Imagine for a moment that you're a detective, but you know you're
not the kind you'd find in some noir novel.
Right. No trench coat, no rainy St.
corners. Exactly.
You're not dusting a whiskey glass for fingerprints.
Your your beat is much, much smaller than that.
We're talking about a scale that is, I mean, it's literally
invisible to the naked eye. It is.
You're investigating A suspect that is infinitesimally small.
You can't see it, you can't touch it.
And you can't even, say freeze it to get a better look because
that might fundamentally change its behavior, how it interacts
with the world around it. But despite all of those
limitations, you have a very specific, very demanding
requirement. You need to know exactly what
this suspect looks like. And we're not talking about a
rough sketch here. We're not talking about a
general idea of its shape. We need the architectural
blueprints. Yes, you need the precise 3D
structure. You need to know exactly how its
skeleton is angled. You know, down to the degree.
You need to know who its neighbors are, how tightly the
bonds are holding it all together.
And even how the electron cloud is shifting around it.
So here's the question. If you can't see it or touch it
or photograph it, how do you solve the case?
How do you interrogate a molecule?
Well, if you're a chemist, you don't pull out a magnifying
glass, you pull out a magnet. A really, really, really big
magnet. You essentially force it to talk
to you using the laws of quantum physics.
Welcome to the deep dive. Today, we are tackling one of
the absolute Titans of modern science.
A real heavy hitter in the analytical lab.
We're doing a deep dive into NMR spectroscopy.
Nuclear magnetic resonance. It is, and I don't think this is
an overstatement, arguably the most powerful tool we have for
figuring out the structure of molecules in detail.
It's the closest thing we've ever invented to having, I don't
know, X-ray vision for chemicals.
That's a great way to put. It and we have a serious stack
of research and lecture materials here today.
We're working from a collection of notes that they really cover
the full spectrum of this technology.
They do. We've got materials on the
fundamental principles. This is from a course on
structure methods in inorganic chemistry.
And then we have to really advanced stuff.
The almost sci-fi world of solid-state NMR.
And it really does get into sci-fi territory, especially
when you start talking about the engineering that's required to
make any of this work. So our mission today is to take
you on that journey. We're going to start with the
very basic physics of a spinning nucleus.
What makes it tick? Why it even behaves like a
little magnet in the first place.
Then we'll get into the machine itself, which is just a beast of
engineering. From there, we'll learn how to
decode the secret messages these atoms sending us.
And finally, we're going to build all the way up to a
technique called Magic angle spinning.
Which, I promise you, is every bit as cool as it sounds.
I was hoping you'd say that. It's a technique where we
literally spin a sample at, I mean thousands of mph just to
trick the laws of physics. Or at least to cancel out the
parts of physics that are, you know, being annoying.
Exactly the parts that are getting in our way.
So the mission is to understand how we go from a simple tube of
clear liquid to a complex 3D map of reality.
But before we get to the giant magnets and the magic angles, we
have to start with the suspects themselves.
Right, because it turns out not every atom is willing to
cooperate with this kind of investigation.
There's AVIP list. A very strict VIP list for who
gets to participate in an NMR experiment.
You can't just put any old substance in the machine and
expect to get the signal. This was one of the first things
in the reading that really surprised me.
I sort of, I've assumed, you know, you put matter in a super
strong magnet and something has to happen.
You'd think so. But we're talking about a very
specific property called nuclear spin.
Now, when I hear spin, I'm thinking of a top, or, you know,
a planet rotating on its axis. But this is quantum spin, right?
It's different. Yes, and this is where our
everyday intuition starts to fail us a little bit.
When we say spin in quantum mechanics, we don't necessarily
mean the nucleus is physically rotating like a basketball on
your finger. It's an intrinsic property of
the particle. It's a form of angular momentum.
It's just something the particle has in the same way it has mass
or it has charge. So it's like a fundamental tag
that's just attached to it from the start.
Exactly. Yeah.
And for NMR to work, for nuclear magnetic resonance to happen at
all, the nucleus has to have a spin that is not 00.
We denote the spin with the letter I.
If I equals 0, the nucleus is silent.
It's invisible to the machine. It doesn't matter if you have a
magnet the size of a planet, that nucleus will not talk to
you. And looking at the source
material, the rules for who has been and who doesn't are,
they're surprisingly specific. They are.
It feels a bit like a club bouncer checking IDs at the
door. Oh, let me see your protons even
number. Sorry you're not coming in
tonight. That's a really good analogy.
It is a lot like that, and the criteria are all about the
composition of the nucleus, just the count of protons and the
count of neutrons. OK, let's breakdown these rules
because they dictate everything we can and cannot see in the
molecular world. Rule #1 This covers what the
notes call the Silent Majority. This is the big one.
This is the rule that excludes a lot of the atoms we deal with
every single day. The rule is simple.
If an atom has an even number of protons, A&D and even number of
neutrons, its netspin is 0. Equals 0 spin.
Correct. On a quantum level, everything
just pairs up and cancels out, and this is a huge deal because
of who falls into this category. Just think about the most common
elements in organic chemistry. Carbon and oxygen.
