I want you to picture a ballroom, a massive, gilded
ballroom. And it's filled with, I don't
know, a billion statues. And these aren't just any
statues. They're all perfectly paired
couples, you know, frozen in an embrace.
They're totally, still, totally silent.
Now imagine that somewhere in this endless sea of stone
figures, there is one single dancer.
Just one. Just one.
And this dancer is alive. They're spinning, they're
moving, they have this, this frenetic energy.
That is a very evocative image to start with.
I'd do my best. Now, if you were just standing
at the door of this ballroom looking in, you probably
wouldn't even see that one dancer.
They'd be completely lost in the crowd.
You'd need some kind of special way to find them, a way to make
all the statues invisible and make that one dancer glow like a
flare. And that, in a nutshell, is
essentially what we're talking about today.
Exactly. We are talking about a technique
that I have to say, sounds like absolute science fiction.
It involves these massive Electro magnets blasting samples
with microwaves and and detecting the fundamental
magnetic personality of the electron itself.
It's a tool that can ignore the billion paired up molecules in a
sample and just zoom in with laser like precision on the one
unpaired weirdo in the mix. That weirdo, as you call it, is
actually the key to some of the most interesting and important
chemistry in the universe. Well, today we are doing a deep
dive into electron paramagnetic resonance or EPR.
And I have to say, looking through the research for this,
it really feels like the detective story of the Chemistry
World. It's specialized, it's
incredibly sensitive, and it requires some serious detective
work to interpret the clues. It absolutely is a detective
story. And just to clear the air right
at the start, because the names can be a bit confusing, you
might also hear this technique referred to as ESRESR electron
spin resonance. OK.
So are they two different machines?
Is this like AVHS and Betamax situation?
No, not at all. They are the same beast
fundamentally. ESR electron spin resonance is I
guess the older term. It really focuses on the fact
that we're resonating the spin of the electron.
EPR electron paramagnetic resonance is the broader, more
modern term. It kind of acknowledges that the
electron isn't just spinning, it has orbital motion to it's part
of a whole paramagnetic system. But honestly, in the lab you'll
hear people use the terms completely interchangeably.
The physics underneath is exactly the same.
OK, that's good to know. So let's unpack this.
Our mission today is to understand how we can track and
map these these unpaired electrons.
But before we get to the how the magnets in the microwaves, we
need to talk about The Who you mentioned the molecular dancer
in my ballroom analogy. Who exactly are we looking for
with this machine? That is the single most
important question to start with.
The primary requirement, the absolute gatekeeper for this
entire technique, is that your sample must be paramagnetic.
Paramagnetic. It's a great word.
It sounds expensive, sounds like something you put on a resume.
But can we get a, you know, a plain English definition for the
listener who maybe isn't wearing a lab coat right now?
Certainly, in the simplest possible terms, for a species to
be paramagnetic, it has to have at least one unpaid electron
unpaired. So a loner.
A loner? Yes.
In quantum mechanical terms, we would say the total electron
spin, which we denote as S has to be greater than or equal to
1/2. OK, so let's put that in
context, because when I think of molecules, I usually think of
stability, I think of bonds, you know, everything nice and paired
up. And you absolutely should if you
look at the vast, vast majority of stable molecules.
The water in your glass, the plastic in your keyboard, the
proteins making up your muscles. Almost all of their electrons
are paired up. 1 Electron has a spin we call up and its partner
has a spin we call down. They cancel each other out
perfectly magnetically. They're silent.
They're the statues in the ballroom.
They are. We call those materials
diamagnetic. And here is the absolute kicker
to an EPR machine. Diamagnetic materials are
completely invisible. See, that is fascinating, right?
Because usually when we talk about analytical techniques
like, I don't know, taking a photo or doing an X-ray, the
goal is to see everything. You want a picture of the whole
scene, but you're saying EPR is useful specifically because it
doesn't see everything. Precisely.
That is its superpower. Think about it.
If you're a biologist and you're studying a complex enzyme
reaction that's happening inside a cell, it's in a soup of
proteins, water, salts, buffers, a ton of stuff, just a huge
amount of stuff. If you used a technique that saw
everything, your signal would be completely swamped.
It would just be noise. You're.
Trying to find a needle in a haystack.
But with EPR, because the water and the proteins and the salts
are all mostly diamagnetic, they create 0 background noise.
Oh wow. So if you have just one tiny
radical intermediate or one specific transition metal atom
with an unpaired electron, the EPR will see only that.
So the haystack becomes transparent and the needle glows
neon red. That's a perfect way to
visualize it. It gives you absolute
specificity. If you see an EPR signal, you
know with 100% certainty that you have unpaired electrons.
