Interpreting 1D NMR Spectra: Chemical Shifts and Spin-Spin Coupling Explained

We will look at now how one dimensional NMR spectrum ah can be interpreted what are the different parameters? Um. As, I said this is a course on for bimolecular NMR. So, the idea is to basically introduce very basics of these two concepts of chemical shift and

coupling. We will not go into details ah which we have looked at in the in the previous course. So, let us briefly look at how this chemical shifts are calculated and how does spin-spin coupling affect our ah spectrum?

So, chemical shift so, if you look at a 1 D-NMR spectrum, ah in a general or any NMR spectrum these are the four parameters which you will notice in the spectrum. First see the most important is a chemical shift which is nothing, but the position of

the peak ah and that tells you information on whether it is an alkane, it is an alkene, or it is aldeyhyde and so on it is an amide an aromatic group's etcetera. The chemical shift is the most important parameter, it tells immediately about the possible functional

groups or structure of the molecule ah. So, that is what ah is the first thing to look at. The second is ah ah integral that is how strong is the peak? And, that number the integral gives us the relative number of protons or hydrogen's as we saw in the previous class.

Ah. Here we would look at the area of the peak and that is why it is call integration? . Ah. In proteins and biomolecules this plays a very important role because many of the

quantification applications require this value to be correct. And, the third thing which is the what is called as J-coupling or spin-spin splitting, it is because of the coupling between the hydrogen's and the carbons or hydrogen's. And, this is basically the same thing as the

fourth parameter here. Ah. The spin-spin splitting and coupling constant essentially tells you about, what are the adjacent hydrogens and carbon present in a molecule. And is a very important parameter as far as structure is concerned, because from the coupling

constant or from the spin-spin splitting pattern, we immediately get to know what are the number of neighbouring hydrogens whether is a cautionary carbon it is a tertiary carbon and so on. So, we will look at this chemical shift little bit in more detail now and see how this is

calculated. So, what is the first why does the chemical shift arise in a molecule? And, this something which was briefly covered in the previous class. It basically what happens is you have

a nucleus sitting in the centre of an atom. And, an atom consists of electron cloud and this electron cloud, which is basically not a single electron. It is it is a cloud of electron that tries to oppose the magnetic field at the centre of the nucleus.

And therefore, the magnetic field ah experience by the nucleus is not just B0, it is reduced by some factor and this is why we use the word shielding. So, essentially this electron cloud is trying to shield the nucleus from the external magnetic field. And, that depends

now on many parameters; how much is the shielding what kind of type of shield is it uniform and so and so forth. And, that depends on the structure of the molecule it depends on many other properties.

So, this shielding factor is a very small deviation from the main from 1. So, it is not that the shielding is very high the shielding just is a very small number nevertheless very important number without this shielding we would not be able to do NMR at all even though

we have all the possible of we have the nuclear magnets and so on. Even then without having this shielding affect NMR would have been ah not usable. So, therefore, it was very important to understand this chemical shift concept this is the heart

of the NMR technique as far as structure is concerned. So, we can see this this what what determines the shielding, how much is the nuclear shielded, that we will see the factors as we go on, but now let us see how it is chemical shift value that is how much is this

shielding value calculated ah based on this this parameters. So, now we can see here again remember this equation. So, we are looking at an effective magnetic field, ah which is not different from the main magnetic field because of this

fact. Now, this can be positive or negative we will ah for example, assume time being it is a positive sigma is positive. So, this is smaller than 1. So, this is how ah it depictive the chemical shift effect is depicted here. So, we can

see that because of this shielding factor the energy gap for the CH 3 becomes smaller than the energy gap of CH 2 and smaller higher for the OH. Because, this is the least shielded, this hydrogen is least shielded because of the oxygen here we will see the this concept

of inductive effect shortly ah, but because of less shielding that the energy difference in the alpha and beta states of this hydrogen is proton is high compared to this and compared to that.

So, now this energy difference depends on now remember delta is H into mu. So, the mu that is H into mu the mu value the frequency value changes for this changes for this and changes for this. And, that is why this 3 different atoms or hydrogen comes at different

frequencies and that frequency is converted into a scale called as ppm scale. So, essentially what is going on here is each hydrogen atom is experiencing a different frequency of resonance they are not resonating at the same frequency. They are experience

different resonating frequencies, but they are converted into a scale which become makes it independent of the frequency scale, we will see that shortly how this comes about? .