The building blocks of life itself, specifically their most
abundant isotopes, carbon 12 and oxygen 16.
OK, so carbon 12, that's six proton, 6 neutrons even and
even. Yep, and oxygen 16 is 8 protons
and eight neutrons again, even and even.
So wait, let's just pause on that for a second because that's
that's kind of a big deal. Carbon 12 is what?
Something like 99% of all carbon?
About 98.9%, yeah. And oxygen 16 is 99.8% of all
oxygen. And you're telling me they're
completely invisible to this technique?
In the context of NMR, yes. They don't have a magnetic
moment. They are magnetically inert.
You can put them in the biggest magnet on Earth and they just
they won't interact. They are NMR silent.
That is wild. So the bulk of organic matter,
the very backbone of our bodies, the wood in this desk, the
plastic in this microphone is basically dark matter to this
machine. It's a ghost town.
The machine sees right through. It it's there, but it can't be
seen. So if the main building blocks
are silent, who can we talk to? Who actually gets past the
bouncer? We need the oddballs.
That brings us to rule #2 in the notes.
OK, the rule is if the mass number of the atom is odd, you
get 1/2 integer spin, so something like 123252 and so on.
And this is the sweet spot. This is the sweet spot for NMR.
This is where all the action is which.
Brings us to the real celebrities of the NMR world.
Absolutely. And the biggest celebrity, the
absolute A Lister that shows up in almost every chemistry paper
you'll ever read, is the proton hydrogen one.
Just a single proton. One proton, 0 neutrons.
Its mass number is 1, which is odd, so its spin is 12.
And it's perfect for this. It's perfect, it's incredibly
sensitive, and just as importantly, it is everywhere.
It makes up 99.98% of all hydrogen in the universe.
So when people in the lab say I'm going to go run an NMR, 9
times out of 10 they're not looking at the carbon skeleton
directly, they're actually listening to the hydrogen atoms
gossiping about their neighbors. Most of the time, yes, that's
proton NMR. It's the standard because it's
fast, it's sensitive, and the data is usually really clear.
But. We can look at carbon, right?
We just have to be clever about it.
We can. We have to be clever.
Remember, carbon 12 is silent, but there's another isotope,
Carbon 13. Carbon 13.
It has 6 protons but seven neutrons.
Exactly that one extra neutron brings the mass number up to 13,
which is an odd number spin. It has a spin of 12 and suddenly
it's active. It has a magnetic voice.
We can hear it. But there's a catch with carbon
13, isn't there? It's not as easy as hydrogen.
There's a big catch. It all comes down to abundance.
Carbon 13 is only about 1.1% of all the carbon found in nature.
So if I have a sample of say, sugar, only one out of every 100
carbon atoms is actually talking to the machine.
That's right, the other 99 are the silent carbon twelves.
They're just along for the ride. Which must mean the signal is
much, much weaker. Significantly weaker.
You're trying to hear a whisper in a crowded, noisy room, and
that explains why a Carbon NMR experiment takes so much much
longer to run than a Proton NMR. You have to listen for a much
longer time. A much longer time, sometimes
hours or even overnight, just to collect enough data to
distinguish the signal from the background noise.
And just for completeness, there is a third rule in the notes.
What about the integers? Right rule #3 This is if you
have an odd number of protons and a an odd number of neutrons.
Odd plus odd. In that case you get an integer
spin like one or two or three. Examples here would be something
like nitrogen 14 or deuterium which is hydrogen 2.
Are active too. They are active.
They do have spin, but they're much, much harder to work with.
They have a property called a quadrupole moment.
A quadrupole. OK, it just means their
electrical charge isn't distributed in a perfect sphere.
It's more like a football, and this makes their signals really
broad and often difficult to interpret.
We generally try to avoid them unless we really really need
them for a specific problem. OK, so we've got our VIP list.
We have our protons and our carbon thirteens.
They have spin, they're in the club now.
We take these atoms and we put them in the machine.
This brings us to a concept in the notes called the Zeeman
Effect. The Zeeman effect.
It sounds like a Robert Ludlam thriller, The Zeeman Effect.
It does, doesn't it? It sounds very dramatic.
It's fundamental quantum mechanics.
But you know it is thrilling in its own way because this is the
mechanism that makes the whole technique possible.
So what happens? What is the Zeeman Effect?
OK, so imagine you have a beaker of water sitting on your desk.
Inside that water you have billions upon billions of
hydrogen nuclei. All with spin.
But under normal conditions
they're all pointing in completely random directions.
Up, down, left, right, diagonal. It's total chaos.
Because they're just tumbling around in the liquid.
Right, and because all their tiny magnetic fields are random,
they all cancel each other out. There's no net magnetization in
the sample, it's just a 0 sum. But then you put it in the
magnet. But then you place it inside a
powerful magnetic field, which we call B naughty or B0, and
they're forced to organize the notes.
Use the analogy of compass needles.
Right. A compass needle always wants to
align with the Earth's magnetic field.
It points north. Correct.
So the think of these nuclei as tiny, tiny bar magnets.
When you turn on the big external magnet, they want to
align with it. However, quantum mechanics is
weird, always. Unlike a compass needle that can
point, you know, slightly northeast if you wiggle it.