There's no ambiguity. You're not accidentally looking
at the solvent or the glass tube it's in.
So we're really looking for the radicals, the triplet states,
the transition metal compounds. That's the list.
Those are our dancers. And this selectivity allows for
something really cool, something called in situ tracking.
In situ, so in the reaction itself.
Exactly because radicals are often very short lived, they're
the volatile teenagers of the chemical world, always reacting
quickly. We can sometimes use EPR to
track these unstable intermediates in a chemical
reaction that would be totally invisible to other methods.
So you're watching the fleeting moments of chemistry happen in
real time. You're catching a glimpse of the
dancer mid spin before they change their pose.
I love that. It's like having night vision
goggles that only see heat and it just ignores all the other
visual clutter. Now Speaking of other methods, I
feel like we have to address the elephant in the room or maybe
the the cousin in the room. I think I know where you're
going with this most. People who have taken a
chemistry class or even just had an MRI at a hospital have heard
of NMR Nuclear magnetic resonance ah.
Yes, NMR, the famous sibling, the one that gets all the press.
It really does. NMR is everywhere.
So is EPR just NMR's weird little brother?
Are they related? They are very, very closely
related. In fact, the fundamental physics
parallels each other almost perfectly.
In NMR, we're using a magnetic field to split the spin states
of the nucleus, usually protons or carbon 13.
Right, the core of the atom. The core in EPR we're doing the
exact same thing, but we're splitting the spin states of the
electron, the cloud orbiting that core.
OK, so same concept, different target. 1 looks at the center of
the atom, the other looks at the orbiting cloud.
But looking at the stats, it seems like the power level
involved is, well, it's very different.
Drastically different. Let's just look at the frequency
of the energy we use. NMR typically uses radio waves.
We're talking about the megahertz M Hertz range.
Radio waves. That's pretty low energy.
That's like listening to the Top 40 in your car.
Very chill, very low impact. EPR on the other hand operates
in the microwave range. We are talking gigahertz.
G Hertz. So NMR is listening to the radio
and EPR is cooking your dinner. In terms of the frequency, yes,
we are pumping in a lot more energy and that all relates back
to the magnetic moment of the particle we're looking at.
The magnetic moment. How magnetic it is essentially.
You have to remember the electron is much much lighter
than a nucleus. A single proton is roughly 2000
times heavier than an electron. So the electron is a
lightweight. A total lightweight, but it has
a massive magnetic personality. It's magnetic moment is vastly
larger than that of a proton. So even though it's tiny, it's a
much stronger magnet. A much, much stronger magnet.
And because the electron is so much more magnetic, it responds
much more vigorously to the external magnetic field we
apply. This leads to a huge difference
in sensitivity. I wanted to ask about that.
I was reading through the background on this and I I saw a
note that said EPR is approximately 3 times more
sensitive than NMR and I sat there thinking only three times.
That doesn't seem right if the electron is so much more
magnetic. I see where that confusion
probably comes from. That's likely a very specific
comparison of signal to noise under, you know, some very
specific conditions, or maybe just a typo and a summary
somewhere. In practice, in the real world,
the difference is orders of magnitude.
OK, that makes a lot more sense to me.
Let's put it in practical terms for a chemist in the lab.
If I want to run a standard NMR spectrum, I usually need a
sample concentration in the millimolar range, right?
I need a decent amount of stuff dissolved in my tube.
Which, if you spent six months of your PhD trying to synthesize
a tiny pinch of white powder, is a lot to ask.
It can be heartbreaking to dump your entire life's work into an
NMR tube, yes, but for EPR we can often work with micromolar
concentration. Micromolar, so 1000 times less
concentrated. Or even less.
We need a tiny, tiny fraction of the material to get a
screamingly loud signal. So it's thousands of times more
sensitive in practice. Correct.
It's built to detect minute traces of these paramagnetic
species. But of course, there's a
tradeoff. Nature never gives you a free
lunch. And this brings us to the time
scale of the experiment. We call this relaxation time.
This sounded like a spa treatment when I read it.
Relaxation time, but I'm guessing the electrons aren't
getting a massage and some cucumber water.
Not quite, although in a way it is about them calming down.
Relaxation is effectively how long it takes for the excited
spin to return to its ground state to release that energy it
just absorbed from the microwaves.
OK, so how do the two techniques NMR and EPR compare on that
front? Well, in NMR the nucleus is
heavy and frankly a bit lazy. Relaxation takes seconds,
sometimes many seconds. So it holds on to that energy
for a while. It does.
It's a slow, leisurely process. You can pulse it with energy,
wait a second or two, pulse it again.
It's very forgiving. But electrons.
Electrons are jittery, hyperactive things in EPR.
Relaxation happens in microseconds or even
nanoseconds. It is lightning fast.
