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>> Good morning everybody.
Okay so a couple
of announcements before we get started.
One is there are still some extra credit things
that I'm working on, but I think I have done all
of the mid-term 1 regrades.
If I missed yours, sorry, it was an accident.
Please just send me a reminder.
I don't think so though; I think I've gotten all of them.
As everybody is no doubt aware, our mid-term is Friday.
So what we're going to do is try to finish up the new material
that we need to cover for the midterm today
and if everything goes well hopefully next time we'll just
be a little bit of review sort of recapping what's going to be
on this exam and some applications of NMR.
So, let's try to get through this stuff today.
Anybody have any questions about last time before we go on?
All right.
Cool. Yes?
[ Inaudible question ]
Well, so the only term symbols that I'm really going
to explicitly ask you to write down on this exam are
for diatomic molecules.
So, that's about it.
So we reviewed it in the atomic case just because I wanted
to make sure everyone remembers from last quarter
because it's really analogous to that, but we're not going
to spend a lot of time on that.
For the atomic ones it takes a lot of time to write it down
and we, you know, it's just not the main emphasis.
So for the diatomic molecules you should be able to do stuff
like use your general chemistry knowledge
and write a molecular orbital diagram and then use
that to generate these things and be able
to use the information that's contained in those term symbols
and make conclusions about it.
Yes?
[ Inaudible question ]
That's right.
So there's going to be a whole bunch of selection rules
and frank common factors and deciding which transition
to happen and what the intensities
of different transitions are and how to interpret spectra.
So one thing that showed up on the practice midterm
that we didn't see the first time is looking at spectra
and being able to read things off of them
and learn some information about the molecule and the fact
that that didn't show up last time should tell you something
that, you know, probably you're going to see it again.
So we did, you know, sort of, so rotational
and vibrational spectroscopy especially IR
and Raman we did sort of leave off talking
about that before the last midterm.
So that stuff will be on there.
Again, lots of selection rules and also some NMR.
Again, the NMR questions will be sort of two types.
One is using the matrix representations
of different things that we've been learning
about at a basic level.
We're not going to do anything super advanced
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 or I'm not going
to give you a really complex spectrum and expect you
to generate the structure of some organic molecule.
It's going to be the other way.
We're going to look at the molecule
and predict what the spectrum looks
like because that's really the emphasis in PChem.
I want you to understand the spectroscopy.
Okay so last time we left off talking about T1
and somebody asked a really good question at the end
of class last time about does this relaxation time affect the
line width?
It doesn't.
That's the relaxation in the XY plane which is called T2.
So let's review a little bit what's going on with T1
and then we will talk about the difference between that and T2.
Okay, so T1 is the longitudinal relaxation time.
This is the time that it takes
after you flip your spins down to the XY plane.
This is how long it takes them to come back along Z
and return to equilibrium.
So we ended up last time talking
about the inversion recovery experiment
so this is the experiment that we use to measure T1.
So we flip our spins down and then we do an arrayed experiment
where we wait a little bit of time at the beginning at 0
and then we pulse back into the XY plane and detect.
Then the second time we do the experiment we wait a little bit
longer so the magnetization has a little bit more time to relax
and so the amplitude is smaller and, again,
what we see when we do this as a function of time with longer
and longer delays in there is that we start
with all the magnetization negative and then it comes back
up and goes through 0 and then levels off
to the equilibrium value and this is different
for different nuclei depending
on their local chemical environment.
The reason for this is that in order to come back
to equilibrium the nuclei have to experience local changes
in the magnetic field.
They have to give back some energy
to their environment somehow
and that's why T1 is also sometimes called spin
lattice relaxation.
So, you know, we're giving back some energy to the [inaudible]
and coming back to equilibrium.
Okay so here's an application that was done as a collaboration
between my lab and Professor Shaka's lab.
So if you have an organic molecule where some
of the carbons have a really long T1
because they're not attached to any protons.
So here we only have 1 non-protonated carbon
and that's number 1 here.
We can see that it takes a lot longer
to relax than the other ones.
It's the little tiny one that's labeled C1
in both the structure and the spectrum.
What do we do if we have a sample and we really want
to get the structure of it and it has a lot
of quaternary carbons that are hard to see the signals of?
