the other thing say it is that these can be heroes like cozy Hi bearing the mixing time and I think the best way To illustrate all this information which sounds really abstract is to take a problem the spectral structure problems puzzled problem that occurred a real problem that occurred and show how powerful these techniques are so the problem that came up and was was exemplified in your craw wasteland book is the following an analog to but of a natural product was left in the refrigerator for each team the slowest reaction that you will ever do is basically you leave year chemical In an to be in your refrigerator and then you come back and you take a spectrum and you find out that your stuff is no longer what it used to be this is happening to me too and you're curious about what's going on what has happened to my Cameron so the chemical here is is a very natural product called Rome O'Malley all and the reaction is basically 18 months you can see ACL 3 at 4 degrees Celsius and what is happening chloroform breaks down photo oxidized is you get acid and that's why when I have an important sample I generally like the past my core formed through a plug of aluminum that I've dried a furnace or a flame to take the acid out and take the water and I don't pass my sample through I just take a little glass pipette below plug of glass wool in there but about a centimeter of Weimar for his stride aluminum Union aluminum that I've got myself in the in the pipette past Michael formed through before making my sample but understanding and with light and oxygen "quotation mark former oxidises and you get catalytic amounts of NRC so put in parenthesis catalytic H. blast and put that H plus in in quotes because of cost and call former new photo oxidized it's deeper losses but you're not getting deuterium in a molecule cause it's a catalytic amounts to basically we're getting some reaction In the style of he can 203 class like you've learned in professor event break-ins class that has made this molecule do something and what its form is an isomer we had find CH 2 groups and no alcohol and so the puzzle that we have is the figure out what's happening to our Bromo malleable 5 CH 2 groups no way to know alcohol but still has enough oxygen in it and so we better figure out what's what's happened to our molecule of life so will start with the attempt to use the spectrum here portion of your Proton in your carbon spectrum and 1 thing that's that's pretty clear is the proton spectra really is is a man here we've got 1 peak down here at 4 parts per million it's pretty well resolved we've got a couple of peaks over here that looked kind and normal maybe something dire stereoscopic we've got this big he here around Chopin piano we've got something here at about 1 . 5 ppm that looks like it's a single proton not it's clear what's happening here we've got some single Let's here there was saying Let's 1 2 3 for that have to be methyl groups the integrating the 3 hydrogen we have
a here and a piece here there's a lot of overlap in the specter of fact in the spectrum I pray I wouldn't even know where to begin on lettering that I'd probably you know if I slapped an integral on it you basically see a big rise over here someone would to deal with this is just to go ahead and use the HM QC and that put numbers on directly from the H QC several already taken and labeled US taxis with your your hydrogen can you rub your remit fines and and apples and from stated that spectrum and we got our are carbons here ends so we have have some numbers here In the end it's 6 sofa collating our carbon center protons and just going to transcribe our our numbers here so we have I'm a fine which is number 4 are here this guy here looks like it's Number 10 10 by the time we get over to the next while the played here it's less clear were getting across speak from In a cross from 5 you continue along Internet into this region over here and it looks like we've got a kind of also on top of this 1 but please heat right on top of all of of another 1 here so let's see what we have Over here we have the 1 that's been been labeled as 7 so we've got 8 and 7 kind of 1 of the on top of each other we've got looks like we've got 14 kind of up here 14 and maybe maybe in the middle of the year we've kind of got got 12 this guy immersive .period stands out as the Mefin 1st for then it's a little little hard to see but we have a metal single here she ever met Pol Amat Pol Amat Poland methyl as you move across city have no lying over here 11 and then the next Mathilde years I think God 13 and then 15 if I'm looking at the alignment and then the last last 1 that's coming here is the other Asturian town 7 so that's kind of kind about Rosetta Stone were trying to redress this in a way that we've addressed before I haven't even I tried to label these by letters but if you want your costs could go