Nanoseconds. So the electron absorbs the
energy and spits it back out almost instantly.
Almost instantly. And I want you to file that away
in your mind because that speed difference, that hyperactive
relaxation has huge, huge implications for how we
actually, you have to take the measurement.
It's the reason why if you walk into an EPR lab, you often see
these giant steaming tanks of liquid nitrogen or liquid
helium. We literally have to freeze
things to slow them down enough to see them.
But we'll get to that big chill section in a bit.
I'm looking. Forward to that, but first I
really want to visualize the actual physics.
So we've got this machine. We've established it has a
microwave source, a detector, and a massive electromagnet.
We put our sample in this thing called the cavity.
Now we turn the magnet on. What is physically happening to
that lonely unpaired electron inside my sample tube?
OK, so imagine the electron is a tiny bar magnet, like the kind
you played with in elementary school.
It has a North Pole and a South Pole.
We call this it's magnetic moment.
Got it. Tiny magnet.
Now, when there's no external magnetic field, before we turn
the machine on, that little electron magnet can point in any
direction it wants. It's tumbling around, pointing
up, down, left, right. It has no preference.
All directions are equal in energy.
It's. A free spirit.
It is. But the moment you turn on that
massive external magnet, which we call the field be dollars
dollars, that freedom is gone. The electron is forced to align
and quantum mechanics says it only has two choices.
It's not like a compass needle that can swing around
continuously. It can effectively align
parallel to the field or anti parallel parallel to the field.
So it can either go with the flow or it can swim upstream.
That is a spot on analogy. Aligning with the field, going
with the flow, that's the low energy state.
That's where it wants to be. Aligning against the field.
Swimming upstream is the high energy state.
So we've created an energy gap. Before the magnet was on,
everyone was on the same level. Now we have a floor and a
ceiling. Exactly.
We have split the electrons energy state into two distinct
levels and this phenomenon has a name, the Zeeman effect.
The Zeeman effect. And the stronger the magnet we
use, the wider the gap becomes between that floor and that
ceiling. This is where that equation I
saw comes in. I'm going to try it.
We EG, Mehmub B0, MSC. Don't let the letter scare you.
It looks more intimidating than I'm.
Trying not to, but let's break it down so we know what we're
really looking at. It's actually quite
straightforward. MLR's is just the energy of that
level we're talking about. B dollars is just the strength
of the big magnet you're using, and M lever dollars is just the
spin state. Is it pointing with the field
which we call plus 12 or against the field which is -12?
And then we have the constants, the Greek letters.
Right. And Miller is the Bohr magneton.
That's just a fundamental constant of nature that
basically describes how magnetic an electron is.
You can think of it as the conversion rate between spin and
magnetism. OK, so that's just a number, but
then there's Joel Dollar. Ah yes, the Joel factor.
Now, usually in physics, constants are just constants,
like the speed of light or π the kind of boring numbers you just
have to memorize. But I get the sense that the
Jollers is actually the star of the show here.
It absolutely is. In many ways.
Daters are the whole reason we can use EPR to identify
different chemicals. How so?
Well, for a completely free electron, and by that I mean
imagine an electron floating in the vacuum of deep space,
totally alone, no atoms nearby. For that electron date all is a
fundamental constant. It is exactly 2.000232. 2.0,
0232. 2.00232 Extremely precise. Physics is nothing if not
precise. However, as chemists, we don't
study electrons in deep space. Right, we study them here on
Earth. We study them trapped inside
molecules or caught in the crystal lattice of a solid.
And in those environments the electron isn't truly free, it's
interacting with other electrons.
It has orbital angular momentum. It's feeling the traffic of the
molecule around. It so the local neighborhood
actually changes the fundamental behavior of the electron.
It changes its apparent magnetic personality.
Yes, the local electronic environment shifts the data
value away from that free electron value of 2.00232.
And this is huge. This is everything this shift
tells us about the structure. If I measure a sample and I
calculate AG value of say 1.94, I know immediately I'm probably
dealing with a specific type of transition.
Metal comp complex, little interesting.
If I see AG value of 2.0 O five, I might be looking at an organic
radical on a carbon atom. The G value tells us what the
electron is sitting on. It's like a fingerprint, or
maybe an accent. The electron speaks with a
slightly different accent depending on whether it lives on
a carbon atom or a vanadium atom.
That's a brilliant analogy. The accent reveals the origin
and it gets even more complex and frankly more interesting.
The Nates mentioned something about it being anisotropic.
Anisotropic. Yeah, that's a $10 word that
trips up a lot of students, I'm sure.
It sounds like something that requires a cream from the
dermatologist. It does, doesn't it?
But all it means is direction dependent.
