~

-.-,

~

~

~

;

Chapters in 'Modem NMR Techniques for Chernistry Research' by A. E. Derorne :

.Chapter 5 for the noe effect

.Chapter. 6.1 -6.3 for the SPI and INEPT techniques

~

Other books related to the topics described in this lecture :

.'Nuclear Magnetic Resonance Spectroscopy. A physicochemical View' by R. K. Harris :

Chapter 4

.'The Nuclear Overhauser Effect In Structural And Confonnational Analysis' by D. Neuhaus and

M. Williamson:

Chapters 1 and 2

~

r-

~~~~~~~~~~~

Apri116, 1999, 15:37Lectures 10 & II

Enhancement of sensitivity for X nuclei

Introduction1)

2) The nuclear Overhause effect (nOe )

21)

22)

23)

24)

25)

26)

27)

28)

Definition

Qualitative descriptionThe Solomon equations

Dependence of noe on molecular motion

The nOe in idealistic system

The nOe in realistic system

Homonuclear nOe measurements

Heteronuclear nOe measurementsr

3) Polarization transfer

31)

32)

33)

34)

Selective population transfer

The INEPT experiment

Refocused INEPT

Characteristics of polarisation transfer experiment

4) Inverse detection

41)

42)

43)

What is inverse detection ?

AdvantagesThe reverse INEPT

r'-

~

Page 1/17

Apri116, 1999, 15:37 PI) Introduction

For X nuclei (13C, 15N ...), it is difficult to obtain a good spectrum because of the low natural abundance and

the reduced sensitivity

Isotope Natural Spin I

abundance

.yaFrequency

(MHz)

Relative

sensitivityb

1H

2H

13C

99.98

0.016

1.108

99.63

0.37

100.00

100.00

1!2

1

1!1

100.00

15.35

25.19

7.22

10.13

94.08

40.48

26.75

4.11

6.73

I

0.01

0.016

1.0x 10-3

1.0xI0-3

14N15N

1

1/21.93

-2.71

25.18

10.84

1%

31p

1/2

1/2

0.83

0.07r-"'

a: rad.G-l.s-lb: At constant field

r

How can we increase the sensitivity of an X nucleus ?

-By using the nOe effect

-By polarization Transfer

-Inverse detection (lH detection)

2) The nOe effect

21) Definition

-Manifestation of the attempt of the total system to stay at them1al equilibrium

-Change in the intensity of an NMR resonance when the transitions of another one are saturated

-Does not depends on scalar coupling

r-- Depends on relaxation through di polar coupling

-The noe enhancement 11I(S) is detined as the fractional change in the intensity of I on saturating S:

11I(S) = ~ (1)

f', lo: equilibrium intensity of I

22) Qualitative description

A t wo spin system I and S

-At thermal equilibriumBolzmann distribution (Fig. 1 )

Page 2 / 17

Apri116, 1999, 15:37

Energy levels and population of a AX system

-Nae experiment: saturatian af bath transitians af S (Fig. 2)

~~ N-8/2

saturated?"'a~ N-8/2

~

13a N+O/2

~ Saturated

N+o/2"' aa

Populations after saturation of the S transitions

r

r"

N+8/2

0.0. N + o / 2

Cross-relaxatjon after saturation of S transitions

23) The SOLOMON equations

The intensity of I and S is proportional to Iz and Sz

Iz and Sz are proportional to the population differences between the states

klz = N(X(X -N(X~ + N~(X -N~~ (2)

Page 3/17

April 16, 1999,15:37kSz = Na.a. -N~a. + Na.~ -N~~ (3)

The rate of change of Iz with time is:

~-~-~ ~k dt -dt dt + dt ~-dt (4)

The ways in which population can arrive at and leave from the aa state gives (Fig. 3):

~ = -(WlI + WlS + w v No-a + WlI No-~ + WlS N~o-+ W2 N~~ + constant(5)

(6)

At thermal equilibrium, ~ = O with Ni(O) = equilibrium population

(Wl1 + WlS + W2) Naa(O) -Wl1 Naf3(O) -WlS Nf3a(O) -W2 Nf3f3(O) = constant

r'Tbe population differences from equilibrium can be written (Ni -Ni(O)) = ni. Therefore:

~ =-(WlI+WlS+W2) naa+WlInap+WlSnpa+W2npp (7)

dIzand calculate dt

r , ~~ ~

.:;ind the similar expressions for dt ' dt ' and dt :

~ = -(WII + W1S + W2) n(X(X + WII n(X~ + W1S n~(X+ W2 n~~

+ (WII+ W1S + WO) no;~ -WII n(X(X -W1S n~~ -Wo n~(X

-(WII+ W1S + WO) n~(X + WII n~~ + W1S n(X(X + Won(X~

+ (WII + W1S + W2) n~~ -WIln~(X -W1S n(X~ -W2 n(X(X (8)

(9)

(10)

Combination of (2) and (3) gives: 2 (N~~ -Naa) = -k (Iz + Sz) and 2 (Na~ -N~a) = -k (Iz -Sz)

JS weIl as: 2 (n~~ -naa) = -k (Iz -Iz(O) + Sz -Sz(O)) and 2 (na~ -n~a) = -k (Iz -Iz(O) -Sz + Sz(O))

Substitution of (10) into (9) gives:~ dIz I

dt = -(Iz -Iz(O) + Sz -Sz(O» (Wl + W2) -(Iz -Iz(O) -Sz + Sz(O» (WII + WO)

which gives the Solomon equation:dlz Idt = -(Iz -Iz(O» (WO + 2 Wl + W2) -(Sz -Sz(O» (W2- WO) (11)

At steady state, dlz / dt = O and Sz = O, giving: D= -(Iz- Iz(D» (WO + 2Wl1 + W2) + Sz(D) (W2 -WO)

W2 -Wo

Wo + 2 W 11 + W2Thus, Iz -Iz(O) / Sz(O) = (12)

"f'S

yl

since Sz(O) =

Page 4 / 17

April 16, 1999,W2 .Wo

(13)(l -10) -~TlI(S) = 10 -11 Wo + 2 Wli + W2

(W2- WO)

April 16, 1999, 15:37 P-Wo fastest when the molecules tumbles at a rate of about 1kHz

W 1 fastest at a tumbling rate of = 400 MHz

W2 fastest at a tumbling rate of = 800 MHz

Small molecules in non viscous solvents tumble at a rate of around 1011 Hz, while large molecules tumble at

rates about 107 H z

w

positive nOe

negative nOe

no nOe

For small molecules, W 2 > Wo

For large molecule, WO> W 2

Intermediate size molecules, W 2 = Wo

242) Quantitative considerations

-10 -9 -8log '.c

FICURE 2-5

Varia:ion 01 dipolar transiljon probabilities \'1,- W,- and ~.I. withr.- sho'Nn for spectrome:cr frequencies of ICO and 270 ~.IHz.

Calculated ror a pair or protons I Å apart.

-Extreme narrowing limit

'tc very short, ro 'tc « 1: .Small molecules in non viscous solvents

2 'tc 3 'tcWo & (19); Wl & c (20);W2&~

r6(21)7 r6

25) The nOe in idealistic system

(22)

(23)

1l1(S) = ~ ~

yl PIS

and

-For a homonuclear IS system

5 + 0)2 'tc2 -40)4 'tC4«(1)1 -(l)S) 'tc « 1 (S) = 10 + 23 (1)2 'tc2 + 40)4 'tc4 (24)yl = yS, roI -= ros

Page 6 / 17

)J.le can now write the noe enhancement in term of molecular tumble rate

April 16, 1999, 15:37

-In extreme narrowing conditions ro 'tc « 1"'

-For large molecules (proteins, nucleic acids) W} ==W} ==O

I111(8) = 2

111(8) '= -I

"-For a heteronuclear IS system

T11(S) = ~

2 yl

In extreme narrowing conditions ro 'tc « I

Examples

13C{1H}1) 13C (I) signal up on saturation of lH (S) resonance

~ = 4 noemax13C (lH) = 2

')IC

~) 1) 1SN { 1H}ISN (I) signal upon saturation of lH (S) resonance

:r!:!. ~ -9.87 noemax13C (lH) ~ -4.94 negative noe enhancement

'YN