A spin 12 nucleus only has two allowed choices.
It's quantized. Two discrete states, no in
between. No in between.
It can align with the field, we call that the alpha state or the
low energy state. Or it can align against the
field, the beta state, the high energy state.
So it's either standing on its feet, meter standing on its
head, that's it. That is it.
And the splitting of the energy levels, the creation of a low
energy level and a high energy level where there was none
before. That is the Zeeman effect.
Now here's the part in the math that I found fascinating.
You would think intuitively that everything would just want to be
in the low energy state, right? You'd think so.
Like a ball rolling down a hill, it's just easier.
Physics usually favors the lowest energy state.
That's a good rule of thumb, but we're at room temperature and
thermal energy, just the ambient heat of the room, is constantly
kicking these atoms around. There's battle going.
On there is it's enough energy to kick a lot of them up into
that high energy standing on their head state.
So you've got this constant battle, the magnet trying to
pull them all down into alignment, and the heat trying
to scramble them all up again. So who wins?
What's the score in that battle? The score is incredibly,
incredibly close. The difference in the population
between the aligned spins and the opposed spins is defined by
something called the Boltzmann distribution, and the difference
is tiny. How tiny are we talking?
We are talking minuscule at room temperature inside a standard
NMR magnet, for every 1,000,000 spins pointing against the field
in the high energy state, a million, you might have
1,000,010 pointing with the field in the low energy.
That's it. A difference of. 10 out of a
million, that is. It that tiny excess, that
handful of extra nuclei that the magnet managed to win over from
the heat, that is the only reason NMR works at all?
Wow, that tiny net magnetization is the only thing we can detect
that blows my. Mind so we are building these
massive multi $1,000,000 machines, cooling them with
liquid helium just to talk to those ten extra guy if the.
Populations were exactly equal 5050.
The signals would cancel out perfectly, we would see
absolutely nothing. We are operating on the absolute
razor's edge of detectability. It really just.
Speaks to the sensitivity of the equipment we're using, which
brings. Us nicely to our next segment,
the machine itself, because you can't just use a fridge magnet
to get that separation. Oh no to.
Get a difference of even 10 per million.
You need a magnetic field that is monstrously strong.
The notes mentioned superconducting magnets, yes.
In the early days of NMR, they used a big electromagnet.
It's basically huge iron cores wrapped in tons of copper wire.
But they were limited. They got really hot.
I can imagine to get the field strengths we use today, which we
need to widen that energy gap and get a better, stronger
signal, we need fields up to say 23 Tesla.
OK, let's. Contextualize 23 Tesla for a
second. A strong fridge magnet is what,
.01 Tesla? Something like that, Something
in that. Ballpark.
Yeah, it's tiny. And an MRI.
Machine at a hospital which is basically just a giant NMR for
people. That's usually 1.5 or maybe 3
Tesla, correct? So 23 Tesla is an immense amount
of energy concentrated in a very small space.
So how do you? Generate a field that's strong
without melting the building down.
You have to. Eliminate electrical resistance.
If you tried to pump that much current through a normal copper
wire, it would just glow white hot and vaporize instantly.
So we use superconducting alloys, usually something like
niobium tin or niobium titanium. When you cool these materials
down to near absolute zero, their electrical resistance
drops to exactly 00. Resistance means zero heat and
the current. Just flows forever unimpeded.
But to keep them that cold, you need a constant supply of liquid
helium, which is why these. Magnets are always housed in
those giant thermos looking canisters.
Exactly. The coil of wire is sitting in a
bath of liquid helium at about four Kelvin 4 Kelvin.
That's -269°C, just 4. Degrees above the coldest
possible temperature in the universe.
It's just an. Extreme environment to enable an
incredibly sensitive measurement.
But the notes also emphasize something else about the magnet
shimming. It says the field must be
extremely homogeneous. This is.
Absolutely. Critical homogeneity just means
sameness. If the magnetic field is 23.0000
Tesla at the top of your sample tube, it better be.
Exactly 23.00000 Tesla at the bottom and in the middle.
And on the left and on the right.
It has to be perfectly uniform across the entire sample.
Why does that matter? So much because the.
Frequency at which a nucleus resonates its musical note, so
to speak, depends directly on the strength of the magnetic
field it's feeling. So if the field is lumpy, little
stronger over here, a little weaker over there, then
identical nuclei in your sample will be singing at slightly
different notes. It's like an.
Orchestra where every musician is slightly out of tune.
That's a perfect. Analogy.
Instead of getting a sharp clear note, which is a sharp peak in
your spectrum, you get a fuzzy, muddy sound, A broad ugly peak
because. Shimming is the process of
tuning the orchestra it. Is we use a series of small
extra coils to tweak and nudge the magnetic field, smoothing
out all the limps until it's as close to perfect as we can get
it, I always thought. Shimming was such a funny word
for high tech physics. It reminds me of sticking a
folded piece of cardboard under a wobbly table leg that.
Is exactly where the term comes from.
It's an old carpentry term. We're just shimming the magnetic
field instead of a table leg to make it perfectly level.
So we have. Our frozen Monster Magnet.