It's really hard to overestimate how much this wastes your time
because when we're doing NMR pulse sequence the whole pulse
sequence that we're doing takes milliseconds.
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 carbons
that have a long relaxation time.
So, we're wasting most of our instrument time just sitting
around and there are different ways to deal with that.
Here's one that we came up with.
So, in this case, we have instead
of our normal 5 millimeter NMR tube that's about this long,
it has the same diameter and everything but it's more
like 5 feet long and there's a lot of sample in there.
So then inside the probe there's a step remoter
that moves the sample up and down and it's all filled
with the same sample but in between the pulses
as we're signal averaging, we move the sample up and down
so that each pulse happens on a different part of the sample.
So in other words, we're beating the relaxation time
by not pulsing on the same physical sample
for different scans of the experiment.
So, we pulse on some region of the sample that's in our coil
and then when we go to take the next scan the sample gets moved
up and we pulse on a different part of it
and then it gets moved up again and we pulse
on a different part of it.
By the time it comes back
down the long relaxing C13s have hopefully already relaxed.
So that's one way we can make use
of building different probe technology
to beat some NMR parameters that are otherwise problematic.
So here's what that looks like.
So we get for this molecule we can see
for the stationary tube we have recycle delays.
That's the delay in between scans so like I pulse
down to the XY plane and then wait in the top case a quarter
of a second before pulsing back and then 1 second
in the middle one and 4 seconds in the bottom one.
You can see that the signal isn't very strong in these cases
because even if I wait 4 seconds the signal hasn't relaxed all
the way back to equilibrium before I add it up,
whereas in the case
of the moving tube the very bottom one we're pulsing
at a different sample every time
and so stuff has plenty of time to relax.
So hopefully that illustrates the idea if you can see,
you know, how we can try
to manipulate the stuff then you understand where it comes from.
Okay so now let's talk about T2.
So this is a different phenomenon.
So T1 has to do with the magnetization being
in the XY plane and then it relaxes back to equilibrium
by giving some energy to the environment.
T2 happens in the XY plane.
It's dephasing.
So our spin states get out of phase in the XY plane
but there's no energy transfer involved in T2.
This is what determines the line width.
So here's a good illustration of this.
When we give our 90-degree pulse all the spins
in the sample are aligned along Z
at least the first approximation when we're looking at this
in terms of the bulk magnetization vector
and then we pulse into the XY plane,
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, as they process,
they don't stay together.
They're going to process at different rates and spread out.
This can happen for a number of reasons.
So one is chemical shift as I said.
Another one could be local [inaudible] in the sample.
So we can see things that look like differences
in chemical shift but they're actually due to just differences
in the local magnetic environment due
to your sample is a funny shape, it's filled with little granules
that are not uniform and things
like that can really affect the measured line width.
So often it's important to determine,
okay, what's the real T2?
What's the fundamental line width of the sample separate
from things like what kind of an environment is it in?
Is it made up of a bunch of little granules
that have different magnetic susceptibilities at boundaries?
So here's what the functional form of this thing looks like.
It's also just an exponential decay but this is the dephasing
that occurs in the XY plane and that tells us the line width.
Okay. So now how do we measure T2?
So you might think from I've just said
that it's the exponential decay parameter
that determines the line width of the transform signal
and time domain so you might think a good way
to measure it is to just either measure the FID and then fit it
and find the decay constant of that exponential
or you can imagine that we just transform the spectrum
and get a line width and measure that line width
and that would tell us T2 and if experimentally
if everything were perfect, that would work really well
but it doesn't because as I said there are all sorts
of other effects like maybe your magnetic field isn't s
homogenous as you think it is or maybe your sample is
in a whole bunch of little granules that give some kind
of differences in local magnetic field that have nothing to do
with the chemical composition of the sample.
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 XY plane.
So you can imagine that you have your spins pulsed
down to the XY plane and then they spread out
and they're going all around in different directions
and then we wait some amount of time here it's called tau over 2
so the fan out and then we give 180 degree pulse.
So that reverses the fast ones and the slow ones.
So then we wait the same amount of time and they come back
and at that point everything is refocused
and we can measure the signal.
If we repeat that a bunch of times,
that tells us the actual T2 of the sample.
