preparation mix evolution detection - uw–madisoncic/nmr/guides/other/c636f14/fall2014c636/... ·...

Two-Dimensional NMR: General Scheme

t2t1

Copyright © 2005 Charles G. Fry. All Rights Reserved. Pg. 1

There are four sections in all 2D experiments:

preparation mixevolution detection

aqd0

For homonuclear COSY (the simplest example), this reduces to:

d1

p1p0

updated: 28Oct2014(cgf)

Two-Dimensional NMR: General Scheme

t2t1

Pg. 1

There are four sections in all 2D experiments:

preparation mixevolution detection

aqd0d1p1p0

t1

d0 aq

t2

t1

F2

t to F in 2D NMR2 2

Pg. 2

t = d0 + n/sw11

t1

I(t )1

F2

t1

FT(t )1

..

..

.

F1

F2

a

a

b

b

t to F in 2D NMR1 1

Pg. 3

Fourier Transforms in 2D Spectroscopy (topspin)

t1

{aq1,td1,1/sw1}

t2 {aq, td, 1/sw}

t1

F2

F2

t 1

F2

F1

xf2

rser #

xf1

xfb

Pg. 4

transpose

(n/a - rsc #)

Resolution in 1D Spectroscopy

Pg. 5

DW=1/SW

AQ

T2

Resolution in 1d NMR is usually determined by the acquisition time(but limited by shim quality and relaxation time):

1d (true) resolution ~ 1/aq

Resolution depends on an abilityto differentiate two very similartime-varing signals.


Pg. 5

DW=1/SW

obtainableresolution

= 1/AQ

AQ

T2

FFT



The Fourier transform providesa simpler representation of thedata for humans to “see” thedifference.


Pg. 5

DW=1/SW

obtainableresolution

= 1/AQ

AQ

T2

FFT

obtainablelinewidth=1/ T� 2

��



The fundamentallimitation of naturallinewidth remains.

Resolution in 2D Correlation Spectroscopy

2D NMR works identically, but limitations ondata set sizes (td and td1) make the digitalresolution a key factor. It may appear that:

dig. res. F2 ~ sw/(td/2) =

but the 1st full zerofill does assist. Zerofilling istypically not done in (F2), however, so the

equation above is (with no zerofill) correct.

t2


1/aq dresF2�

Pg. 6

= sw/td

SW (Hz)

digitalresolution

in Hz/pt


A minimum of one zerofill is always performedin (F1), however:

dig. res. F1 ~ sw1/(2 td1/2) =

1/(2 at1)

t1

�

� � dresF1 =sw1td1

Pg. 7

= 2 SW1/td1�

=SW1td1

SW1(Hz)

digitalresolution

in Hz/pt

withone

zerofill

A minimum of one zerofill is always performedin (F1), however:

dig. res. F1 ~ sw1/(2 td1/2) =

1/(2 aq1)

Typical values for 1H cosy:

sw = sw1 = 8ppmtd1 ~ 256@300MHz; td1 ~ 512@500MHz

dresF1 ~ 9 Hz/pt

t1

�

� � dresF1 =sw1td1


Pg. 8

H1 13C

4800 Hz 16000Hz400pts 400pts

= 12 Hz/pt = 40Hz/pt

4800 Hz2048 pts

~ 2 Hz/pt

F1

F2

Evolution n is Crucial in 2DCorrelation Spectroscopy

, ot Resolution,

Although we are using J-couplings in acorrelation (cosy) 2D experiment, we do notneed to the coupling.resolve

Pg. 9

F2 (ppm)

1.21.62.02.42.83.23.6

F1

(ppm)

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

F2 (ppm)

1.21.62.02.42.83.23.6

F1

(ppm)

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

F2 (ppm)

1.96

F1

(ppm)

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F2 (ppm)

1.96

F1

(ppm)

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6a 5a�

I I + I Sy y x z Iy + I S + Sz x y Although we are using J-couplings in acorrelation (cosy) 2D experiment, we do notneed to the coupling.

The experiment instead must thecoupling during , and thus produce a

: , and

t1

The J-coupling evolution creates an antiphasespin state :

= +

resolve

evolve

crosspeak .I during (F1)t1

I ( ) I cos( J )y yt t1 1�

S in (F2)t2

I S

I S sin( J )

x z

x z � t1

Pg. 10

t1

t2


, ot Resolution,

Pg. 11

F2 (ppm)

2.02.53.03.54.04.55.05.5

F2 (ppm)

2.02.53.03.54.04.55.05.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5diagonal crosspeak

5.7ppm proton in

5.7ppm proton in

t

t1

2 or 3.0ppm proton in t2

I( )I( )t t1 2I( )S( )t t1 2


, ot Resolution,

start withI proton,

evolveto S

Pg. 12

F2 (ppm)

2.02.53.03.54.04.55.05.5

F2 (ppm)

2.02.53.03.54.04.55.05.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

3.0ppm proton in

3.0ppm proton in

t

t1

2 or 5.7ppm proton in t2

S( )S( )t t1 2S( )I( )t t1 2


, ot Resolution,

start withS proton,

evolveto I


= +

The trignometric terms are multipliers to theintensity of and inthe 2d spectrum. The closer gets to ,

the larger the will become.