being seen you I become like the Indian prime and God knows what here so maybe this is a better strategy alright let's take a look at how far this strategy is going to get us in the Kosovo and so what we're going to do is look to the next to the next page here In here so cozy spectrum Herman normally at this point we want to try to build up some of the structure so let us get a clear black poor and see how the half are go so again I will start to transcribe my numbers here so for 10 10 8 and 5 kind of heaped on top of each other 14 12 14 8 and 7 kind of heaped on top of each other 3 19 11 that I remember to do but it looks like and the previous 1 1 will guide in this year's election announced that 2nd looks like I miss that will guide over here which 12 of right off of 12 year so we've got well so we've got another dire stereoscopic so let's see let me go and transcribe all of those numbers over here so we have 9 11 12 15 and 13 here and then step so cozy and this is the case sensitive cozying up I talk about this technique on Fridays lecture to used a cozy crossed peaks that assorted square this is if a sensitive technique and you can extract your coupling constants out of the spacing of the spots here which is good when you've got heavily overlapping heavily overlapping spectrum but what we can really do is walk away very far through this so for example if we look at this crossed the great this is for clause 2 so this is for to 10 over here for both of these so OK that's that's at least a got so worrisome of flying we have seen before H and see 10 aides to let's see let's see how far we can go with this so now if we go off of 10 10 crosses into this Mass here so we've got 10 across the the 8 1 5 Over here right so we've got 10 10 8 8 1 5 and then here a Water 7 Over there so we're probably getting tend to 8 but it's really really kind of hard to be sure at this point right here so if we say wells work on a stock over here let's come off of 3 and see if we can do any better so I will say I let's try this Crosby here this is very Cross will it's going to be crossed 5 A 8 so that's kind of confusing then in this whole region here we've just got severe Over and so now we basically basically have done as much as we can with the closings obviously kind of unsatisfying we've got something here across 7 birdies at 14 and 12 overseas aid is at 7 is that all of these just not really getting much and that's that's basically where where we get that so at this point I wanna come back to this issue of toxicity in the 5th HS QC taxi H QC sitting on rights and just just a review
here this is this is the cartoons spectrum I gave you of of Pope and all 4 H & Q C in the cartoons spectrum I gave you open all taxi ride so this is this is 1 probe and all so it's H scene it's true it's too H 3 and obviously obviously this is trivial but it's a schematic and so when we when we look at this and we looked at a chance to say we said OK if we number carbon resonance 1 2 with 3 of the letter our proton resonances 80 B see indeed then we can go ahead and transcribed that information over to for example the taxi and start to see our our crossed speak so here we got let's see if we do this here we've got 1 we've got and we've got 3 D and with cozy in Toxey what we're doing is basically saying OK 1 day Tuesday every day and were saying OK 3 D is crossing with Tim city 2 1 a is crossing with To saying and this with this would come from the cozy and and this guy is new to the toxicity House a specific the toxicity right this is 0 1 1 8 2 3 right so we know what this molecule that this is believed that this is C C 1 2 age 2 ways that this is seen to waged to see this is C 3 H 3 days your cozy gives you this cross speech here and this cross peak here your taxi gives you that extra cost so what you've got the taxi is you get basically this correlation allows you to walk through and the reason Toxey can be really powerful is if you've got a region where you've got heavy overlap but it got 1 proton that's not overlapping you can make your way through it we saw this in the Vale thing with the whole beta proton region with a very crowded and if you had to work your way through that sort of beta gamma Proton region going from method in like ISO Lucena seen to beta and gamma Proton step out for protons in is by cozy we would have gotten lost in that region around 2 parts per million but by having the Toxey you could just say all right we've got men age that's exposed to regard an alpha proton it's exposed I conceded that in nature that alpha proton correlates with these beta protons these metals separate sectors of taxis really powerful in some cases so what ancient Piercy toxicity is is is it's basically White toxicity but gives you the did this version of the C 13 dimension and what's nice about having the dispersion of the sea 13 dimension is there's a lot