So, you can think about this as like a race.
The starting gun goes off and the runners take off
and the ones that are really fast get way out in front
and then the ones that are kind of slower or in the middle
and then the lazy ones are just kind of walking along and then
if you have another starting gun and everybody has to turn around
and come back, if they go the same pace they're all going
to get to the finish line
at the same time even though some went farther than others.
Spin echo does exactly that and it enables us
to separate effects of local, you know,
issues with homogeneity of the sample or homogeneity
of the magnetic field from the actual spin-spin relaxation.
>> Is there a reason you get the spin echo for the spin lattice?
>> Well, it's a totally different phenomenon.
So the spin lattice relation goes this way
and the spin-spin relaxation is in the XY plane.
So they're different things.
So the spin echo doesn't really tell you about that.
So the way we measure that is with the inversion recovery.
So we put the signal, the magnetization down
and then do an arrayed experiment
for it to come back up.
So the T1 that's the longitudinal relaxation is an
energy transfer process.
So that's how we've said, okay,
in our pulse NMR experiment the system doesn't spew
out a photon.
It has to release the energy in other ways.
That's how it does it.
It's bumping into things and interacting
with little dipoles locally and releasing that energy.
The transverse relaxation or T2 is just dephasing.
These things get out of phase with each other
and it's not an energy transfer process.
So they are quite different phenomena.
Okay. So let's get back to our sort of practical picture of NMR
and we're going to tie it
into the quantum mechanics again at the end.
So we've talked about different properties in an NMR spectrum
that can tell us something about your molecule.
So we had the number of NMR signals in the spectrum.
So the number of inequivalent protons
if it's a proton 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 it's pretty good in the case of protons.
Now we have another couple of parameters that we didn't know
about before that can tell us something
about the sample, T1 and T2.
In fact, those do get used pretty often to tell us things
about not only molecular motion but also molecule structure.
So let's move on to the last major parameter that we can use
to get something about the spectrum at least in the case
of a spin 1/2 nucleus and that is the spin-spin splitting.
So here's an example of a spectrum
that has some splitting going on
and here the resonance has a pattern that tells you something
about what's going on with its neighbors.
So let's just review the rules about this in kind
of a qualitative way before we get into how it works.
So if you have equivalent protons,
they don't split each other's signals.
So if you have say a methyl group
and it's not near any other protons it's just isolated then
you get just get one peak; they don't split each other.
If you have some set of N non-equivalent protons,
that's going to split its neighbor into N plus 1 peaks.
For protons we see the splitting if they're not equivalent
and they're on the same carbon or adjacent carbons.
If they're further away from that,
usually the coupling is too weak to see.
Okay so now imagine that I have a C13 labeled sample.
So all of my carbons are C13 labeled.
C13 is a spin 1/2 and protons are spin 1/2.
In all of these spectra that you look at in organic chemistry,
we talk about the splitting between the protons
and nearby protons, but we also know
that C13 is a reasonable NMR nucleus
and it's 1% natural abundance, but that is enough
that you should be able to see some of it.
So why don't you see splittings
between the proton and the carbon?
Anybody know?
[ Inaudible comment ]
Yeah. That's not exactly right.
You can see, so the quantity is low like you have C13
at natural abundance it's 1% it turns out that
for most small molecules that is plenty you should be able
to see it.
The reason you don't see the splittings is
that the carbon is actually decoupled from the proton
as part of the pulse sequence when you do the experiment.
I think it's really important to point this
out because nobody tells you this when you learn
about these things in sort of the practical context.
So if you don't want to see splittings from C13
in your proton spectrum, what you do is instead of just having
that simple experiment where you apply a pulse to protons
and then wait and detect their signal, while you're detecting
on the proton you apply a high-power RF field
to the carbon to just scramble its magnetization.
So instead of being able to interact with the protons during
that acquisition period, the carbon is just moving around,
the signal is moving around in spin space in a randomized way
and you're not seeing it.
There are lots and lots of different ways to do that.
So what I've described is continuous wave decoupling.
You just apply a pretty high field
to the carbon magnetization and scramble it.
There are lots and lots of symmetry-based methods
that are smarter than that that enable you
to get better decoupling for lower RF power.
