about NMR spectroscopy and kind of how NMR spectroscopy works.

I'll call it concepts in theory and for me what I want

to do is give my perspective on NMR

which is not a highly mathematical perspective.

In fact, everything I write up here today is going to really be

in terms of numbers is actually going to be simple arithmetic

and most of it is more an embodiment of the idea rather

than a specific calculation that you quote need to do.

So where NMR begins is with the concept that a nucleus

of certain sorts and I'll just write a proton for now,

has a spin to it and when you have a spinning charge it

generates a magnetic dipole.

And if you apply a magnetic field,

we'll call that magnetic field B naught,

then you have two different spin states or more

and you'll see examples of this in the case

of nuclear quadrupoles but let's start with the case

of a proton or a C 13.

You have two spin states that can exist, quanti-spin states.

The spin of the nucleus can either be spin up,

so if it's spin up, in other words in the same direction

as the applied magnetic field then this is going to be lower

in energy so I'll put, by up I mean aligned with B naught

and if it's spin down meaning aligned

against B naught then we're higher in energy and we'll refer

to throughout our discussion.

We'll refer to the lower energy state as the alpha state

and to the higher energy state as the beta state.

Now different types of nuclei have different spin properties.

Rather than trying to start with generalizations

about rules I'll come to those in a moment

because at some point you'll be wondering

in your project well could I study chlorine 35 or something

like that, let's just start with typical nuclei studied.

So if you go for example, to the 400 megahertz NMR spectrometer

in my building in Natural Sciences 1,

you'll find that that instrument can study protons.

I'm going to write a couple of numbers for these.

I'm going to write the atomic number and the mass number.

And it can study C 13 and it can study F 19

and it can study P 31.

And these are common nuclei that are often studied by NMR.

They're easy to study.

What do these nuclei have in common?

They have a one-half indeed and what,

forgetting their spin state what property

on the blackboard do they have in common?

>> Odd numbers of protons and neutrons.

Odd numbers of protons and neutrons

or more specifically we can group them

that their mass number is odd, specifically that the sum

of their protons and neutrons is odd.

So nuclei with an odd mass number have a nuclear spin

and the quantum characterization

of nuclear spin is what's called a spin number

and we'll call the spin number i. It really doesn't matter what

we call it but they call it i and so that number is going

to be one-half and that gives you all the ones up here

but if we want a generalize more nuclei

with an odd mass number will have a spin number of one-half

or three-halves or five-halves, etcetera.

So that's the more general idea.

The ones with one-half are easy

because they have what's called the nuclear dipole.

If you have three-halves or five-halves or one as we'll see

in just a moment you have what's called a nuclear quadrupole

and then those tend to be harder.

So all the ones here of i equals one-half have spin states

so we have the quantum number

and then the two spin states they can have

and so the spin states are plus or minus one-half.

So that's all of these H 1, C 13, oops, F 19 we'll come

to nitrogen in just a second and P 31.

Now a nucleus with a spin number

of three-halves can have spin states of plus or minus one-half

or plus or minus three-halves

and this is what you call a nuclear quadrupole.

Most of the time, many of the times nuclei

with nuclear quadrupoles don't behave as if they're NMR active.

In our next lecture we'll get to the concept of relaxation.

Relaxation basically is how quickly you flip

between the two spin states or in this case,

between the four spin states or three in some cases

and often they flip very quickly

which means you can't study them by NMR.

Relaxation is affected by properties like symmetry as well

and I'll get to that in a moment with another example.

But if I give I an example of a nucleus with a spin state

of three halves, of boron there are two different isotopes.

There are B 10 and B 11 and B 11 has, I think they both do

but B 11 has a spin state of three-halves and if you look

at the NMR spectrum of borohydride

from this one what you see

in the H1 NMR is you see four lines equally spaced

and of equal height due to the hydrogens coupling

with the nuclear quadrupole and it's very unusual

because normally we think about splitting into a doublet

or if you're thinking a triplet or a one to two to one triplet

or quartet or one to three to three to one triplet,

but what's happening here is the hydrogen C boron

and they see either the boron having a spin state

of negative three-halves or negative one-half

or positive one-half or positive three-halves

and so you see the four spin states

and that gives are rise to four lines.

All right but so let's look at some other nuclei

with an odd mass number.

[ Silence ]

So one very important nucleus in biomolecular NMR is N 15.

Nitrogen 15 has a spin number of i equals one

and indeed N 15 is often studied.

Most nitrogens, not N 15.

We talked about this when we talked

about mass spectrometry we said that the natural abundance

of N 15 is 0.38 percent and that's really, really low.

The isotopic abundance of C 13 spin active is one-and a half

percent is 1.1 percent and you know

that carbon NMR is not very sensitive.