less overlap in carbon 13 you get a digital resolution that gives you maybe go a thousand points 1024 points said Digital resolution you grow resolve sort of to about two-tenths of the PPE and you may be able questionable higher by 0 going and collecting more data but basically you've got a lot of dispersion In your C 13 dimension in other words you can't dimension sure you've got a lot of digital resolution but you pick some of the plates and as we saw on the proton spectrum those multiplied so often overlap value often in the carbon spectrum use ingredients are going to be all almost fully disperse enough that they don't overlap and your QC underage NBC's techniques are going to be sharp enough to resolve all or most of them and do it all what we have the ancient QC Toxey techniques were going to be able to get a lot more resolution in the in the interim now that's nice is you can vary the mixing time in this experiment do the experiment with a series of mixing times so that you're getting the dispersion of this dimension and using it kind of like a proposed in other words if we have a short mixing time we can go the problem say self-identified call this summer if I call this a 3 D and this to see this 1 a and I call this 1 and 2 and 3 weeks from here to here in other words we can go from 3 D 2 2 and we can go here from 1 8 2 2 and that's sort of a cozy life behavior in this F 1 dimension of course you can do the same thing in the other dimension just as well In other words we can go like from 3 D 2 to saying Over here but what's nice about having the common dimension is if were caught in a quagmire of overlap in the proton dimension we can get ourselves out by going in the carbon dimension and what's also is you can vary the mixing time so you can hop your way from 1 to the next and the next so in this schematic when we got to a longer mixing time now we've up from 3 D 2 2 and then we've had from 2 told 1 CIA basically able of build up a chain at any point using the carbon dimension any point where you have a clear shot from which of well I didn't disadvantage to using a longer mixing time always is you wouldn't get that sequential information here you wouldn't get it going from 1 to the next the next Monday at disadvantage of along mixing finds you go to a long and you've got relaxation working against you and signal-to-noise but the main thing is here you're walking your way through and the best way to see this now is really to go ahead and to look at this applied to our current problem of the Brom O'Malley also isomer so I'd like to do at this point is to go to the next page and so you 1st a schematic but then will go to the real spectrum and then use the real power of varying the mixing time to really build up this structure alright so this is a schematic and again I've taken this from from your textbook reading so this is a schematic where we're going to walk away along the aft to dimension remember that's the less powerful dimension the F 1 is going to be that carbon dimension and so what the author has done here is taking a series of slices all along the line at 61 ppm along the line of which was 61 and the other in the ancient 61 I think was with the was so he's taken alliance said this is the 1 that we call the number 4 and what he's done is this is just the HM Tuesday or interest you say as I said fur for your intents and purposes you techniques are the same here he's made a schematic will see the real thing in just a moment of uncertainty is using agent used so are the agent see taxi that mixing time is short mixing time and is relative it's going to depend on the magnitude of coupling the bigger the coupling constant the mother quickly coupling information will
travel so in other words if you have a 10 hoods coupling constant things will transfer and in the water refused Ms you'll start to see across the for the next top if you ever really small coupling constant it's going to take longer and of course if you're completely at right angles you're going to get much much lower transfers so here's a short mixing time this is in the schematic it's 14 ms and so that basically has taken us from to 10 and so that's what we have over here and then we suspecting that a came in next because we had the 8 overlapping with 78 overlapping with 5 and here as you increase the mixing time and now where we're going here hm QC taxi with longer mixing time this is 36 ms now you next cross the comes in here and so we've come over let me show you the actual spectrum and you'll be able you'll be able to see so here is the here's the 14 ms mixing time actual spectrum and this is a schematic of the the slices that we just just look so this is the 14th alright 40 Angus have written 40 millisecond up on top and so this hot here our C 4 h see 10 it's too at this point and as I said if we continued on we'd see Annex stop here I'll