We don't have time to talk about them, but I do want you
to remember that we have to have decoupling in order
to get reasonable spectra of these things, you know,
without seeing all kinds of splitting.
It's also a useful tool at times to be able
to say turn off the decoupling during a situation
where you would actually find some utility
in seeing the coupling between the C13
and the proton and you can do that.
You can control all of these things experimentally.
Okay. So if we're back to talking about protons,
here again j coupling is through bond we don't usually see
splitting between protons that are separated by more
than 3 sigma bonds and that's just
because the j coupling here is very weak.
So that's why we get the rule that the splitting is
between protons on the same carbon and on adjacent carbons.
Again, they have to be non-equivalent.
So it's relatively are that we have non-equivalent protons
on the same carbon but it can happen.
If you have a rigid structure where things are not moving
around in flexible way, like if you have a ring structure,
for instance, and there are 2 protons
that have different chemical environments you can have
non-equivalent protons on the same carbon.
Okay so now let's look at the splitting patterns here.
So, if we have a proton
and it has 1 neighbor that's not equivalent,
it's going to be split into a doublet.
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 the neighbor is up
or 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 frequency.
If we have 2 non-equivalent neighbors, it gets split
into 3 speaks and also the intensities are not
equal anymore.
We have a triplet that has intensity 1 to 2 to 1.
Why? Again, it has, now it has 2 neighbors.
They can either both be up or both be down
and those are the little peaks on either side and then
in the middle you can have 1 up and 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 the 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 2 down and 1 up.
So that explains why the splitting patterns look that way
in these spectra that you're used to looking
at in organic chemistry.
So one more thing to tie this together you may have also seen
these things where the peaks lean toward the group
that it's adjacent to.
Have you heard that sort of a as a heuristic to use to look
at to interpret these spectra where you have, you know,
differences in intensity and they're not exactly 1 to 2 to 1
or whatever you would expect.
The reason for that is that the splittings are not
quite equivalent.
You get things with or I'm sorry,
it's not that the splittings aren't equivalent,
those are equivalent, the energy
of these different states is not exactly equivalent.
So all up is a little bit lower energy than all down
and so that's why you see these differences in the intensities.
Okay, so we have hopefully tied all of this practical stuff
into thinking about what the actual spin states are doing
and how that's affecting the local environment
of each of these protons.
Let's look at what that looks like.
So this is called the product basis.
So now we have instead of just we talked about looking
at individual spins and our eigenstates there are alpha
and beta.
Now let's talk about the case where we have 2 coupled spins.
So our overall wave function is going to be a linear combination
of these coupled spins.
We can have alpha-alpha, beta-beta,
alpha beta and beta alpha.
The notation that you'll see is
if these spins are really far apart in chemical shift,
they'll be called A and X and if they're close together
in chemical shift, they'll be called A
and B. That's just notation, but we will see it
so it's important to recognize.
Okay, so if you have no field,
then all of these states are all on top of each other.
They have the same energy.
Then if we add magnetic field, we have to take
into account the splitting for the Zeeman interaction of I1.
So the first spin.
Then there's also the Zeeman interaction for I2.
So these things get split again.
Again as I mentioned these levels get shifted up
and down according to the j coupling
and as I said they're not exactly equal,
which is why we see some differences in these lines.
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 time down in quantum mechanical terms
but exactly the same concept.
Okay so now if we write this in terms of the Hamiltonian,
it has a j coupling term.
So this is Zeeman Hamiltonian again so we have an omega not
for I1 and I2 times the respective Z spin operator
for each one.
So those are just the independent Zeeman Hamiltonians
for our 2 spins.
You'll also see these called I and S
in the literature instead of I1 and I2.
Then we have this j coupling term that's also in terms
of a product of 2 IZ operators for each of the spins.
So if we apply the Hamiltonian to these coupled spin states,
we get essentially an energy we can,
obviously it's the eigenvalue of it is going to be an energy
because it's a Hamiltonian, but we can look at it
in frequency terms because that's what we're going
to measure in the NMR spectrum.
Just have to remember that E equals H nu and then convert
to omega it's the angular frequency.
We're going to have these 4 different frequencies
that we see where the peaks show up that result in or 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 j coupling.
So we have all kinds of different combinations
of adding and subtracting this.