So, this is how the calculation is shown here? So, essentially the the main thing is the chemical shift value when we calculate in ppm scale is based on a reference and it does not change with field strength. This is a very important parameters; that means, if

I go from 300 megahertz spectrometer ah to a 700 megahertz spectrometer and take the same molecule ethanol or any other molecule. Its chemical shift value in ppm should not change. And, that is how why that has happened that comes from this formula or calculation

shown here. So, let us say that we have a reference frequency, which is our rotating frame frequency and there is standard B0 gamma into B0 and that is the processional frequency of a reference

nucleus ok. So, we can take any nucleus as a reference and assume that it has "zero" chemical shift. So, remember this is an assumption many a times people are confused that ah reference molecule has actually "zero" chemical shift now we are setting in forcing it to be 0 and

is an arbitrary. So, let us say that references frequency is ah has chemical shift 0. So, it has a perfect condition resonance shown like this. Now, our proton of interest is not having 0 frequency

it is having a finite chemical shift values that is not 0. So, it is frequency now will be like this. So, what we do next is we can subtract these two . So, when we subtract these two and divide by B gamma B0, you can simply do yourself this calculation you will

get this sigma in this in this way. So, this sigma that is a chemical shielding factor chemical shift or shielding factor is now mu minus mu reference divided by mu reference. So, what is mu reference? Mu reference

is basically the magnetic field strength, which remember was in 10 to the power 6 in megahertz and this is the difference between the frequencies. So, what happens is now since mu ref is a megahertz range the value of sigma will become

10 raised to minus 6, because this 10 raised to the power 6 goes up to the numerator as 10 raised to minus 6. And therefore, we use our ppm. So, sigma becomes in the value in the order of 10 raised to minus 6 and that is why we use a word parts per million or

ppm. So, what happens is because you are subtracting reference frequency and again dividing by the reference, the chemical shift value the shielding value in ppm scale becomes independent

of the frequency. That is it is becomes independent of this number, whether it is 700 or 300 because you are dividing it by that number. So, is kind of scaling. So, that are that is shown here.

For example let us say I have two frequencies . So, that question here is how much is the difference? If two nuclei have 1 ppm difference in chemical shift value. So, let us say 1 chemical shift value is sigma 1, which is given by this it is same as the last formula

in the last slide. Another proton is having another chemical shift values, which was again is the same formula accept that only thing which is changing here is mu 1 and mu 2. So, you can see that now if I subtract the 2 the difference I am considering as 1 ppm which

is what was shown here. So, that is 1 ppm means 1 into 10 to the power minus 6. So, therefore, if I subtract these 2 frequencies sigma 1 minus sigma 2, then if you look at this equation if I subtract this what will I get I will get mu 1 minus mu 2 divided by

mu ref. So, the mu ref it goes to this side that is how it is written here coming from this equations. Now, that is 10 raised to the power minus 6 is this number? And, that multiply with 500 into 10 to the power 6, because let us say we are at 500 megahertz

. So, if you go to 500 megahertz spectrometer if the 500 mega spectrometer is used, then you are now the difference in the two frequencies, which are only 1 ppm apart now the difference

actually is 500 hertz. So, you see the difference now actually depends on the frequency there is a spectrometer frequency, but that is in the hertz scale. In the ppm scale they are still 1 ppm. So, suppose I go to 900 megahertz the spectrometer

or 800 megahertz spectrometer. If I do the calculation there again the difference will remain the same they are still 1 ppm away from each other, but in the hertz scale this number will become 800 megahertz. So, 800 will come here and this will become 800 hertz.

