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NMR Spectroscopy: Principles and Applications

Nagarajan Murali

1D - Methods

Lecture 5

1D-NMR

To fully appreciate the workings of 1D NMR experiments we need to at least consider two coupled spins. Sometimes we need to go up to three coupled spins, particularly when we look at hetero nuclear spins such as Carbon-13 isotope. We will start from the simple one pulse NMR experiment in terms of the product operator approach and discuss various aspects of the pulse sequences.

HamiltonianTwo Spins I=1/2 and J Coupling

Let us use the two spin Hamiltonian in which each spin with spin I=1/2 and J Coupling between them.

We can also write the equation with notation I and S for the two spins as

In subsequent discussions we will drop the hat from the operators and represent them as normal face italic character for convenience.

1202012112202101 case for the Hzin JJ zzzz IIIIH

s rad and frame rotatingin 2 1-2 zzzz SISIH

ISSI J

s rad and frame rotatingin 2 1-21122211 zzzz IIIIH

J

Pulse Calibration

1 2

bx

t

zz SI bbbb sincossincos yzyz SSII bo

x

Simple 1D

1 2 3

90x

tI S

J

1

2

3

zz SI

90x

yy SI

)sin()cos(

)sin()cos(

tStS

tItI

SxSy

IxIy

tSI zSzI )(

tSIJ zzIS )2()sin()sin(2)cos()sin(

)sin()cos(2)cos()cos(

)sin()sin(2)cos()sin(

)sin()cos(2)cos()cos(

tJtIStJtS

tJtIStJtS

tJtSItJtI

tJtSItJtI

ISSzyISSx

ISSzxISSy

ISIzyISIx

ISIzxISIy

Simple 1D

1 2 3

90x

tI S

J

1

2

zz SI

90x

yy SI

As we know the physical properties of the operators we could have directly predicted the NMR spectrum from point 2 in the sequence. The operators at point 2 are in-phase y magnetization of spins I and S and thus the spectrum should be a in-phase doublet with splitting J at frequencies I and S. Also it is enough to follow one spin through the pulse sequence.

Optimum Pulse Flip Angle

It is not optimum to use /2 flip angle for the pulse as the experiment is repeated several times for signal averaging and then one should wait more than 5 times the longitudinal relaxation time to build up the equilibrium magnetization.

tr tr


If we assume that the transverse magnetization is completely decayed by the time the next signal averaging pulse is applied, we can calculate the steady state z-magnetization and the corresponding transverse magnetization can be calculated.

Mz(0-) Mz(0-) Mz(0-)

tr tr


The detected signal can be deduced to be

And the signal intensity as relative S/N plotted for various (tr / T 1) as a function of the flip angle is given below.

b

b

sin

cosexp1

exp1

)0(

1

10

T

t

T

t

MMr

r

x


The maximum signal is not at b=/2, the optimum flip angle, known as Ernst angle, b is given by

For shorter recycle time bopt decreases. For tr~T1, bopt ~ 68o .

)/exp(cos 1Ttropt b

Optimum Recycle Delay

The optimum recycle delay for a pulse angle of b=/2 can also be plotted as a function of the ratio of tr/T1

And the delay tr ~ 1.3 T1 is optimum.

1D with Decoupling

The one pulse experiment gives a doublet for each spins when there is a J-coupling between them. Spin 1 multipletfrequencies depend on the state of spin 2 in a or b state. If selective RF irradiation (applied during detection) rapidly changes mixes the a and b state of spin 2 the spin multipletwill collapse and this process is called decoupling.

1D with Decoupling

1H – spectra with decoupling (homonuclear decoupling).

1D with Decoupling

Decoupling is particularly useful in recording 13C spectrum.

1D with Decoupling

There are variants of the basic experiment to enhance the 13C spectrum.

Spin Lock

90x SLy

zI yI yI

yI1

16

During the delay t the Iy coherence of the spins do not evolve and is locked along the y-axis along which the RF is applied. This process called spin locking.

Spin Echo90x

180y

At the end of 2 period chemical shift evolution is refocused.

zI90x

yI )sin()cos( IxIy II

zI I

)sin()cos( IxIy II 180y

yI

))(sin)((cos)sin()sin()cos()sin(

)sin()cos()cos()cos(22

IIy

IIyIIx

IIxIIyI

II

II

zI I

Spin Echo –J Modulation

90x

180y

At the end of 2 period the anti-phase coherence is generated.

SI

J

t

)2sin(2)2cos( ISzxISy JSIJI yI zzIS SIJ 2)2(

:4

1

J zxSI2

)sin()sin()cos()sin(2

)sin()cos()cos()cos(2

JttIJttSI

JttIJttSI

IxIzy

IyIzx

FID

Using the knowledge that shift evolution is refocused, the J evolution can be calculated.

Spin Echo –J Modulation –Spectrum Editing

The dependence of echo on J coupling can be used to edit carbon spectrum to identify C, CH, CH2, CH3 type carbons.