Okay so I don't expect you to memorize this at this point
as far as keeping all of the signs straight.
I do expect you to understand and be able
to tie this back together to what this means
as a physical picture.
So, you know, for instance if I gave you this I might want you
to draw a spectrum of these 2 coupled spins and point
to where the different peaks are for instance.
That's something that might be a reasonable thing
to know how to do.
So, it's important to be able to make the connection
between the practical stuff that we all already know
and how we write it down in quantum mechanical terms.
Okay so let's go back to what stuff looks
like in the product basis.
So we already looked at this in terms of the spin states
but let's check out the spectra again.
So if we have a proton that has no coupled hydrogens,
it's going to have a singlet unless, of course,
I turn the C13 decoupling off
and then it's going to be a doublet.
So here's another fact about this stuff.
The j coupling between the carbon and the proton are going
to be a little weaker than between the protons
and so we won't see necessarily as many couplings to carbons.
We'll usually just see the directly bonded carbon
if we have a non-decoupled spectrum.
Okay so now on the next picture we have 1 coupled hydrogen
so that gives us a doublet and, again,
if we turned off the C13 decoupling we would get a
doublet of doublets.
We would have a splitting for the 2 protons
and then each one would be split by the value for the carbon.
So, for 2 coupled hydrogens we get the triplet with the pattern
of intensities that we talked about and et cetera.
So one of the important things as far as figuring
out what the spectra are telling you is being able
to interpret the pattern of intensities in terms
of the different spin states.
So, yeah?
>> C13 if we were to have it
on decoupled would the splitting come first or second?
>> That's a really good question.
So, the question is if your C13 isn't decoupled would you take
that into account before or after the other one?
The answer is if you're trying to draw the spectra,
you would have to know the values of the j couplings
to draw them and you'd draw the one that's bigger first
and then split the little one based on that.
So it would depend on the actual values.
Yeah?
[ Inaudible question ]
Okay, which case are you talking about?
[ Inaudible question ]
Well, so you're detecting the 1 hydrogen and it has 1 neighbor,
right, and its neighbor can either be up or down
and so it has 1 peak for interacting with the up state
of the neighbor and 1 peak for interacting with the
down state of the neighbor.
[ Inaudible question ]
Right so that's what I was saying
when you have the peaks leaning towards that's why
because you have very small differences in energy.
You can't always see them; they're really, really small.
All of these things have small energy differences anyway.
So you can't always see it but sometimes you do.
Okay. So let's look at some equivalent spins
in some cases where, you know, as we just talked
about what happens when you have 2 different j couplings
which one do you apply first?
So here's a molecule that's kind of rigid
and it has the possibility
to have inequivalent hydrogens on the same carbon.
So in the first case,
there aren't any coupled hydrogens so that's easy.
The second one is a doublet.
Again, that's easy.
You only have 1 inequivalent proton on the adjacent carbon,
but then if we look at the third one we have the blue one
and the red one and here that's,
it looks like that's the larger coupling,
but then we also have this interaction with the green one.
So we split the signal into the larger doublet
or the doublet that's farther apart
and then the smaller coupling comes in as a little splitting
on top of each of those.
So, it's important to be able to tell the difference
between a doublet of doublets,
which is what this is and a quartet.
Of course, you tell the difference
by looking at the intensities.
So here they're all the same size
and for a quartet you have this 1 to 2, 2 to 1 intensity ratio.
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 by using the NMR spectrum.
Okay. So we can take this one step further.
If we have one more proton that splits these things
and is inequivalent, then that one here it's clear
that the coupling is going to be smaller
because it's another bond away and so that splits each
of these things further.
So, you just keep, apply the largest coupling first
and then keep going with this branching pattern.
Again, the relative intensities of the lines tell you a lot
about how things are connected.
So here is again a pictorial representation of that.
We have the methyl group -- question?
[ Inaudible question ]
I don't know it just is.
That's how it works for this molecule.
You would have to, if you have a situation
where it's farther away,
then you can definitely predict it's going to be smaller.
Otherwise, there are a bunch of rules that can help you predict
which couplings are going to be smaller than what.
For purposes of this class right now I would probably just tell
you the coupling values.
Some of them are larger than others and it's not, you know,
predicting which ones are which from looking at the structure.