show you how to get that you've been out of even out of the short 1 but here's the real power Of the technique is you can go up so you here for example were saying OK we're following unintended but then for example as we go here and you see that this is your right this is your 1610 10 crossed speak so this is levied transcribe all of our numbers saw Gulf War 10 10 8 5 14 12 14 8 7 3 19 11 12 down here 15 13 7 so it's nice to be here and come here and say All right we're hopping from of arms from Tehran would a bizarre next stop I'll just ride it is tend to aid but that's really powerful you only have to deal with this ambiguity here you have the same right I think this is a not fine and I think this is a fight because you come in the carbon dimension and say all clearly were hopping from 10 38 and if we increase the mixing time you won't even have to get into this quagmire here because in that schematic will we went to the 36 Ms mixing time the next thing that would show up at the 36 ms mixing time would be across the right over here I like the that anyway builds up and builds up part of the molecule that builds up 1 spin system In the molecule cause now we're going to see 8 H 2 all right let's at this point tackle the next been system in the molecule and so what's nice is we've got a nice clear shot offer of 63 you can work off of other parts you want but let's just work all of C 3 now this is the 14 millisecond 1 and so here we go on from here through the and at this 13 of the 2nd 1 5 is starting to pop off not only is his popped up and then were starting that have the next 1 popped up which is to that's the I'm having a little trouble seeing my alignment here it is too and to 12 so were starting to build up another spins but don't take my word for it because on the next page I'll show you the time course so the author of this 1 ahead they did mixing times of 6 ms 14 ms and so on and so forth so what we're gonna do now if you just look at the strip under 3 with varying next time so we stake in Toxey spectra with a whole bunch of mixing times I was out of the the "quotation mark many books so I assume it's the authors there it's it's out Croatian in what you're
reading assignments so it's on there and I forget who the author arch Chapter 11 so think American Airlines Chapter 11 or so anyway that's not so this is all about we are looking at tracks the 4 C 3 alright so here we have gone from C 3 H at 6 milliseconds to see fell alive age In so let me let me start to back this up on the blackboard go we're going from Soon through To see 5 h and that's what 6 ms and you can see the next 1 is just popping popping up here at 13 it's getting there the back up so we've gone from 5 h to see 12 H 2 all right at 24 ms received 12 h to past pick is well-developed and by the time we're coming up to 36 ms were getting a new Crosby son now all honesty 3 tracks were hopping from 12 H 2 up to see 14 2 so we're literally building up this change in the crowded region all of our whom O'Malley all isomer and now as he continues up to 48 ms now we see a new peak developing that's actually developing rather well by the next 1 so we're going from Steve 14 age 2 up to see 7 it's too so that's basically gives us there's spin systems without ever having to deal with the quagmire of the posed no Dome O'Malley all so we have a bunch of stuff that we still lead the deal we have an oxygen we have a bone meal we have in London carbon chilled 0 carbon 6 there unaccounted for for the Syriac wants and then we have our isolated methyl so we have all of these metals single and so we have seen 9 H 3 see 11 at age 3 13 H 3 agency 15 h the rate that we need to put together at this point for of putting the pieces together I'm going to turn to and so on I'm going to turn to the H spectrum he and we can start just about anywhere generally I like to start on isolated peaks In so let me just say that what he's just taken some slices so this is just for license from each 1 dimension so the authors have taken 3 h they've taken our C 9 H 3 see 11 8 3 see 13 these are methyl Singh would see 13 aged 3 and see 15 3 and we can just move along R H NBC tracks isolated metals are great because you can use them they're going to be on a quater and end right there isolated the single it's they're going to be on the clock there are always going to give cross speaks with carbons the 3 Bond crossed speaks to the super super powerful so for example I see 11 is giving cross speaks of Assisi Eleven aged 3 is giving across speech here with 13 H 3 so 13 aged 3 it is another isolated Mathilde so isolated Nepal's give across big that's and Jim Dine that felt so that's cool so we have see 11 aged 3 NRC 13 it's the rating and they're going to have the cross through a quarter Carter all right what else this see 11 age 3 crossed with C 11 aged 3 crosses with see follow now that's really powerful because if it's crossing with 3 bond coupling is gonna put us through the squat carbon on 2 a carbon it's part of a spin systems so that gives us across here and now show this in the 1st spectrum but we have a couple of problems carbon 1 into a better way downfield so we have this crossing with carbon see 11 h crosses with carving 1 next carbon 1 common 1 has 1 more balanced on a number higher than Winder said 80 parts per million double down field of 80 parts per million have oxygen the Molokai oxygen is in the Carbondale what is it it