So, you see the difference the in chemical shift value between 2 peaks definitely changes in a hertz scale it become 700, 800 depending on the spectrometer, but it is difference in the ppm scale will always be constant. So, that is the beauty of chemical shift scale

that it does not affect the chemical shift value in ppm scale, it affects only the chemical shift value in the hertz scale. That is why chemical shift scales are very popularly used. So, this is what is basically shown here is because of this term here mu ref, which came

from the previous equation or previous slide mu ref changes with field strength and mu ref is nothing, but this term and this is depending on your B0 . So, if you have 500 megahertz has one B0 800 megahertz will have a higher B0. So, the reference frequency definitely

changes with spectrometer. So, therefore, when you calculate in hertz scale it changes, but what does not change is a difference in the the ppm scale . So, we can see this is what is depicted here that if you take in a hertz scale. So, this

is left side is frequency scale, frequency meaning in hertz scale and right side is the delta scale which is in ppm value. So, you can see two peaks or a set of peaks always remain in the same whether you are a 250 megahertz and 500 megahertz, or it 750 or 900 megahertz

in different spectrometer the peak pattern the three peaks will not change. But, now if we calculate the difference between the 2 the peak let us a green and this blue peak their difference is not same they are actually changing. And, they are linearly increasing

because of this frequency changes because of this magnetic field change. So, you see the difference now the difference is that although they look same in the delta scale they are actually the frequency scale the hertz scale they are not the same, the

chemical shifts they are factory changing. So, therefore, ppm scale is a very preferred scale, because it bit makes it independent of the spectrometer that you are using and therefore, it is very handy and useful ah to use whereas, hertz scale tells us that

they are going apart. So, the resolution you see the resolution is going up, because I am separating the peaks more and more. So, as you go higher and higher magnetic field, it is not that the chemical

shifts are not changing they are changing in hertz scale and that helps to increase the resolution. And, that is one of the reason why in biomolecules there is a lot of effort to go to higher magnetic field, because the resolution is improving as we go up. And,

this resolution linearly goes up and therefore, it is very useful to have a hertz scale or higher frequency ah in for biomolecules. So, what are the different factors which affect the chemical shift? So, this is just now we

alluded to one factor which is the effect of inductive effect ah, but we look at ah quickly through all this again this is something which has been covered ah very nicely in various test book in the previous course, but we will have a quick glance because in biomolecules

all of these have an effect. And therefore, it will be useful to understand the effect ah how ah how they affect the spectrum? . The first one is the simplest effect that is the inductive effect and that is nothing,

but related to the electronegativity. So, you can see a very simple drawing here, that if you have a carbon molecule in a ah in a biomolecules we do not have chlorine. Let us take an example of some molecule which

has ah ah carbon attached to this chlorine. So, because of this electronegative atom which is highly electronegative, it pulls the electron from the carbon. Therefore, the electron density the how the electron cloud is distributed changes. And therefore, that in turn changes

the electron density around this proton. So, this proton is also affected indirectly because of the electron a negative electronegative effect of this chlorine. So, this can happen with other ah electronegative ah atoms like

nitrogen, oxygen, carboxylate groups and so on. So, therefore, what chlorine essentially is doing is it is deshielding it is taking away the electron from the hydrogen. So, therefore, hydrogen becomes partially positive charged.

And, by taking away the electron density from hydrogen it is removing reducing the shielding factor, the sigma value which we saw in the previous slides, it is reducing and that makes it go closer to as much as deshielded as possible.

So, that is one of the simplest effects and this is shown further here for some alkyl halides. So, we can see fluorine we know is a most electronegative atom. So, that has the highest deshielding effect on this particular hydrogen. So, we can see that therefore, it

becomes very high chemical shift deshielded it goes down field that is to 4 ppm. And, as you go lesser and lesser electronegative atoms the deshielding effect is reduced and you can see that it is going low.

So, the the this is the trimethyl silane which is the less least deshielded or most shielded is the reference, which we normally take it as it. Again remember this is not that chemical shift value is 0, we have forcing this this peak to have a 0 value, with respect to that

we are actually calculating the others. There is an arbitrary 0 concept arbitrary reference which is put a 0. So, you can see the shielding effect is very clear very linear with respect to the inductive effect.

Now, this is another example where we have taken a little bit away. So, you see this is a little higher second order. In the sense it is not directly attached to an electronegative, it is away from the electronegative atom 1 by 1 hydrogen here. So, this is the second

hydrogen away from here. This is directly attached and whereas, this is three two carbons away this hydrogen. So, we can see the effective reduce the for this which is closest to bromine has a highest

shielding effect, ah de shielding effect. And this is the less deshielding and this is the most shielded, it is almost it is very away from Br that is bromine. So, therefore, it is having the least deshielding effect.