Explain that. Imagine you have a molecule
that's flat like a pancake, and it's trapped in a solid crystal
so it can't move. The electron in that pancake
feels a different magnetic environment depending on whether
the big magnet is hitting the pancake from the top, the flat
side, or from the edge. Oh, I see.
So if the magnet is perpendicular to the pancake,
the electrons are kind of running in circles one way.
If it's parallel, they're running a different way.
That's a great way to think about it.
And as a result, the G value, which remember sets the energy
gap, actually changes as you rotate the sample in the magnet.
No way. Yes, if you measure a single
crystal you you might see the GL value shift from say $2.00 all
the way to $2.20 just by turning it 90°.
That seems like it would make things incredibly complicated.
It does, but it also makes it incredibly powerful.
It means if we measure very carefully, we can map out the 3D
electronic structure of the molecule.
We can tell how the orbitals that hold that electron are
oriented in space. That is wild.
But what if the sample isn't a perfect crystal?
What if it's just a liquid? Great question.
In a liquid solution, the molecules are all tumbling
around incredibly fast, they're spinning like crazy.
So all those directional differences, top, side, front,
they all get averaged out. So you just see one single
number. You just see one single sharp
number, the isotropic average. So liquids give you the average
accent, but solids can give you the specific directional
dialects. You can absolutely say that,
yes. So the whole workflow is if you
put the sample in the machine, hit it with microwaves, you
measure the absorption, you calculate this $2.00 value, and
then you play detective to figure out the structure.
That is the basic workflow in a nutshell, yes.
Now I want to talk about the data itself, right?
Because if you are listener were to walk into a lab and look at a
computer screen running an EPR experiment, you might be very
confused. When I look at other chemistry
graphs, like say a UV VS or an infrared spectrum, I see peaks,
I see hills, the line goes up, it forms a mountain, and then it
comes back, right? A classic absorption peak.
But looking at the source images for EPR, these don't look like
hills at all. They look like a squiggly line
that goes up and then sharply dives down, crossing through the
center line into the negative, and then it comes back up.
It looks like a sine wave or maybe a heartbeat on an EKG.
Yes, that is a classic confusing point for beginners.
In standard continuous wave or CWEPR, we don't actually record
the absorption curve directly. We record the first derivative
of the absorption. Calculus strikes again.
Why on earth would we do that? Is it just to be difficult?
Sometimes it feels that way, but no, there's a very good reason.
It's purely an engineering solution to dramatically improve
the sensitivity. OK, remember we're looking for
tiny, tiny signals. If we just tried to measure the
absorption the hill, it might be so small and broad that it gets
completely lost in the electronic noise of the machine.
Like trying to see a small bump on a really bumpy Rd.
Exactly. So we use a clever trick called
magnetic field modulation. We wiggle the main magnetic
field up and down just a tiny bit, very, very fast while we
slowly sweep through the measurement.
And that wiggling does what? It allows us to use something
called Phase sensitive detection.
It's an electronic filter that is tuned to look for a signal
that is wiggling at that exact frequency.
So it filters out all the random noise.
It's an incredible filter, just kills the noise, but the
mathematical output of that whole process just happens to be
the slope of the line, the derivative, rather than the
height of the line. So the point where the line
crosses 0, that sharp dive in the middle of the signal, Yeah,
that's actually the very top of the absorption hill.
Exactly that zero crossing is the resonant field.
It's the point where the slope goes from positive as you're
going up the hill to negative as you're going down the other
side. Got it.
So we're looking for that zero crossing.
Now let's circle back to that Big Chill topic we pinned
earlier. The whole freezing thing.
Right, the cryogenics. You said electrons relax.
They lose their energy really really fast.
Microseconds or less. Why is that a problem?
Well, it's a problem of balance. It's a Goldilocks problem.
We have two main types of relaxation we worry about T
taller and T Audi $2.00 T dollar is called spin lattice
relaxation. This is the process of the
electron dumping it's extra energy back into the surrounding
environment, the molecular lattice.
Now, if this process happens too slowly, if the electron holds on
to that energy for too long, we have a big problem.
Remember, our experiment is trying to pump electrons from
the floor to the ceiling. But if the ceiling gets full
because the electrons won't come back down.
The upper bunk is taken. You can't put anyone else up
there. Right.
You can't promote any more electrons.
The signal saturates. The absorption just stops
because there's nowhere for the electrons to go.
The signal vanishes from your screen.
OK, so too slow is bad, but you said earlier the electrons are
usually really fast. They are.
And that brings us to the opposite problem.
If the relaxation is too fast, if the electron jumps up and
falls back down almost instantly, we run head first
into a fundamental law of the universe, the Heisenberg
Uncertainty Principle. Oh boy, here we go.