r-"\-When ro 'tc increases, "I(S) decreases and can become negative

5'tc = { } 1/2«(J)I + (J)S)2 -6 «(J)I -(J)S)2

The zero crossing is then given by

7 maj 1996, 19.45

(j;s

-~,,1(S) -(PIS + P*)PIS = 2 O'IS

1 2p*-=2+-

1lI(S) PIS

~ & ~r6

11I(S) 'tc": I. ...I. ...I. ...I. ...I. ...La -

~

s. -

NOE

%4a -

~'\'

»-

)a -' ,I. -

1-

-la I. ...I. ...I. ...I. ...I. -J.I -2.S -U -I.S -1.1 -I.S I..

IOgCIlTc

Fig. 7: Reduction of steady state noe due to leakagc as a function of (J)'tc, with different

intemuclear distance rIS. P* is constant at 0.1 s-I.

r---

I. ..'. I. ...I. ...I. ...

a r. 2.0

(" 53 - 53 -

I. ...I I. ...I. ...

b r = 4.0

...

NOE NOEX

1-

-sa -sa -

.la~ - -1~3 -

I. ...I. ...I. ...I. ...oJ -2 -I' I 2

I. ...I. ...I. ...I. ...-J -1 -I. I IOgWTc

Fig. 8: Reduction of steady state noe due to leakage as a function of rott, with different

values of P*. The dotted curves are for P* = O. The other curves are from top to bottom,

P* = 0.02, 0.05, 0.1, 0.2 and 0.5 s-l.

Page 9117

April 16, 1999, 15:37 F

10 WTc0.1

Fig. 6: Dependence of max. theoritical noe enhancement on rox 'tc for X { 1 H} experiments

26) The nOe in realistic system (External relaxation rate P* )

{\ W2-WO yS (}IS--

yl PIS

="y'S1lI(S) = ~ Wo + 2 w Il + W2

0"15 Cross relaxation rate between I and S

(JIS > O when noe > O W2 > Wo

(JIS < O when noe < O W2 < Wo

(j)'tc < 1

(j)'tc > 1

direct dipolar relaxation rate constant for relaxation of spin I by spin S.PIS

-In a realistic system, PIS is not the only relaxation mechanism P*

1: spin-rotation, c sa, quadrupolar relaxation etc

inteffi1olecular dipole-dipole relaxation by paramagnetic speciesP*

rhe noe enhancement becomes

P* reduce the noe enhancement

P* is independent of!IS since it refers to interaction of lother than that with spin S.

If fIS is reduced, bath alS and pIS increase

The cantributian af P* decreases and the nae increases taward its thearitical value

nOe depends on internuclear distance, hut only when there is external relaxation

-Effect of P* on the Steady state noe

Page 8/17

Apri116, 1999,15:37HomoDuclear Doe measuremeDts

Practical considerations

r--

~

-Detection of few percent of intensity changes

-Important

Sample preparation

Frequency stability

-Solvent

A void protonated solvents

Increase the rate of intermolecular dipole-dipole relaxation

Reduce the intramolecular enhancement (increase of p*)

Avoid solvents with broad deuterium lock signals

DMSO and Acetone -d6 strong and sharp lock signal good solvents for noe

CDCl3 weak lock signal no good for noe

D20 broad lock signal no good for noe

-SampleRemoval of all impurities that lead to spin-lattice relaxation

paramagnetic metal ions

molecular oxygen

The noe difference experiment

In theory Saturate one resonance and then compare the intensities of others with their

equilibrillm vallles.

Integration of resonances with and without a period of presaturation

~n practice Not accurate enollgh to detect small noe's

Noe difference method

(A)

n

(B)

Page 10/17

.

Apri116, 1999, 15:37"28) Heteronuclear noe measurements