)sin(2)cos( ISzxISy JISJS yS zzIS SIJ 2)( CH:

ISzxy JISS with sin2cos

CH2:

zzIS SKJ 2)(

cossin4cossin2cossin2cos 22zzyzxzxy KISISKSS

CH3:zzIS SLJ 2)(

....cossin2cos3 zxy LSS


The functional dependence can be used to identify the protonation of carbon. For =, C and CH2 amplitudes are opposite of CH and CH3 carbons.

33

22

cos:

cos:

cos:

1:

CH

CH

CH

C

o180or

1cos :1

ISIS

JJ


Each multiplet in the carbon spectrum of the spin system may be represented by a vector, then the evolution can be pictorially represented.

APT-Attached Proton Test

The APT experiment uses the functional dependence of and edits the carbon spectrum (a) Normal carbon 1D, (b) edited spectrum with =, and (c) = /2 only the quaternary carbon is selected. The first carbon pulse is not a /2 pulse to optimize S/N with fast repetition times.

Polarization Transfer

There is a class of experiments that are called polarization transfer experiments and they transfer magnetization of abundant high g nuclei magnetization to low abundant low gnuclei – such as proton to carbon. One such type of experiment is called INEPT (Insensitive Nuclear Enhancement by Polarization Transfer).

INEPT

)sin(2)cos( ISzxIISyI JSIJI ggyI Ig zzISxx SIJSI 2)(,,

yy SI2

,2

)sin(2)cos( ISxzIISyI JSIJI gg

+y -y b-a

IS

ISs2J

1 with Jsincos)sin(2 ttSJSI yI

FIDISxzI gg

If I=1H and S=13C then gI/gS=4, we have 4 times more signal than normal 1D.

INEPTOne can also illustrate the evolution pictorially.

Refocused INEPTThe INEPT sequence can be extended to give in-phase multiplet so

that decoupling can be performed. Such a pulse sequence is called refocused INEPT.

g

g

sincos22

with

sincos22

2

2

222

2

2

yxzSIJ

xzI

IS

ISyISxzSIJ

xzI

SSISI

J

JSJSISI

zzIS

zzIS

Editing with Refocused INEPTThe refocused INEPT can also be used to edit carbon spectrum as

we did with APT experiment.

23

2

2

cossin3:

cossin2:

sin:

with

CH

CH

CH

J

Editing with DEPTTo Edit using the refocused INEPT one has to vary the delay to get

the desired . Instead, we modify the pulse sequence to achieve the same effect. The flip angle of 1H pulse is varied to achieve the same result.

232 cossin3:;cossin2:;sin: CHCHCH

Editing with DEPTA suitable linear combination of the four spectra on the left yields

the edited spectra on the right.

DEPT-45o

DEPT-90o

DEPT-90o

DEPT-135o

0.707CH + 1.0CH2 + 1.061 CH3

0.707CH + 1.0CH2 + 1.061 CH3

CH

APT vs DEPT

In APT experiment quaternary carbon is also seen whereas in the DEPT only carbons attached to protons are seen. DEPT allows separation of carbons, thus aiding unambiguous identification.

APT with =135o CH and CH3 are down; C and CH2 are up. DEPT

X-Nucleus PW Calibration

J2

1

90x

180y

bx

zx

ISzxISy

SI

JSIJI

2

)sin(2)cos(

yI

zzIS SIJ 2)(

yx IS b

bb sin2cos2 yxzx SISI

zzIS SIJ 2)(

bb sin2cos yxy SII

b=0 the signal is maximum.b =900 there is no signal as the multiple quantum coherence is unobservable.

Coherence Transfer

)sin(2)cos( ISzxIISyI JSIJI ggyI Ig zzISxx SIJSI 2)(,,

yy SI2

,2

)sin(2)cos( ISxzIISyI JSIJI gg

The conversion of 2IxSz to 2IzSx is an important aspect of pulsed NMR and is known as the coherence transfer step. Coherence transfer is extensively used to obtain coupling net work information in multi dimensional NMR.

Coherence Transfer – Selective Correlation Experiment

Let us consider two protons coupled to each other and in the experiment (a) we apply a selective 90o x-pulse on spin 1 and after a delay apply a non selective 90o pulse along y that rotates both protons. In (b) we do the same but the selective pulse on spin 1 is applied along -x. Also say that we are on resonance to spin 1 i.e. 1=0.


1221121 sin2cos)()( JIIJIab xzy

xxzy

yy

zzxy

zz

zy

x

zz

IJIIJI

II

IJIIJI

IIJ

II

I

II

21221121

21

21221121

2112

21

1

21

sin2cos

2

sin2cos

2

2

xxzy

yy

zzxy

zz

zy

x

zz

IJIIJI

II

IJIIJI

IIJ

II

I

II

21221121

21

21221121

2112

21

1

21

sin2cos

2

sin2cos

2

2

01 01


1221121 sin2cos)()()( JIIJIabc xyzy

xxzy IJIIJI 21221121 sin2cos xxzy IJIIJI 21221121 sin2cos

01 01

An uncoupled third spin

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