Quantum mechanics. Greatest hit.
You can't know everything at once.
That's essentially it. The principle in this context
states that the uncertainty in the energy of a state times the
uncertainty in the time it exists for is roughly a constant
delta, EA, prox bar, a last bar. OK, let's translate that into
something we can visualize. It means that if the time delta
T or, which is the lifetime of our excited electron stay, is
very, very short, then the uncertainty in the energy delta
E must be very, very large to compensate.
And since energy corresponds to the frequency or the position on
our graph. A large uncertainty in energy
means the line on our graph isn't a sharp, crisp spike, it
becomes a broad, fuzzy smear. So if the electron relaxes too
fast, the line gets so incredibly wide that it
effectively just flattens out and looks like the baseline.
Exactly. It blurs out of existence.
So let me get this straight. If it's too slow, you see
nothing because of saturation. If it's too fast, you see
nothing because of Heisenberg blurring.
We need a Goldilocks zone. We do.
We need it to be just right. And for many interesting
systems, especially transition metal complexes at room
temperature, the relaxation is way, way too fast.
Why? The thermal energy in the room,
the vibrations of the molecule, it's all just knocking the
electrons around too much. The lines are hopelessly broad.
You see nothing. So how do we slow them down?
We put them on ice. Serious ice.
We cool the sample down with liquid nitrogen to get to 77
Kelvin, or for the really jittery fast relaxing cases we
have to use liquid helium to get down to 4 Kelvin. 4 Kelvin that
is 4° above absolute zero. That is colder than deep space.
It is at that temperature all that thermal motion effectively
stops. The lattice quiets down.
This dramatically lengthens the relaxation time the delta tuler.
Which in turn shrinks the energy uncertainty, the delta E.
And suddenly, that broad, invisible smear sharpens up into
a beautiful, crisp, readable signal.
So when we see a photo of an EPR lab and there are these giant
stainless steel tanks of cryogens and white vapor curling
along the floor, it's not just for show.
It's not just to look like a man scientist's layer.
No, though it does add to the ambience.
It is absolutely fundamental to the measurement for many, many
samples. Without the cold, the physics
simply won't let you see the data.
That's amazing. OK, so we've frozen our sample.
We've tuned in our microwaves, we found the signal, we've
calculated our G value. But usually we don't just see
one single line crossing 0. We see a pattern comb of lines,
a forest of lines. Sometimes this is where the
detective work goes from identifying this suspect to
interrogating them. This is hyperfine coupling.
This is my favorite part. This is where you get the
fingerprint of the molecule. This is where the molecule
really tells you its life story. So the idea is that the electron
isn't just floating in a void, it's usually orbiting A nucleus
and many nuclei, like hydrogen or nitrogen or vanadium.
They have their own spins. There are little tiny magnets
too. Correct.
So now you have a situation where the electron is feeling
the massive magnetic field from the machine's electromagnet, but
it's also feeling a tiny local magnetic field from the nucleus
it's sitting right next to. It's like you're trying to
listen to a loudspeaker at a concert, but someone is
whispering right in your ear. That's a really good way to put
it. That little whisper changes what
you hear. Imagine the nucleus is another
tiny bar magnet right next to our electron.
That nuclear magnet can also point up or down.
If it points up, it adds a little bit to the total magnetic
field the electron feels. If it points down, it subtracts
a little bit from the field. So the single energy level we
had before now splits. It splits again.
Instead of one line where the electron flips, you now have two
slightly different fields where it can flip.
One for the nucleus up case and one for the nucleus down case.
And this creates the pattern. This creates the pattern and the
notes distinguish between 2 main ways this interaction can
happen. The 1st is dipole dipole
coupling. Dipole dipole.
That sounds like the magnets on my fridge interacting with each
other. It is exactly that kind of
interaction. It's an interaction through
space. But just like we talked about
with the anisotropy of the G value, this interaction is very
direction dependent. So in a liquid.
In a liquid solution where the molecules are tumbling rapidly,
the dipole dipole interaction averages out to zero.
It completely vanishes. OK.
So if we're looking at a liquid sample, we don't see dipole
dipole, but we definitely still see splitting.
So that must be the other one, the Fermi contact.
Yes, and the Fermi content interaction is, well, it's a bit
spooky. It's purely a quantum mechanical
effect. Also, classical physics says 2
objects can't occupy the same space at the same time, but
quantum mechanics says that an electron in a spherical's
orbital has a non 0 probability of being found at the nucleus.
Wait, you mean literally inside the nucleus?
Like the electron cloud overlaps with the space where the protons
and neutrons are. Literally occupying the same
physical space, the electron's wave function has amplitude at
the nucleus. This creates a direct, very
strong magnetic interaction that doesn't depend on direction, so
it doesn't average out when the molecule tumbles.