It's kind of behind the scope of what we're doing right now other
than if it's farther away obviously it's going
to be a smaller coupling.
Okay, so again, here's a good pictorial representation
of the case where we just have one neighbor
and this tiny little arrow pointing with
and against the main magnetic field is that little,
you're seeing the neighbor as a spin up or spin down and adding
to and subtracting from it.
Okay, other things that we should mention.
We've covered most of this, but I stuck this in here
because I wanted to make sure to point
out that coupled spins always have the same coupling constant.
So if we have 2 sets of signals so say we have
that 1 proton that's next
to the methyl group the 1 proton is going to be split
into a quartet and the methyl group is going to be split
into a doublet but the spacing in between those is going
to be the same value because those things are coupled
to each other.
They have the same coupling constant.
So that's also a nice clue when you're using the spectra
to interpret and find out the structure of a molecule things
that are coupled to each other are always going
to have the same coupling value and coming back to your question
of how do you know which j coupling is which,
here's a table of sort of some standard values
of what these coupling constants might be.
There are some theoretical treatments of this.
Gaussian is pretty good for calculating NMR parameters
and you can calculate these things
and the physics is pretty well understood.
Also sort of in parallel
with calculating it people have just measured vast tables
of information, you know, organic chemists
over many years have compiled just a bunch of tables
of different compounds and what their couplings are.
So we have both of these sources of information to draw
on about what coupling constants are.
Again, for purposes of Pchem, I will give you values
of j couplings that I want you to do something with.
It's kind of beyond the scope of what we're doing.
Okay, so you should be able to look at spectra
and tell me why they look the way they do.
You should be able to take a molecule
and draw its NMR spectrum including if I say what happens
if we turn the carbon decoupling off what does it look like?
You should be able to deal with that too.
You might see nuclei for things other than, for things other
than proton and carbon.
So, you should be able to be prepared for that
and you saw some examples in the homework
where there are different types of a nuclei other
than protons and carbon.
The principles are the same.
So, NMR is pretty versatile.
We can do this with anything that has a nuclear spin.
Other things that our spin 1/2 nuclei are, you know, N15,
phosphorous 31, there are lots of these things around.
Also there are quadrupolar nuclei
that have more spin states, you know, more than just plus
and minus 1/2 and we may have to deal with those.
Okay so here's some more complicated splitting patterns.
So, if we look at something like nitrobenzene here HB
and HC just have 1 set of neighbors where as HA is split
by 2 equivalent, 2 inequivalent 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 explain why they look the way they do.
You should also be able to use symmetry to determine
that the protons on either side of the benzene ring
if we take a plane, you know,
this way through the molecule are the same.
Again, don't forget the difference between a quartet
and a doublet of doublets.
They mean very different things in terms
of what the proton is adjacent to and you can tell
by looking at the intensities.
So the quartet has different intensities that's one thing
that's different about it, but if you look closely,
it also has the different splitting pattern.
So in the quartet, the splitting between the peaks is the same
in every case because it's based on a single j coupling
where as the doublet of doublets has 2 different values.
Here's another example of a doublet of doublets.
So proton C there has 2 different coupling values.
So you should be able to generate things like this
for molecules about this complexity;
maybe a little bit harder and you should be able
to get the splitting patterns right.
Okay and, again, so that's what I want to say about proton NMR.
It does apply to all kinds of other nuclei
that we might want to look at.
Again, you will also see C13 spectra.
The main difference here is
that for one thing the chemical shift range is much larger.
So for protons, everything happens
about in a range of about 0 to 12 ppm.
For carbon 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 range
and C13 has a much larger one?
It's polarizability of the electron cloud.
So, proton just has 2 electrons around it at most
and it doesn't have much opportunity
to have chemical shift in isotropy or differences
in the local magnetic field whereas C13 has a lot more
electrons around it.
Its electron cloud is more polarizable.
We get a larger chemical shift range.
From that you would expect that something like xenon,
which is also a good spin 1/2 nucleus,
would have a huge chemical shift range
because it has a really big polarizable electron cloud
and you'd be right; it does.
That's something that people take advantage
of in some applications particularly in imaging things
like lung tissue and void space
where it would otherwise be hard to image.