So, this is something which all of us are aware of this is just ah being in this the second factor which also helps ah inductive effect is the number of electro negative. So, you can see in chloroform we have three carbons, ah which is three colorines [chlorines]

sorry. So, three chlorines have the maximum deshielding effect. And therefore, this hydrogen is highly shielded compared to this hydrogen compared to this which has only one chlorine. So, these are the basically different ah deshielding shielding effects. Now, let us look at this

concept of chemical equivalence and this is also very important concept. So, chemical equivalence basically means any two hydrogens. If, they have identical chemical environment, they they will end up with the same chemical shift value.

Now, having chemically equivalent is basically mean same chemical shift, but same chemical shift need not mean chemically equivalence. So, the reverse is not true which is written here, that two nuclei may have accidentally the same chemical shift value does they cannot

be considered as chemically equivalent because the above condition has to be satisfied . So, you see here there is a condition very important condition these two hydrogens should be in interconvertible in their positions by symmetry operations, which means I should

be able to take those two hydrogen is which are equivalent having the same chemical shift. And, if I change their replace one with other it should have the same symmetry in the atom in the molecules.

So, let us look at the the case here is shown here look at this molecule here it is basically has a rotational symmetry. So, you can look at these three hydrogens if I rotate it and this hydrogen comes here, this hydrogen goes here. It does not affect anything it remains

these three hydrogens are kind of chemically equivalence because they are all rotating and therefore, their positions are equivalent. Is it is equally distance from these three whether it is in this position or in this position or in this position . So, because

of this rotational symmetry it there because it has a rotation n fold symmetry axis these three hydrogens are equivalent. Similarly, we know the centre of symmetry here if this hydrogen is inverted is has a

inversion of symmetry. These two hydrogens have the same chemical environment. And, they are related by symmetry operation, they can be converted from here to here, here to here without any change in the structure of the molecule. Remember symmetry operation basically

means if you rotate or a take a reflection around any axis it should not change the structure. So, that is what is shown here these two hydrogens are chemically equivalent. Now, we can look at more examples. So, this is another case where there is an mirror is

an plane of symmetry not an axis of symmetry. So, if you look at this plane of symmetry these two hydrogens are mirror image. Therefore, they are identical they are equivalent. And therefore, that will not change whether I take this hydrogen here or here the structure

will not change. So, this is another example. So, we can keep having ah different examples. Ah. We will go to what is the most important is the methyl? So, methyl groups are known

to be always strong peaks in NMR spectrum. In fact, in biomolecules Methyl's play a very very important role ah and we will look at the methyl groups as we go along. Now, here these three hydrogens why are they equivalent there is no symmetry concept here,

they are equivalent basically because they are rotate very fast around this axis. So, you see this is the axis here they rotate very fast around it is axis and because of that rotation they become equivalent, because the average out in their environment, because

of this averaging they are essentially equivalent in the chemical shift. So, Methyl groups always you will see in NMR spectrum are are essentially a group together. So, they will be three times stronger or even more compared to any other protons in the spectrum and they are very

easy to identify. Ah. Chemical Magnet the second concept which is very important in NMR is the magnetically equivalence. So, we saw just now chemical equivalence. Let us look at a example here.

So, if you see here this X which is the hydrogen this is some functional group, this can be another functional group, if we look at these two hydrogens there there is a symmetry here. If I draw a line here I just shown by this mouse there is a axis of symmetry.

So, you may say that this hydrogen is equivalent to this hydrogen and this hydrogen is equivalent to that hydrogen which is fine. So, they are chemically equivalent, but if you look at this hydrogen it is coupling to this HB here is not the same as it is coupling to this

HB here . So, you see this is very far away this is 1 bond, 2 bond, 3 bond, 4 bond away whereas, this is 3 bond away, 5 bond away in fact. So, you see this this two hydrogens are coupled J-coupled we will reach will come too shortly,

their coupling is not the same as that J-coupling between this hydrogen is the same. So, therefore, although these two hydrogens are chemically equivalent they are not magnetically equivalent, because they are coupling to the neighbouring hydrogens is not the same.