We have our field shimmed to perfection.
Now we need to prepare the suspect, the sample.
The notes here say complete dissolution is essential for
solution. NMR.
Yes, this is the standard method for most small molecules.
You have to dissolve your sample in a solvent.
But you have to be very careful about which solvent you choose,
right? You can't.
Just use tap water. Well, think about.
It water is H2O, It is packed to the gills with protons, billions
and millions of them, and your. Sample.
The drug of the molecule you just made might be very dilute.
Exactly. If you ran that sample in
regular water, the signal from the water's protons would be
like a jet engine roaring, and your sample signal would be a
tiny whisper. You'd never hear it.
So we. Use deuterated solvents right
we? Take a common like chloroform
CHCL 3 and we replace the regular hydrogen, the proton,
with its isotope deuterium, hydrogen 2, hydrogen 2 and
deuterium has completely different resonant frequency
from a proton. It's effectively invisible in
the channel we're listening to, so it's like putting.
An invisibility cloak on the solvent so we can see the salute
clearly. That's.
Precisely what it is OK. Samples in the tube, magnet is
on, nuclei are aligned. We've got our tiny ten in a
million excess pointing up up. Now how do we get the signal?
Do we just, I don't know, put a tiny microphone up to the tube,
not? Anymore, In the old days, what
we call continuous wave or CWMR, it was kind of like that.
We used to slowly sweep the frequency.
How do you mean? It was like turning the dial on
an old analog radio searching for a station.
You'd go 99.1 megahertz static, 99.2 static, 99.3 BEP.
Found one and that must have. Taken forever, it did. 5/10/15
minute for a simple scan. It was incredibly slow and
inefficient, but now we use. The pulse method pulse NMR.
Or more accurately, Fourier transform NMRFTNMR.
Instead of carefully searching for each individual frequency,
we basically hit the sample with a sledgehammer.
A sledgehammer. Made of radio waves, yes.
A short, very powerful pulse of radiofrequency energy.
And because the pulse is so short, we're talking
microseconds long. It contains a widespread of
frequencies. It basically contains all the
frequencies we might be interested in all at once.
The analogy I loved from the reading, and I want to really
dig into this, was the idea of striking a bell.
It is the perfect. Analogy for this.
Imagine you have a large church bell.
If you wanted to figure out what frequency it rings at, you
wouldn't tap it with a tuning fork at 100 Hertz, then listen,
then try 101 Hertz. No, that would.
Take all day. You'd go crazy, right?
You just take. A big hammer and you hit it.
WHECK and the Bell. Rings it.
Rings at all of its natural resonant frequencies
simultaneously. It produces a complex rich tone
that fades overtime. We do the exact same thing to
the molecule. We hit it with the RF pulse, and
that excites all the different nuclei at the same time.
So physically. What is happening to those spins
when the pulse hits them? The pulse.
Imparts energy and it rotates that net magnetization we talked
about. It tips it over a standard 90°
pulse, pushes it 90° from the Z axis where it's aligned with the
magnet, so from standing. Up into.
The transverse plane, the XY plane 2 lying.
Flat on its back? Exactly.
And once those spins are in that transverse plane, the main
magnet B naughty grabs hold of them and they start to precess.
They start to spin around the Z axis like a spinning.
Top that's been tipped over and it starts wobbling in a circle
before it falls. That's the.
Exact motion, and as this net magnetic moment spins around, it
passes by a receiver coil which is just a fancy loop of wire
inside the machine and a. Moving magnet next to a wire
that induces a current it induces.
A tiny voltage, and that voltage is our signal.
That is the. FID, the free induction decay
The FI. D Free induction.
Decay. It really sounds like an indie
rock band from the early 2000s. It would be a.
Great band name, I agree, but physically it's the raw signal
coming out of the machine. It's free because it happens
after the pulse is off, Induction because it's an
induced voltage, and decay because as the spins relax and
go back to equilibrium, the signal fades out to nothing.
Now the. Notes show a picture of an fid
and it doesn't look like a nice neat graph with peaks.
It looks like a squiggle. It looks like the audio file of
a complex chord being played on a piano and then fading out,
that is. Exactly what it is.
It's a complex chord. It's every nucleus in your
molecule singing its own unique note, all at the same time, all
added together. It's what we call a.
Time domain signal, yes. It's amplitude versus time.
And you're right, you can't just look at that squiggle and say,
oh, look, there's a methyl group over there.
It's impossible. For a human to read completely,
we need. To decode it, we need to
mathematically separate that complex chord back into its
individual notes. And that's where the magic comes
in. The Fourier transform, the FT,
the mathematical. Magic trick it really.
Really feels like magic. The Fourier transform is a
powerful algorithm that converts a signal from the time domain,
our squiggle, into the frequency domain, which is intensity
versus frequency. It takes the.
Recording of the Symphony and turns it back into the sheet
music that is a. Beautiful way to put it, yes, it
breaks the complex wave down into the individual sine waves
that built it up. And because we pulsed everything
at once and did this conversion, we get the entire spectrum in
about 5 seconds 5. Seconds instead of 5 minutes a
huge. Leap forward, so the output.