This is what gives us those beautiful sharp splitting
patterns we see in liquid phase EPR.
That is mind bending. The electron is basically
haunting the nucleus. OK, so let's try to predict some
of these patterns because there's a simple rule for this,
right? The two I plus one rule.
Simple algebra I is the quantum number for the spin of the
nucleus. The rule is simply $2.00 plus
other one, and that tells you how many lines you get from
coupling to that one nucleus. OK, pop quiz time.
If I have a hydrogen atom, a proton, I know from NMR that
hydrogen has a spin of 12. So you plug that into the
formula $2.00 * 12 plus. That's 1 + 1 = 2, so I should
see a doublet 2 lines. Correct A1 to 1 doublet.
What about, say, nitrogen 14? The notes say that has a spin of
1. So $2.00 * 1 + 1 = 3 three you
get a triplet 3 lines of equal intensity.
And the physical distance between those lines on the
spectrum, what does that tell us?
That distance is what we call the hyperfine coupling constant,
and it's usually denoted as Earth.
The magnitude tells you how intimate the relationship is
between the electron and that nucleus.
So a big value. If A is big, the lines are
spread far apart. That means the electron is
spending a lot of time very close to that nucleus.
The spin density is high. If it's small, the electron is
probably further away, barely visiting.
So it literally maps the electron density.
It's a way of saying the electron lives mostly here, but
not so much there. You've got it.
It's a map of the unpaired electrons home.
This is the perfect time to walk through the case studies from
our source material because this is where we take all this theory
and alley it to actual chemical mysteries case study #1
Vanadium. Specifically a complex called
Vinay CAC Tutu. Yes, a classic EPR standard.
A lot of people use this to calibrate their machines.
So we have a vanadium atom at the center.
The main isotope is vanadium 51, and it's almost 100% abundant in
nature, which is convenient. It has a nuclear spin.
I have a 72. 72 That's a hefty spin.
That's a lot of magnetic options for the nucleus.
So let's do the math $2.00 * 72 plus fullest dollar.
That's $7.00 + 1 = 88. So you would predict that you
should see 8 evenly spaced lines, and if you look at the
spectrum, that's exactly what you see, 8 distinct jagged
heartbeats spread across the screen.
But the notes point out a subtle detail.
The lines aren't all perfectly identical.
It's not a perfect comb. The ones on the very outside the
far left and far right lines, they look a little shorter and
maybe broader. Yes, they are broader and
shorter. This is a very cool, subtle
effect that's caused by that tumbling we were talking about
earlier. The molecule spinning around in
the liquid. Right.
If the molecule is very big or if the solvent is thick and
viscous like syrup, the molecule might not be tumbling quite fast
enough to perfectly and completely average out all that
anisotropic stuff we discussed. We call this the slow tumbling
regime. So just by looking at the line
with, by seeing that the outer lines are fatter than the inner
lines, we can actually get information about how fast the
molecule is physically spinning in the solution.
We can't. It gives us dynamic information.
We can learn about the viscosity of the solvent or the
hydrodynamic size of the molecule itself.
We can tell if our molecule is maybe binding to something big
like a protein, because that would slow it down and broaden
those outer lines. That is incredibly cool.
It's like having a tiny speedometer for molecules.
OK, let's move on. Case study #2 The benzene
radical anion which is 66 feet age 6-6 dollars.
Right time for some organic chemistry.
So benzene is a flat ring of 6 carbon atoms with six hydrogens
attached around the outside, and we've just added one single
extra electron to this whole ring system.
And this is a thing of pure chemical beauty.
In your classical intuition, you might think, OK, the electron
just sits on one of the carbon atoms, right?
But quantum mechanics says, no, that electron is delocalized.
It is smeared out, running around that entire ring like
it's a racetrack, visiting all six carbons and all six
hydrogens equally. So it's coupling to all six
hydrogens at the same time? Yes, and they are all equivalent
to each other. So in this case we use a simpler
rule. The number of lines is just one
plus other dollars, where N is the number of equivalent nuclei.
OK, so N is 6, so $6 + 1 = 7 lines and.
You do, but here the lines definitely aren't all the same
height. The notes show a graph where the
middle line is huge and tall, and the outer lines are just
tiny little blips. The whole pattern looks like a
bell curve. Why is that?
Why the different intensities? Right when you have multiple
equivalent nuclear. I like this.
The intensities of the lines follow Pascal's triangle.
It's a binomial distribution. I need a refresher on that.
Think about flipping 6 coins. The outermost line in the
spectrum represents the state where all six of the hydrogen
nuclear spins are pointing up. There's only one way to do that.
