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  • >> All right what I'd like to do today and on Monday is to talk

  • 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