Of this transformation is the spectrum we all know and love
from chemistry textbooks, the graph with all the peaks on the
page. Now we get to the real detective
work. Now we decode.
The message we have? These peaks.
Some are tall, some are short, some are single lines, some are
split into patterns. What are they telling us about
the molecule in? Solution.
NMR. They tell us a number of things,
but let's focus on the big two for now.
Chemical shift and coupling. Let's start with.
Chemical shift, Yeah, This is the location of the peak on the
horizontal axis, right? Correct.
We measure it in a unit called PPM or parts per million, and
the location the chemical shift tells you about the electronic
environment of that particular nucleus.
Electronic. Environment.
That sounds a little vague. What does that mean in practical
terms? It basically.
Means who are your neighbors and what are they doing?
Remember, a nucleus is surrounded by a cloud of
electrons, right? And those electrons are also
charged particles and they're moving in loops in orbitals.
They create their own Piney little magnetic fields.
So they're like. Little magnets too, and these
tiny. Fields usually oppose the big
magnet that we've applied. They effectively shield the
nucleus from the full force of the external field.
So the nucleus. Is kind of hiding behind a wall
of its own electrons, yes. And if a nucleus is well
shielded, it feels a slightly weaker magnetic field.
It spins a little slower. It shows up on the right hand
side of the graph at a low PPM value.
We call that upfield. But what if you?
Attach that carbon or that proton to something greedy like
an oxygen atom or a chlorine atom.
Electronegativity. Exactly.
An atom, like oxygen is an electron hog.
It pulls that electron blanket away from the carbon, so the
carbon. Is left out in the cold.
It's exposed. It is.
Deshielded it feels more of the full force of the big magnet, so
it spins faster. It resonates at a higher
frequency and its peak shifts to the left on the graph to a
higher PPM value. We call that downfield.
So chemical. Shift is basically a
neighborhood check. If your peak is at 10 PPM,
you're living in a nice quiet suburb surrounded by other
carbons and hydrogens. If you're 2 PPM, you're living
right next to a factory. Like an oxygen double bond.
That's a great. Way to think about it.
It tells you what kind of functional group you're looking
at. But then then there's coupling.
This is where it gets really, really detailed.
This is the neighbor. Effect you mentioned earlier, we
call it. Spin, Spin coupling.
What it means is that a nucleus isn't just feeling the big
external magnet, it's also feeling the tiny magnetic fields
of the specific nuclei that are right next door to it through
the chemical bonds they're whispering.
To each other through the bonds they are.
And this can be communication creates splitting a single peak,
instead of being a sharp line splits into two or three or four
smaller picks and multiplets. These are the multiplets.
And the pattern tells you exactly how many neighbors you
have on adjacent atoms. If you have one neighbor, that
neighbor's spin can be either up or down relative to the big
magnet, so there are two. Possibilities.
Two possibilities. So your signal gets split into
two distinct peaks of equal height at double it, and if you
have two. Equivalent neighbors while
their. Spins can be up, up or down,
down or 1 can be up and 1 can be down and there are two ways to
get that up, down or down, up. So that's.
Three possible empty states, right?
Which means your signal splits into three peaks, a triplet with
a one to two to one ratio of heights.
This is the famous. N + 1 rule they teach in organic
chemistry it is. But the lecture notes we have
here go deeper than just counting neighbors.
They talk about the coupling constant, which is denoted by
the letter J. This is the.
Physical distance between the tips of those split peaks,
right, Right. And it's measured in Hertz, yes.
Not in PPM, but in Hertz. Yeah, and the coupling constant
is an absolute treasure trove of structural information.
It tells us about the nature of the bond connecting the two
atoms. How so?
For example, the lecture notes highlight the one bond carbon
hydrogen coupling, which they write as $1.00 JCH 1 bond.
Coupling OK and the notes point. Out that this value changes in a
very predictable way based on the hybridization of the carbon
atom hybridization. So whether it has single, double
or triple bonds, exactly. It's just a fancy way of saying
how the electrons are arranged in the bonds and CP33 carbon
like in ethane, all single bonds tetrahedral shape has a coupling
constant of about 125 Hertz. OK, one. 25 I'll remember that
now an SP2. 2 carbon like in ethane with a double bond flat
shape that value jumps up to around 160 Hertz a noticeable.
Increase, but then you get. To an SP carbon like in
Acetylene with the triple bond linear shape and the coupling
constant is huge. It's 250 Hertz.
Wow, that's double. The first one, 125 versus 250,
it's a massive. Difference, and it has to do
with this character of the bond. This orbital is spherical and
it's held very close to the nucleus.
OK. The more character a bond has,
the closer the bonding electrons are to the nucleus and the
stronger the magnetic communication is between the
carbon and the hydrogen. So just by.
Taking a ruler to your spectrum and measuring the distance
between the peaks, you know if you have a single, double or
triple bond, without a doubt. It's an incredibly powerful
diagnostic tool, but the. Section in the sources that
really made me feel like Sherlock Holmes was the
inorganic chemistry part, specifically the bit about the
platinum complexes. Oh, this is a.