You need to have a reasonable sample size, more than you have

for protein typically

and sometimes often collect data for much longer.

Well by the time you're down to .38 percent studying it

at natural abundance is pretty hard so often you do this

with isotopic labeling.

Two dimensional N 15 based techniques are a mainstay

of protein NMR spectroscopy and in general

since most proteins are expressed these days what you do

is you simply grow up your e-coli

with N 15 ammonium chloride and they absorb that and use it

to make up the amino acids

and then you can get a fully N 15 labeled protein

which is very useful.

N 15 is starting to become more important

in some natural product structure determination.

Alkaloids as you may have seen for example

in Neil Gard's [assumed spelling] talks have lots

of nitrogens in them and so being able to figure

out the positions of those nitrogens can be very important.

In the case of something like an alkaloid

or a synthetic project you might not be able to put N 15 in

and NMR spectrometers are becoming more sensitive

and so it becomes not completely nuts to think

about using N 15 techniques in your NMR.

At the end of the course I may talk

about some two the dimensional techniques with N 15

at natural abundance that people are doing just

because I think it's useful but that won't be until the end

of November or December.

Another common, well not common, another nucleus is oxygen,

O 17 remember we said is only low natural abundance.

It's only very low I should say.

It's only.04 percent and oxygen 17 has a spin number

of i is equal to five-halves so that's a nucleus

that can have six spin states, negative five-halves,

negative three-halves, negative one-half, positive one-half,

three-halves, five-halves, etcetera and so it has sort

of doubly damned and so it's not generally studied.

All right so that takes care of our nuclei

with odd mass numbers.

Now the next class I'll talk about is

if you have an even mass number and an even atomic number

so that's easy those are nuclei like C 12,

O 16 and the answer is very simple.

Those have a spin number of i equal zero.

They have no spin and those are NMR inactive.

Since you don't have different spin states you can't have

quanti-transitions between spin states

so there's no way they can be studied by NMR spectroscopy.

So the last class then becomes nuclei with an even mass number

but not atomic number so that would include nuclei

like deuterium, nuclei like N 14.

I guess that would be the common ones we'd encounter

in organic compounds.

These all have a nuclear quadrupole.

Remember a quadrupole is anything

that doesn't have a dipole, i.e. just spin up, spin down,

i.e. i equally one-half so these all have a nuclear quadrupole

and a spin number i equals 1, 2, 3, etcetera so for example,

if you take deuterium you have a spin number i equals 1

and so you have three spin states available to it

and you know the direct manifestation of this that many

of you have seen with your own eyes?

Who's run a C 13 NMR, most of you?

What solvent did you use?

Chloroform, right, the first solvent most of us reach

for because it's pretty cheap as solvents go and pretty good

at dissolving organic chemicals.

It's cheap because it doesn't have

that much deuterium in it, right?

You only have one deuterium for all that weight of chlorine.

You need to deuterium to get the deuterium lock

for NMR spectroscopy and what do you always see

when you run an NMR spectrum in deuterochloroform?

>> A triplet?

>> A triplet and a very interesting sort of triplet

so for CDCl 3 in the C 13 NMR you see a one-to-one-to-one

triplet centered at 77 ppm.

>> These are really jammed together.

>> It's really jammed together.

The separation between the lines is 32 hertz,

in other words the distance

between these two lines is 32 hertz.

The distance between these two lines is 32 hertz.

If you're running your spectrum on a 500 megahertz spectrometer

that means the carbon NMR is running at a 125.7 megahertz.

I'll come back to that in a second

which means 1 ppm is 125 hertz

which means the lines here are separated by about three-tenth

of a ppm and that's on a big roughly 200 ppm scale

so as James said those lines are really close together

and the manifestation is it's a one-to-one-to-one triplet

because to a first order approximation a third

of your deuterons are in spin state negative one.

A third of your deuterons are in spin state zero and a third

of your deuterons are in a spin state of positive one

and we'll see in a moment that they're minuscule,

minuscule differences in the population of the spin states

and that's really, really important.

We'll also see in a moment that that number 32 comes back

when we see something else.

All right most of the time--

so deuterium is kind of special among nuclear quadrupoles

in that most of the time nuclear quadrupoles,

nuclei with quadrupoles undergo rapid relaxation

but deuterium is special.

It's relaxation is slow and I'll just say to put it

in simple terms is effectively like NMR inactive.

So many of the nuclei with nuclear quadrupoles

like chlorine 35 and chlorine 37 how do we know that those have,

all right I will take that back.

We can't know that they have a nuclear dipole

or a nuclear quadrupole but we know they have a spin number

of one-half or three-halves or five-halves or seven-halves.

They happen to have the higher ones so we never see J coupling.