So, for example, the coupling of HA to HB is different from this HA to this HB. So, although A and A are same they are A A prime. So, this is the nomenclature typically used for denoting spin systems, ah which will not going to detail, but the idea is they are

chemically equivalent. So, chemical shift will be same, but magnetically they are not equivalent . So, that does not affect much ah in the spectrum ah. So, we will not go into detail of magnetic

equivalence, but what affects the most is a J-coupling. So, which is shown here. The J-coupling essentially see if you look at any NMR spectrum, you will never see a single peak you will always a multiple structures like this. And, that is, happens because of

this phenomenon called J-coupling or scalar coupling. J-coupling has a very rich history ah and how it was this code is very interesting. Ah. We you can have a look at it in an different ah textbooks how it was actually discovered

and found out. So, we use different words for J-coupling sometimes in textbooks you will also use we use the spin-spin interaction, you will see the word scalar coupling and so on. So, J-coupling essentially happens only when there is a covalent bond between

two hydrogens. So, that is why we use the word through bond interaction. So, let us go through J-coupling ah briefly how does J-coupling affect the spectrum? So, this is shown here as an example. So, we let us say you have a spin system or a

molecule like this. So, you have a 2 this carbon has 2 equivalent hydrogen. So, let us considered as chemically equivalent and this is not this is one hydrogen we are looking at. So, in the NMR spectrum this hydrogen will be coupled to this hydrogen and this

hydrogen . But, because these 2 are equal ah equivalent this hydrogen we will look at them as 2 equal hydrogens. So, it is number of peaks for this hydrogen we will follow a rule known as n

plus 1 rule. Therefore, and is the number of chemically equivalent hydrogen to which this yellow colour is coupled. So, it will now show as a triplet ok. So, the triplet meaning 3 lines, now the intensity of the 3 lines are not the same , but we will

see that soon is using concept called Pascal's triangle. Now, let us look at these 2 hydrogens. So, we looked at this yellow colour here now in the same molecule let us say what happens so, these 2. So, these are chemically equivalent

as we assume, the remember you not be equal equivalent. In fact, in biomolecules molecules like these sorry moieties like this are never equivalent. So, we will see that when we come to the biomolecule part, but let us assume that right now a some molecule they are equivalent.

In that scenario these 2 are together as 1 entity. Now, this one entity is couple to another one hydrogen. So, according to the n plus 1 n is equal to 1, because these 2 together are couple to only 1 more and that is a doublet.

So, these 2 peaks these 2 meaning 1 peak for these 2 hydrogens we will show up as a doublet and the peak for this hydrogen we will show up as a triplet in the NMR spectrum. So, this is what is called as the n plus 1 rule ah where only aplies when there is an equivalent

hydrogens ok. So, we can actually see here more examples. Now, what happens if the coupling between let us say we have 2 protons. So, this is the all protons here. So, this is this is

1 hydrogen A this is another hydrogen B remember this is a just a schematic drawing do not think of it as a bond here. It is actually a CH let us say and is there is another CH here, another CH here ok.

So, this CH hydrogen in centre is coupled to 2 protons so, 1 proton this side and 1 hydrogen this side. Now, these 2 hydrogens B and C let us say are having completely different environment. So, they will be having different coupling to this hydrogen here. So, which

is written as J1 and J2. So, if J1 is equal to J2 then it will be a chemical equivalent case and it will become a triplet, but if it is not same then what does this how does this spectrum look? So,

that is how it is analysed here. We can take a particular peak here, that is without any coupling. So, let us say that C and B did not exist, if C and B did not exist A would have no coupling and it will only have a single peak. But, now it is coupled to this 2 hydrogen

1 on this side 1 on that side and with different coupling values. So, in such a scenario this peak first we will get split into 2 peaks and it will shown as J1 here, because of the J coupling that is shown here, it gets shown split into 2

and each 1 of them is having a half the intensity as previous. So, remember J-coupling simply splits the peak into 50 50. So, 1 peak is half another peak is half of this original peak. So, it is 1 is to 1 .