Classic application of coupling constants distinguishing between
isomers and isomers. Are just molecules that have the
same atoms, but they're arranged differently in space, right?
So. Let's take the example from the
notes. You have a platinum atom in the
center and attached to it are two chlorine atoms and two
phosphorus containing ligands. These PT three groups and.
You can arrange those four pieces in two main ways.
You can put the two phosphoruses next to each other at a 90°
angle, that's the CIS isomer. Or you can.
Put them on opposite sides of the platinum at 180°.
That's the trans isomer, and to the naked.
Eye. If you had a bottle of each,
they'd both probably just be white powders.
You couldn't tell them apart. Not a chance.
But in an NMR spectrum, they scream their identities at you
and the key. Is the coupling between the
platinum and the phosphorus atoms right?
Well, even. More telling is the coupling
between the two phosphorus atoms themselves through the platinum,
and the rule is simple and powerful.
Transnuclei couple much much more strongly than CIS nuclei.
Why is? That why does being on opposite
sides make that magnetic connection so much stronger It
comes. Down to the orbitals of the
central metal atom. Again, in the trans arrangement,
the two phosphorus ligands are on opposite sides of the
platinum. They're both interacting with
and communicating through the same dorbitals on the metal.
They have a. Direct Line of sight through the
platinum Adam, that's a great. Way to put it, they're sharing
the same phase of the orbital lobes.
This makes the communication channel incredibly efficient.
The signal is strong. And in the CIS arrangement in
CIS. They're at 90° to each other.
They're interacting with different orbital lobes on the
platinum, and these lobes often have different quantum
mechanical phases. So the communication.
Is poor. It's like trying.
To have a conversation around a corner versus talking to someone
face to face, it's much less efficient.
The source. Notes say that the phosphorus
phosphorus coupling in the CIS compound is an order of
magnitude smaller than in the trans compound.
An order. Of magnitude, that's a factor of
10. It's the difference between a
shout and a whisper. So you run the spectrum, you
measure the J value and boom, you know the exact 3D geometry
of the molecule. No ambiguity, no guessing
required. OK, so this.
Is all incredibly powerful, but up until now we've been living
in a very happy, clean world. We were talking about solution
NMR. The sample is dissolved, the
molecules are tumbling around happily in the solvent, which is
fantastic. When you can actually dissolve
your sample but. Life isn't always a liquid.
No, it's. Not sometimes.
You can't dissolve your sample. Maybe it's a piece of polymer
plastic, maybe it's a bone fragment from an archaeological
dig, or a ceramic. Catalyst, or a protein that's
embedded in a cell membrane. If you dissolve it, you destroy
the very thing you're trying to study.
Exactly. So you have no choice.
You have to analyze it as a solid.
This brings us to segment 4, solid-state and Mr. And from
reading the materials, this sounds like playing the game on
hard mode. It sounds like.
Nightmare mode it is. Absolutely hard mode, because as
the notes make very clear, the moment you stop the molecules
from moving, the physics gets very, very ugly.
Why? Why does stopping the movement
ruin the nice sharp signals we just talked about?
Think back. To the liquid, we said the
molecules in a liquid are tumbling wildly.
Brownian motion. They're spinning and flipping
millions and millions of times every second.
Complete chaos. It's a controlled chaos.
And that rapid tumbling is absolutely crucial because it
averages out all of the interactions that depend on
direction. It's like looking at a fan
that's spinning at high speed. What do you see?
You don't see the. Individual blades you just see a
transparent blur. A disc Exactly.
You see the average of the blade being in every position.
The tumbling does the same thing for the molecule.
It averages out all the messy magnetic interactions to zero,
and that leaves you with those beautiful sharp, clean peaks,
but in a solid. The fan.
Stops. Now you see the blades, the
molecules are locked in place, and because you have a powder
with millions of tiny crystals, the molecules are locked in
every possible orientation relative to the magnetic field.
And the result. Is not a sharp peak the result?
Is a broad, ugly, featureless BLOB.
The broadening. Nightmare.
The notes act like this is a crime scene.
They list 3 specific villains that are responsible for this
broadening the three. Villains of solid-state
broadening. It sounds very dramatic.
It does. Let's.
Name and shame them. Villain #1 CSA Chemical shift
Anisotropy. Anisotropy.
Is a fancy word that just means directionally dependent.
OK, the electron cloud that Shields a nucleus isn't usually
a perfect sphere. It's often shaped more like a
cigar or a pancake or a dumbbell.
So the amount. Of shielding depends on which
way the molecule is facing, yes. If the molecule is standing up
vertically relative to the magnet, the electrons shielded
one way, giving you one chemical shift.
If it's lying down horizontally, they shielded a different way,
giving you a totally different chemical shift.
So 1. Orientation might give you a
peak at 100 PPM, and another orientation of the exact same
molecule gives a peak at 150 PPM precisely.
And in a powder sample, which is just a scoop of powder in a
tube, you have millions of tiny crystals facing every possible
direction at once. So you get.
Every possible chemical shift all at the same time instead of
a. Sharp line.
At the average position, you get a massive smear.
We call it a powder pattern that spans the whole range of
possibilities. It just covers up everything
else a huge. Mess.