I S

I S sin( J )

x z

x z � t1

crosspeaks

crosspeaks

I ( ) I cos( J )y yt t1 1�

diagonal peakst1 1/2J

Pg. 13

F2 (ppm)

2.02.53.03.54.04.55.05.5

F2 (ppm)

2.02.53.03.54.04.55.05.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5diagonal crosspeak


, ot Resolution,


= +

It is not necessary to achieve full antiphasecreation with , but only that the

evolution be sufficiently long to produceobservable crosspeak intensity (i.e., crosspeaksunambiguously bigger than the noise).

I S

I S sin( J )

sin( J ) « 1

x z

x z �

�

t

t

1

1

I ( ) I cos( J )y yt t1 1�

t1=1/2J t1

� is OK.

Pg. 14

F2 (ppm)

2.02.53.03.54.04.55.05.5

F2 (ppm)

2.02.53.03.54.04.55.05.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.511

6a

Are these realcrosspeaks,or artifacts?


, ot Resolution,


It is not necessary to achieve full antiphasecreation with , but only that the

evolution be sufficiently long to produceobservable crosspeak intensity (i.e., crosspeaksunambiguously bigger than the noise).

sinebell

= +

Crosspeaks willalways be observed (on any properlyfunctioning, high-field spectrometer) when:

in proton-proton COSYs, and within

because of the apodization.

I S

I S sin( J )

sin( J ) « 1

x z

x z �

�

t

t

1

1

sin( J ) 0.25� t1

I ( ) I cos( J )y yt t1 1�

t t1 1=1/2J

But how much < 1 is OK?

� is OK.

t1 = aq1/2

Pg. 14

F2 (ppm)

2.02.53.03.54.04.55.05.5

F2 (ppm)

2.02.53.03.54.04.55.05.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5

F1

(ppm)

2.5

3.0

3.5

4.0

4.5

5.0

5.5


, ot Resolution,

t1

t2

Size of J-Couplings Observed in 1H COSY

From the considerations stated on the previouspage, we can arrive at an important empiricallyverified rule-of-thumb for 1H cosy. Start with:

make some substitutions:

= sin( J at1/2) = sin( J td1/4sw1)

and now solve for J:

J4 sw1

td1arcsin(0.25) ~

sw13 td1

Thus crosspeaks will be observed when:

��

��

�>

�

sin( J ) > 0.25

sin( J )

�

�

t

t

1

1

J > sw13 td1

=1

6 aq1observed � �

Copyright © 2005 Charles G. Fry. All Rights Reserved. Pg. 15

~

~

~

Better quality data (reduced artifacts,superior sequence, more ns) will allow less-intense crosspeaks to be observed (e.g.,

those 10%), increasing the factor of 6 toperhaps 15). Smaller J’s can then beobserved for the same and .

td1 sw1

at1at

Summary of Evolution for 2D NMR Experiments

For 1H COSY:

Typical: J 3 Hz sw1/(6 td1)

Increasing decreases J .

Increasing the evolution time decreases J (long-range COSY).

Fix delays to 1 2 J , so only chem shift (digital) resolution is an issue.

is set experiment time and signal-to-noise.

Delays become long, so experiment is modified from HSQC.

Still fixed delays at approx 1 2 J , so is a compromise between exp. time and s/n.

obs

obs

obs

� �

td1

td1

td1

t1

/

/

1

CH

CH

as a compromise between

n

For heteronuclear 1-bond cosy, HSQC:

For heteronuclear n-bond cosy, gHMBC:

Pg. 16

t1

d0, td1 aq, td

t2

S/N, and : Time of 2D Experimentsns td1

The S/N improves for peaks duringthe complete 2D experiment.

all

T2 (linewidth) can restrict from this

important use of instrument time. Forlarge MW (small T ns

td1

2), increasing is

usually best. For small MW, increasingis most often best, as this improves

both S/N and resolution.

Pg. 17

1D: S / N

2D: S / N ( )

Time 1D: ( + 1)

Time 2D: ( + 1 +2 1

)

��

��

�

��

ns

td1 ns

aq d ns

aq dtd1

swtd1 ns

�

� �

Can increase or to improve S/N.td1 ns

preparation mix evolution detection - uw–madisoncic/nmr/guides/other/c636f14/fall2014c636/... ·...

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