Up, up, up, up, up. So it's a rare event.
A very rare event, so it's a small.
Short line, but the big line in the middle.
The big line in the middle represents the state where three
of the spins are up and three are down, and there are many
different combinations that give you that exact result.
Oh, I see. You could have up, up, up, down,
down, down, or up, down, up, down, up, down, and so on.
There are 20 different ways to get a three up 3 downstate, so
that state is statistically much more likely to occur.
So the line for that state is much taller.
Much taller. The intensity ratio for six
equivalent spin 12 nuclei is 1.6.15.15.6.1.
It's mathematically perfect. It is, and when a chemist sees
that beautiful symmetric pattern, they know for a fact my
unpaired electron is symmetrically spread over that
whole ring. If the ring were bent or broken,
that perfect symmetry would be gone and the pattern would
collapse into a mess. Nature following in the
textbook. I love it.
Now let's level up the complexity.
Case study #3 The tetrazine anion, which is called BPATC.
This is a molecule with a lot of nitrogen in it.
Yes, it has a central ring with four equivalent nitrogen atoms,
and we know that nitrogen 14 has a nuclear spin of 1.
Okay, math time again. One nitrogen gives 3 lines, Two
equivalent nitrogens gives 5 lines.
What about four? It turns out that four
equivalent spin one nuclei gives you 9 lines, and if you look at
the spectrum, it's perfect 9 evenly spaced lines of varying
intensity. This proves again that the
electron is delocalized over all four of those nitrogen atoms in
the ring. But then things get crazy.
The notes show us a tungsten complex made with this molecule.
The formula is MOBI Opco 42 Two. This thing looks like a monster.
It is a more complex structure, yes.
And the spectrum is described as a quintet of quintets.
What on earth does that mean? This is where we see a
superposition of couplings. This is where the detective has
to feel back multiple layers. In this new big complex, the
structure has lower symmetry. The electron isn't seeing all
four of those nitrogen atoms equally anymore.
Because the big tungsten metal atoms are attached to it.
Exactly. The tungsten atoms distort the
ring. Now the electron sees two of the
nitrogen strongly and the other two nitrogens more weakly.
So it's a hierarchy of interactions.
Exactly. First, the electron couples to
the two strong nitrogens. Two equivalent nitrogens with
spin one gives a quintet 5 lines.
The intensity ratio is 1.2.3.2.1.
OK so in my mind I'm picturing 5 big broad lines.
But then each one of those five big lines is split again by the
much weaker interaction with the other two nitrogens.
The weak ones. Right, so each big line splits
into its own smaller quintet. A quintet of quintet.
So you'd see 25 lines in total, but they'd be organized in these
5 distinct clusters. That's exactly what you see, and
by analyzing which coupling is big, that's the wide spacing
between the clusters, and which coupling is small, that's a fine
spacing within each cluster, we can map exactly how the electron
sits on that distorted molecule. You can actually say it spends
more time on the north side of the ring than on the South side.
It's an incredible level of resolution.
It really is the ultimate spy tool for mapping out electronic
structure. I want to talk about one last
case study because it solves a mystery using isotopes, which I
thought was so clever. It's the satellite mystery.
Ah yes, the zirconium case. This is one of my favorite
examples of how important it is to look at the noise.
So we have a spectrum for a zirconium species, and at first
glance if you're rushing it just looks like a big doublet in the
middle of the screen. 2 strong lines.
Right. A simple doublet and a doublet
usually means coupling to one spin 12 nucleus.
In this particular molecule, there was a single hydrogen atom
nearby. So mystery solved, right?
The electron is coupled to the hydrogen.
Not quite, because the notes say that if you zoom in and you have
to look really, really close, way down near the baseline
through these tiny little blips on either side of the main
signal, they call them satellites.
This is the isotope detective work.
Zirconium is a metal, and in nature it's a mix of different
isotopes. Most zirconium isotopes have
even mass numbers, and they have no nuclear spin.
They have I-0. So for most of the atoms in the
sample, the vast majority the zirconium is magnetically
invisible. The electron just seize the
hydrogen, hence the big doublet in the middle.
Correct, but there's also zirconium 91.
The rare one. The rare $191.00 has a nuclear
spin of I dollar and 522, but it's not very common.
Only about 11.2% of all natural zirconium is this one isotope.
So in about 89% of the molecules there's no zirconium splitting,
but in 11% of the molecules there is splitting from the
metal. In in a nucleus with spin 52
gives $252 + 1 equus 66 lines. So flanking that big central
doublet, you see these faint tiny sets of 6 lines.
Those are from the 11% of molecules that contain a
magnetic zirconium nucleus. And the fact that we can see
them at all, what does that prove?