Okay. So now let's talk about some applications of NMR.
So, what we've gotten to so far covers pretty much what I expect
you to deal with for this exam.
We're going to talk about some applications.
So in the context of measuring T1 and T2, we've talked
about arrayed experiments.
So we've already seen the concept
where we have an experiment and we have some time delay
that we're going to increment and make it longer and longer
and longer each time we do the experiment.
In NMR, it turns out that we can do this
in a more coordinated way and [inaudible] transform the result
and get a 2-dimensional NMR spectrum.
So let me explain what I mean by that.
So here is the very simplest 2-dimensional NMR experiment.
It's called COSY, correlation spectroscopy.
If we look at the last pulse here, the blue one
and the free induction decay,
that's our normal 1 pulse NMR experiment.
So, if we just did that part of the sequence,
we would see a 1-D spectrum.
So each one of these free induction decays
in this picture represents just that part of the experiment.
So now what happens if I put another pulse
and delay in front of it?
So, if we look at the pink one, if I have a 90-degree pulse
and then I don't wait any time
and I do another 90-degree pulse, I'm just going
to put the magnetization along 0 and I'm not going
to see anything for the first point when I detect it, right?
But then if we step through this and wait a little bit more time,
we're going to see some signal and this is going to grow in.
If we look at the free induction decay that we see,
we have as we array that delay, we see the starting amplitude
of the FID that we get in what's called the direct dimension;
that's the part that we're directly measuring
with the last pulse, that's going to be modulated
in a periodic fashion as a result of the delay
because we're going to have anything
from you do a 90-degree pulse and then another one
and see no signal all the way to we let it relax and then
to a point where it's going to be
at an optimal point for detection.
That will be an oscillatory signal
in the indirect dimension.
Then what we can do is [inaudible] transform these
things in 2 dimensions and we get information
about what spins are correlated to each other.
A typical thing that we might use
to correlate them would be j coupling.
So now we've learned about how they're coupled by j coupling.
Here's what something like that might look like.
This particular one is correlated
through dipolar coupling, but because it's a solid spectrum,
but we see the same kind of thing.
So in this case, the blue spectrum is C13
and the green one is N14.
So notice that we only see the C13s that are coupled to an N15
and vice versa and you can think about this as a topological map.
So we have the FID in both dimensions
and then we transform it and get peak.
So, if we took a slice through either dimension,
we would see our normal 1D NMR spectrum coming up this way
or going off to the side.
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 map.
So everywhere there's a dot
that means there's a C13 coupled to an N15.
Here's what that looks like for a protein.
So this is a proton nitrogen HSQC.
So everywhere there's a peak there's a proton coupled
to a nitrogen.
All these little annotations on it are annotations indicating
which amino acid residue in the protein they belong to.
We can't actually figure that out just by looking
at this experiment, it's too complicated.
We need to do a lot of 3 dimensional experiments
where 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 their structures.
So, what this looks like, so we have 2 overlay spectra here.
So, the black one is gamma S crystal
and it's a protein that's one of the structural proteins
of our islands [phonetic].
This is something that we worked on in my group.
There's also a mutant of this protein, which is G18V.
That means the glycine
in position 18 gets mutated to valine.
We're interested in this in my lab
because this is a point mutation that causes a disease.
If you're born with this mutation, you get cataracts
at age 6 and so we're interested in learning
about how is the mutant protein different from the wild type.
So multidimensional NMR spectra really tell us a lot about that.
So, here are some annotations indicating
where peaks corresponding to different residues
in the wild type move around in mutant protein.
By doing a lot of these different kinds
of multidimensional spectra we can build
up a picture of the whole protein.
So the first step is we have to assign it and we have
to get an address for every proton, carbon and nitrogen
in the protein by following along the backbone
through various multidimensional experiments.
So, 2D experiments don't do it.
We need 3 dimensional experiments.
So, for instance, we could have like proton, carbon,
nitrogen as the third dimension and then we get a cube
that has these spheres of intensity in it and we can use
that to map out where things are.
Then in the end we can use that to get the structure.
I'm going to tell you a little bit more about that next time
and we're also going to do a little bit
of review for the exam.
See you on Wednesday. ------------------------------808ed74fcc48--