OK, villain #2 The Polar. Interaction.
This is the direct through space magnetic pull between nuclei.
Think of 2 little bar magnets sitting on a table.
If they're close to each other, they push and pull on each
other's magnetic fields and in. Liquid this averages out because
they're moving so fast averages. To 0, but in a solid they're
stuck right next to each other. A proton sitting next to a
carbon 13 acts like a local magnetic bully.
It strongly modifies the magnetic field that the carbon
is feeling and this effect. Is big.
It's. Enormous.
The notes say that for a typical proton carbon interaction, it
can be greater than 50 kHz. That's an enormous frequency
range that basically just wipes out any hope of seeing fine
details. It's just noise.
At that point and the third villain, quadrupolar.
Interaction. This one only applies to those
nuclei with a spin greater than 12.
Remember we said spin 12 nuclei are nice and spherical.
Well, nuclei with spin 1 or 32 and so on are non spherical.
They're shaped like a football. They have an electric quadrupole
moment and that interacts. With the crystal it interacts.
With the electric field gradients within the crystal
lattice, and this interaction is usually the strongest of them
all. It can be hundreds of kHz wide,
so we have. CSA Day, polar coupling and
quadrupolar interactions all conspiring to turn our beautiful
informative spectrum into a useless broad mound of noise.
It really does seem hopeless. Why do we even bother with
solid-state NMR? It would be.
Hopeless, if it weren't for some truly incredible engineering and
physics tricks. We can't let the molecules
tumble, so we have to find another way.
We have to artificially make the solid behave like a liquid and
this leads. Us to what is without a doubt
the coolest term in the entire stack of materials.
Magic angle spinning MAS. It sounds like sorcery, doesn't
it? But it's pure beautiful geometry
and mathematics. Explain.
The magic part. Why is it magic?
What's the trick? The trick comes.
From looking at the math that describes those interactions, we
just complained about the CSA and the dipolar coupling.
When you write out the Hamiltonian equations, the
physics formulas for how they brought in the signal, they all
share a common angular term. The exact same piece of math
shows up in all of them. The same.
Geometric factor is responsible for all the trouble in large.
Part Yes and that term is 3 Cos 2.
OK, 3. Cos 2.
I'm visualizing the equation in that.
Equation Theta is the angle between the axis of the
interaction in the molecule and the main magnetic field B
Naughty. Now back in the 1950s a few
clever physicists, Andrew and EADS are the names that come up.
They looked at that equation and had a brilliant idea which was
they said wait a minute, what if I can make that whole term 3 Cos
2/1 equal to 0? If I can do that, the entire
interaction term just vanishes from the equation if that term
is. Zero.
Then the broadening effect goes to 0.
Gone so. You just do the algebra.
You set three Cos of 1, then Cos 2 = 13.
You take the square root, then the inverse cosine and the
answer is drum roll please. Approximately.
A 54.74° The magic angle The magic angle.
It's a fundamental geometric constant.
It's the angle of the diagonal that runs through a cube
connecting opposite corners. So what do we?
Do with this angle we. Physically build a machine that
tilts the sample tube to exactly 54.74° relative to the main
magnetic field, and then we spin it.
How fast are? We talking fast.
Very, very fast. We're talking about spinning in
the kHz range, so 10,020 thousand, sometimes up to
100,000 rotations per second. That's faster.
Than a jet engine turbine much? Faster.
The rule of thumb is that your rotation speed has to be faster
than the magnitude of the interaction you're trying to
average away, so you spin. This tiny tube at 10s of
thousands of RPMS at a perfect 54° tilt and when you.
Do that. You are mechanically forcing the
time average of that pesky 3 coast term to become zero.
To the nucleus it looks like it's tumbling isotropically.
The solid thinks it's a liquid that.
Is essentially hacking the laws of physics, you're saying?
I don't like this term in the equation, so I'm going to
physically engineer a device to rotate my entire sample to
mathematically delete it. That is exactly.
What we're doing and the result is absolutely stunning.
The broad ugly blobs collapse. The featureless smears sharpen
up into distinct high resolution peaks.
The notes have a. Great example they do.
A comparison of the spectrum of tyrosine, which is an amino
acid. Without mas, the solid sample
gives you a lumpy, useless hill. You can't see anything.
Turn on mas and you can see a clear, resolved peak for every
single carbon atom in the molecule.
It's night and. Day.
But even with magic angle spinning we still have that
sensitivity issue right? Remember carbon 13 is rare and
it's also lazy. Lazy.
Is a very good word for it. In NMR terms, it has a very long
spin lattice relaxation time, which we call T1, meaning it
takes a. Very long time for it to reset
after you hit it with a pulse. A very long.
Time. After you hit it with that 90°
pulse, it takes a long time for it to relax back to its
equilibrium state, so you can pulse it again and collect more
signal. For some solids, this T1 can be
minute or even hours. So if you need to accumulate
thousands of scans to see the weak signal, and you have to
wait 5 minutes between each and every scan, you'd be there for.
Weeks, the experiment becomes impossible.
It's completely. Impractical.
So we use the protons again, they're our friends.