Why does the chemist care about these tiny little blips?
It proves unequivocally that the unpaired electron is physically
located on the zirconium atom. If the electron were on a ligand
far away, say on a carbon chain just dangling off the side, it
would be too far away to feel the zirconium nucleus is tiny
magnetic field. The coupling constant would be
0. The satellites wouldn't exist.
So the blips of the smoking gun. They say the electron is right
here sitting on the metal center.
Exactly, it confirms the oxidation state and the precise
location of the spin density. And you know, if you were
incredibly rich, you could buy isotopically enriched zirconium
91100% pure. If you have the budget for.
It if you did that and you made your molecule with it, the big
central doublet would vanish completely.
The satellites would become the whole spectrum.
You'd see a massive complex 6 line pattern dominating the
screen. It's just amazing how much
information can be hidden in what looks like noise if you
just know where to look. It's not noise, it's the data.
Fairpoint, before we wrap this up, I do have to complain on
behalf of all the students who might be listening the units.
Why are the units such a headache in this field?
I was trying to follow the math and the notes and it felt like I
needed a conversion chart from three different centuries.
Oh, it is an absolute mess. We we apologize on behalf of the
entire scientific community. It's a historical accident,
really. So we have Gauss and we have
Tesla. Right, the magnetic field, the
dollar field is measured in Gauss G by the old school
physicist or in Milla Tesla Mt by modern SI compliant folks.
For the record, 10,000 Gauss is equal to 1 Tesla.
SO1 Milla Tesla is 10 Gauss. OK, that's manageable.
But then the interaction energy, that coupling constant that's
sometimes reported in Gauss. Yes, sometimes we just measure
the splitting distance on the screen in field units, so Gauss
or Milli Tesla, but physically it represents an energy
interaction. So other times it's reported in
frequency units. Megahertz, Emma.
Hertz. And then there's the one that
really hurt my brain. Inverse centimeters.
Inverse centimeters, my favorite non intuitive unit.
It's a legacy term from optical spectroscopy.
It relates to the wave number of light that would have that
amount of energy. It's yeah, it's.
Confusing. So if I'm a student trying to
solve a problem, I might be given a magnetic field in Tesla
and instrument frequency in gear Hertz and a coupling constant in
inverse centimeters and I have to make them all talk to each
other. It happens all the time, and the
reality is to make sense of a really complex spectrum with
mixed units and overlapping lines, like that tungsten
quintet of quintets. You rarely do it by hand with a
ruler anymore. You use the computer.
You use simulation software. You feed all the parameters,
your G values, your coupling constants, your line widths into
the software and it generates A theoretical spectrum.
Then you just tweak the numbers until your simulation perfectly
overlays your experimental data. The computer is the final
arbiter. Indeed, and it handles all the
unit conversions for you. Thank goodness.
Thank goodness for that. So let's bring this all back
home. To summarize our deep dive
today. EPR is the magnetic sister of
NMR. It uses microwaves to flip the
spins of unpaired electrons. It is incredibly sensitive and
it's incredibly specific because it ignores all the paired up
statues in the ballroom. And through the magic of these G
factors and the hyperfine coupling patterns, it allows us
to map the precise location and the chemical environment of an
electron in a molecule. And not just its static
structure, as we saw with the line widths and the slow
tumbling. It also tells us about motion,
about tumbling, about dynamics. It really is a window into the
electronic structure of these oddball molecules that no other
method can provide. It sees the radicals of the
molecular world. I love that it's the tool for
the rebels. Yeah.
Now, as we finish up, I want to leave you, our listener, with a
thought. We talked a lot today about
freezing samples liquid helium for Kelvin.
We do this to stop the motion to beat the Heisenberg uncertainty
principle to actually see a signal.
To lengthen the relaxation time, yes, that's the key.
But biology happens at 37°C. Life is wet, it's warm, and it's
constantly moving. The enzymes in our bodies that
use radical mechanisms to digest our food or repair our DNA,
they're working at body temperature.
So if we can only see them when they're frozen solid in a block
of helium, are we actually seeing the truth?
That is the big question in the field.
Are we just seeing the dancer frozen mid leap or if we lock
them into a pose that they never actually hold in real life
during the actual bands, how much of the reality of the
reaction do we lose when we freeze the frame?
That's a profound and very real problem.
We are capturing a state, a snapshot, but are we capturing
the function? It's something every structural
biologist has to wrestle with. We'd build these beautiful
models based on the Frozen snapshots, but we must always
remember that the map is not the territory.
Something to Mull over next time you look at a static picture of
a molecule. It's probably dancing when
you're not looking. Thanks for joining us on the
Deep Dive. It was a pleasure, as always.
See. You next time.