has be a rise not a carbon 1 oxygen it's a so that's to carbon 1 so that's kind of kind of all right let's take a lot by the way these guys are close together if you slap a grade on less you'll see there is actually 2 tracks years the track that's on the last actually in which I am so the track that's on the left basically nearest the track that's on the right to see this track over here 1 2 the really and that mirroring this other 1 said this week that we don't even need to solve this but this year for example is the 13 8 story With 11 it's raid that makes sense right because these guys are German also see 11 is going to see what's the 13th seed this 1 over here seen 13 age 3 To see 5 8 right because that seeing the same thing and this last 1 here is the 13 aged 3 to see 1 so I think it's so that's that's that but let's go ahead will come off of the here see knowing that the interest so we've got over here we've got aged 3 To see to that that's so we've gotten isolated method and its off of another plot and that what is C 2 and then we've got let's see what else we have for it we have C 9 H 3 or 4 of CH 3 C 3 H rather OK that's kind a useful and we have seen a line 3 office of C 8 changed to OK so that's that's useful because look at them now that's gonna bring are seen line into this here we know that the 2 0 right to was down practically at 80 parts per million as well so what C to on it's got be on the oxygen so we got our seemed to R C 9 H 3 get a bond here because that's an isolated math also it's going through a quarter to a J coupled wonder not couple to each other so it's not directly funded and it has to go through C 2 the CIA so now we're doing very well if you think about it I can put a check next to worse wanted check next to receive 2 would check next to oxygen check next to see knowing the check next to see 11 check next to see 13 we have just see 15 European get 15 couple of waste if you want you can deal with the crowded tracks here if not you can go top of somewhere else we can do it both ways here so here off of our C 3 8 we can go here and we get C 3 H Tennessee 15 aged 3 OK that's not very useful see 12 H 2 that's not very useful I like to see see 15 all 0 OK that is useful because is we've got another isolated manifold and that Mathilde is isolated so that's going be on the quiet that's going to be on the scene seems said so in other words we have the came age 3 we have our seas sex if we're getting a cross between CH parade and see 15 h that's gonna put it in over here now if you're having trouble coming at it that way you can just look at these remaining remaining 3 crossed which I'll doing a moment alright let's see what other crossed we have we have across speak with C 3 agency 19 it's see 2 OK C 8 H 2 that makes sense see 1983 that makes sense that's no new information 7 8 to appear crowded here will we can get it in another way but that has to come through 6 so 1 way get the connectivity it's just to say OK now we're getting across speak from C 3 h vertices 7 then we have across the C-5 H and across 2 so 5 h that's pretty trivial because that's just a tube on coupling crossed deceived ain't so we're going from 3 To see old that's that's useful because that means we build up through 6 and we also get across speak over here to see it to that cost Pete is coming here if you don't like that and you don't like it that way of doing it you can't just say all right let's deal with these 2 single etc. close together over here you can slap agreed on is if you like this position the grid line right down there right down the center here and you can say OK these three-year offer on the left this 1 and these 2 are off on the right
so if you prefer to do it this way you can come out and say OK this is C 15 aged 3 over C 7 it's true so that is giving you that's giving you this bond as well so if you had trouble that's not a double bond matures meet re-emphasizing that there's more than 1 way to skin a cat over here were coming from you see 15 8 story over to see for h see