This brings us to the second major technique, cross
polarization or CP. OK, how does?
That work protons are. Abundant.
They're sensitive and they relax very quickly.
They're energetic, so we use a clever sequence of
radiofrequency pulses to create a condition where the protons
can transfer their polarization over to the carbons.
We're stealing the. Energy from the protons and
giving it to the carbons we are. We're essentially pumping the
signal from the abundant energetic protons into the rare
lazy carbons. It's like a blood transfusion
for the signal, or giving the carbons battery a jump start
from the protons battery. And what does?
That do for us practically 2 huge.
Things first, the carbon signal gets significantly stronger.
It's an enhancement of its sensitivity.
And 2nd, and maybe even more importantly, we no longer have
to wait for the carbon to relax. We only have to.
Wait for the protons to relax. Exactly.
And the protons relaxation time is short, maybe a few seconds,
so we can pulse and scan much much faster.
An experiment that would have taken a week can now be done in
an hour. And.
Finally, the notes mention one more piece to the puzzle.
Depolar decoupling. That's the third.
Leg of the stool. Even with MAS spinning, those
powerful dipolar interactions between protons and carbons can
still cause a little bit of broadening, so you need to get.
Rid of them. We need to shut.
Them up. So while we are listening for
the carbon signal to come back to us, we blast the protons with
a continuous high power radio frequency signal.
What does that do? To the protons it forces.
Them to flip their spins back and forth, up and down so
rapidly that the carbon just sees an average.
It sees a blur. It effectively cuts the magnetic
communication line between them. It decouples them so to.
Get a really good picture of a solid polymer like the PMA
example, the polymetal methachrylate in the notes.
You you have to combine all three of these things at once.
You have to. And the notes show this
beautiful progression that's worth walking through.
Let's do it. Step a a static sample, No
spinning, no nothing. And the spectrum is basically a
flat line with some noise. You see nothing at all
completely. Useless step B.
Now you keep it static, but you turn on cross polarization.
Now you see a big broad undefined bump.
You have signal, but you have 0 resolution.
It's just a mountain. Better than nothing.
But still a BLOB step C. Now let's turn on Magic Angle
Spinning. The bump immediately starts to
split into a few broad but distinct peaks.
You can see shapes starting to emerge from the noise.
OK, we're getting. Warm.
We're getting somewhere. And finally.
Step D You combine everything, magic angle spinning plus cross
polarization plus high-powered decoupling and suddenly crystal
clear sharp peaks. You can now identify the
individual carbon atoms methyl group, the chapter 2 group, the
carbonyl Co group you've gone from.
A flat deadline to a precise molecular fingerprint of the
polymer. That is the power.
Of modern solid-state NMR. It allows us to look inside
materials that were previously just a black box.
We can see the structure of plastics, of biological
membranes, of batteries while they're operating, of industrial
catalysts, all these things that simply cannot be dissolved.
It's just. Incredible.
We've really traveled from the quantum spin of a single proton
through these giant superconducting magnets all the
way to spinning samples at 54.74° just to cheat the math it
really. Highlights the philosophy of
structural chemistry that was mentioned on the very last slide
of the source material. Which is what?
It's that. No single method tells you
everything. The notes really emphasize this
point. The course philosophy is to
solve structures by combining multiple techniques, right?
Sometimes you need solution and Mr. Sometimes you need
solid-state NMR. Sometimes you need to look at
coupling constants to figure out the geometry.
Other times you need a completely different technique
like X-ray diffraction or mass spectrometry.
You have to be A. Detective who uses every tool in
the kit. A single method is powerful, but
it's by combining them that you really solve the puzzle exactly.
Each one gives you a different piece of the story.
That's a great. Take away.
But before we wrap up, I want to leave our listeners with a final
thought that really struck me while I was reading through all
this. We spent this whole hour talking
about the active nuclei, the ones that have spin, the ones
that talk to us, the protons. The carbon thirteens, the
phosphorus 30 ones, the. Spies.
But remember at the very beginning we talked about the
silent majority. Carbon 12, Oxygen 16.
The ones with. Even protons and even neutrons
and these atoms. Make up the absolute bulk of
organic existence our bodies, the trees outside this building,
the plastic in your phone structurally, they're mostly
built from atoms that are completely invisible to this
incredibly powerful machine it is a very.
Humbling thought. We are building these incredibly
detailed, beautiful 3D models of reality, but we are doing it by
listening to the 1% of the carbon atoms that happen to have
an odd number of neutrons we're ignoring.
The other nine 9% that are silent, we are.
We're inferring the entire structure from a very small,
select group of reporters. Exactly.
We are trying to understand the shape of an elephant by
listening to the fleas that are living on its back and it just
makes you wonder what subtleties of structure, what dynamics are
we missing because we can only hear the loud neighbors that is
the. Perpetual question of science,
isn't it? We can only see the world
through the tools that we have, but as we saw today with Magic
angle spinning, sometimes when you can't see something clearly,
you just have to spin your perspective a little bit on that
note. Thank you for joining us on this
deep dive into the magnetic world of NMR.
It was a real. Pleasure keep spinning.
Keep questioning and we'll catch you in the next deep dive.