But, then there is another coupling J2 and that further splits each of this peaks into further 2. So, we can see here now it has become 2 separate peaks. So, first it is split into this dotted line here, and that each peak which was here further split it into

2 more. So, you will get what is called as a doublet of a doublet. This is not simply a triplet, a triplet would have come if they were all equal values J1 was equal to J2, but because now the J1 and J2 are not the same they become a doublet of a doublet. So,

this is the scenario if the couplings are not equal ah this is what happens. So, now the J-coupling value between 2 hydrogens depends on varieties of factors, ah which is listed here this is similar to chemical shift values. So, we can see that it depends

on the gyromagnetic ratio not ration, is ratio of the 2 nuclei. So, if there is a hydrogen and carbon the coupling will be different compared to hydrogen and hydrogen ah and hydrogen nitrogen will be different and nitrogen carbon will be different and so on.

Similarly, it depends on how many bonds are separate remember this is a through bond interaction, which means it depends on number of bonds separating them if they are separated by more than 3 bonds to hydrogen then the coupling is very small. If, they are separated by 1

bond of course, hydrogen hydrogen 1 bond cannot come it will becomes hydrogen molecule, but you can have hydrogen carbon 1 bond, then it is a very strong coupling . And, if you have carbon nitrogen 1 bond it is also good, but if you have carbon carbon 2 bonds away

then it is very weak. It depends on the structure of the molecule which is also we use a word confirmation and very useful this. So, these are these parameters are very very important in biomolecules. So, one should

remember these things, because this is how it will affect our sensitivity or the pattern what we will see in in heteronuclear NMR then in bio molecules and depends on the hybridization state. For example, in aromatic the hybridisation sp2 whereas, in aliphatic in Methyl's it is

sp3. And therefore, it depends on what is hybridization state the chemical shift coupling sorry coupling spin-spin coupling will also change. If you look at the substituents again it matters.

So, if there is a functional group oh compared to attach to see versus some other functional group, ah then the chemical shift the coupling of carbon 2 protons will change. So, you see there are varieties of parameters which affect the chemical shift and coupling

values ah say coupling here is shown for different types of combinations. As far as our biomolecular course is concerned or this course is concerned, we are mainly interested in hydrogen to hydrogen. Ah. Of course, this is a hydrogen molecule not in ah 3 bond hydrogen, you can see the

hydrogen, hydrogen direct coupling is very strong we will not bother about this this is just a a highest value possible. But, if you can hydrogen to carbon this is exact this is the range which we will be using

in our in our bimolecular experiments and we exploit this high coupling. If, you look at phosphorus which is in nuclic acids, that is also very strong if you look at carbon to carbon double bond, it is also strong carbon to carbon single bond, is also quite good

this is useful in biomolecules. And, bimolecular NMR all these couplings are very useful and exploited ah in designing ah various experiments. Ah. We would not look at fluorine in this course fluorine is not present in biomolecules. Ah.

Fluorine is present in in different ah ah chemical molecules which is not part of this course. And finally, in the one thing is the how does that J-coupling depends on the confirmation.

So, this is the very famous equation known as the Karplus equation, this says that a coupling between 2 hydrogen which are 3 bonds away. So, look at this picture here they are actually 3 bonds away. So, if you draw this molecule you can show like a book like a 2

planes here. So, 1 plane representing 1 hydrogen 1 carbon this carbon and the second plane representing this hydrogen, this carbon, and this carbon. So, you see now the the angle between the

2 plane is known as this torsion angle, a very very important parameter when it comes to biomolecular structure. So, the torsion angle or also used the word dihedral angle. Now is basically this angle and and this coupling between these 2 hydrogens depends on this

angle by this equation. The very famous Karplus equation way back in 60’s was proposed and it has this form we can see this has a form like this is a cosine function cosine square plus cosine.

So, you can see if I know the J value I can guess the phi value from this. Of course, it has multiple possibilities, but still I can narrow down what are the possibilities? Similarly, if I know the dihedral angle value from there this plot suppose I know it somewhere

like 140 degrees, if I go up here I can get the actually the chemical shift sorry the J-coupling of those 2 hydrogen. So, you say interrelation or a connection between J-coupling and the dihedral angle, which is very very very useful in biomolecules ah it is worth

repeating that ah as we go along we will see the alpha helical structure the beta sheet all depend on this J value which is useful. So, we will in the next class we will look at the final aspects of 1 D NMR, ah which

is C 13 NMR ah and look at a brief very few practical aspects and then we will go on to 2 D NMR.