15 H 3 over the C 3 age and so that saying OK we've got a isolated natural over to see for and we've got a isolated baffled to see 3 cinematic or how you approach it you've ended up putting the skeleton together and at this point we have precisely 1 villain left in the molecule we all over Valenciennes and so are remaining villains is over here and serve bromine which explains explained why that carbon is a little bit on the downfield side so at this point let's return to From O'Malley all structure to deal with what's happened here the threat is shifted far downfield it's a it's a tertiary Carbonell shifted downfield mated to an oxygen it's it's surprisingly downfield but it is it is that for a downfield born but we cannot remember when I talked about carbon I said for Continental more that region oxygen is pretty diagnostic for going downfield nitrogen bromine chlorine not so much Pope carbon roughly parallel each other that carbon is a lot more sensitive to substitution patterns Proton you can say like this is really a CH 2 next to an oxygen extra bromine but not so much for carbon where few next to a bromine is financed still Anakin a cluster of tend to 50 ppm or a little further down here so why we rewrite our structure I'm not going to go through the determination of Styria chemistry on it but I think you'll see you'll see what's happened in just a moment so give us all of our numbers here so we have this ring is 6 7 14 12 5 and 3 this ring here it is true a 10 inform and now we have a new enumerating that's attempt hydro few rendering an attack grew furious and has seen 13 age stories and see 11 it's 3 or 4 there and we have are C 9 so since we are all organic chemist let's return back to what's happened here so we started with this compound that contained a strain cycle propane rate and a tertiary alcohols groups here and we had I'll put each in 2002 because of course you catalytic cycle getting driven by each plus even the you're starting it with a minuscule amount of D-plus so you end up coordinating the oxygen getting a tertiary Koble cap and getting a migration here that's going to be very interesting because now you can start to say OK what's going to happen Over here To get us Over there and I will leave you I will leave you to think about the mechanism and the process there has to occur to go ahead and break the this spell inform about oxygen all right I think that note I want to wrap up is and I guess the thing to do now is to think about how you can use this technique to help deal with crowded overlap situation are right we will pick up and talk about a few more techniques on Friday Over here
HK Over here now we will last 10 an H Over here now the last thing we have to deal with it is our parks in our Parkside the way have drawn it Dupri will be that experience at this point but the way I've drawn it now I think you can end up seeing we see and all we from age or lying 2 H. F we see and always from age 10 age 80 and say and also to the CBC Group can that parts are methylene out here like so for the epoxy it gives us stop Parkside Styria chemistry and in a sign so that sets this area center and now we just have our specific residences and self pointing out is HI In pointing back he is and if you look at a model is what we very quickly if I can make my computer and talk to the projector I'll pop that up if not I have a printout if it weren't so quickly enough we talk to each other give us give it 1 moment here in here it comes and if not are on the top floor of the cops are great then let me be Aaron
Sele this is the same model here and what's nice is you can you know what if your experience with these types of rings you can pry prejudice and but building a model to to influence your thinking and being able to query that model and say you know OK what distance to expect In this model is this consistent it is so valuable the other thing you can get better than I can do with my pigeons drawings here is your coupling your died he'd rely calls and it turns out that things are really really beautiful when you look the 3 multiplex here Donna very very dissect the ball in this structure now just how just flash this out and conclude us conclude with this year so the 3 the 3
multiplied that I think they're just just beautiful to to analyze is you can work through this multiplier is a D D D With 14 . 9 8 . 2 0 and 1 . 8 hurts coupling this one's old tough if you push yourself you can get it is a DDD with 14 . 3 8 . 1 4 . 5 and 1 . 9 and this 1 if you really push yourself you could call on the current Q with 3 big couplings it's a DTD with 13 . 9 for the big 11 . 7 and 1 . 8 and I felt very very proud of myself because after working very hard on as multiple it's I just want them in the my first-order waters simulation and there is really matched matched like a fingerprint on them them so that you can correlate that used to live here here our block prior learned a few things from people in class and this they can right minds more symmetrical because it's only first-order I've kept a long time so we'll we'll talk this
afternoon about the and some of the others


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