Gated decoupling experiments

13C-NMR spectra decoupled with noe

13C

lH ON I Decoupling I

OFF-

r". 13C-NMR spectra deccupled withcut nce

f"

13C

ON n n

OFFlH

-13C-NMR spectra coupled with noe

13C

f"

Ul~

r--l I

lH

OFF{\

Decoupler

PD AcqSpectrum

OFF

ON

OFF

ON

OFF

OFF

ON

ON

Coupled, no noe

Coupled, with noe

Decoupled, no noe

Decoupled, with noe

Page II/ 17

~

April 16, 1999, 17:12 I

Polarisation transfer3)

Selective population transfer (SPI)31)

~~

.7 n = -L\H -L\C = -5L\ap

n = -L\H + L\C = -3L\

H2

H1f:'

r-

f3a

~H-[\C=+3[\

n = [\H + [\C = + 5[\

L\H = 4 L\C AC=A'YH ::z 4 'Yc

C2 transition = Cl transition = 2A13C population

~~

~

n = + 5L\

n=-5L\r-'

H2~

HI inverted

Cl transition = --611

C2 transition = + 1011

13C population

Gain in intensity by -3, +5 compared to normal spectrum

.!!!!:-~ 3A

n = -3A

.

Apri116, 1999, 17:14 p.32) The INEPT experiment

(Insensitive Nuclei Enhanced by Polarisation Transfer)

90° 180. 90°x x y

ntntn-lH

"' x

,., a z

~~r.

/x'

c d fe

fl('

/<

uC,"~

/

"y' r.-

>'1:.x'

,Hr, -

H,~

,-, 1'1lf. " ,1,"l(.X x Ii

-r

g9'

z

hz

l

/

'LH(HO

.~r

11 H, / tt H,

C / 'C ,~- .r

/X''HM,C

--

Page 13/17

90.

ffi;>

r

April 16, 1999, 17:14 p'33

9Oox 180°x 90° :f:y 180°y

~tntn n ~lH

x

""9'

z

h

1 z

1r:I

1

~

Page 14/17

-~

Apri116, 1999, 17:02 p?4 Characteristics of polarisation transfer experiment

Sensitivity

-Enhancement of sensitivity of I by Error!

INEPT I = lo Error!

INEPTNucleus Max noe

31p

13C

29Si

15N

57Fe

2.24

2.99

-1.52

-3.94

16.48

2.47

3.98

5.03

9.87

30.95

""

I'""'-'

The repetition rate of the pulse sequence is determined by Tt of protons

The il delay

-Maximum sensitivity:for an ISn system:

L\ = ~ sin-1-.!.-

1tJ n 1/2

-~ectrum editing according to multiplicity

CH:

CH2~

C..~3

I & sin (n J A)

I & sin (2 n J A)

I & ~ [sin (n J A) + sin (3 n J~)] I -6 :

~

i

CH2 CHJCH I

6

I I I I I I I I I. I ,

,. " '. J, Jo J' JO I' II".

Page 15/17

.y

7 maj 1996, 19.45

4) Inverse detection

What is inverse detection ?

-Use of the sateIIites lH-{X} which are in the feet of the peaks in the proton spectum and which represents

only some % of the principal peak.

-Example lH spectrum <?fCHCI3

~~

I'""""

12C

no coupling with 1 H one peak of intensity 99

14C

13C

1=0

I = 1/2

Traces.

1.08 %

Coupling with 1 H a doublet of intensity 1 %

width lJ13C-lH and symmetric / major peakr

-The NMR information is transfered from the X nucleus to the proton detected nucleus.

t ~

(\

:-T-"---~ ~~~--,.-~ \...:.-- , ,,~~ ~ '.. ~ :--., , ,-

J.. .,. '" ,. ..1. .," .". .1...,." .

1 H spectrum of CHC13 in inverse detection

Page 16/17

.o .~ ~o 00 o. o o. ., .o12' ICI e) 'O "I 11 1 -11 -le -58 -e3 -ll3

H(~rl

I = O 99%

.

Apri116, 1999, 17:02 p-42) Advantages

Gain in sensitivity

Obtention of NMR parameters for nuclei with low 'Y

The reverse INEPT experiment

180:. 90:.'Hn n r=1/4J rf')n1.

-J ~ .;;iJr""

z

H CpH

t (.

~

y'.cx.n("

90°, 180~. 90 '1°'1j( x

~~~.:-.:~-a b c d (e) f g !

HCH./'

'C.I 130°, 90°i I' ,.

n r:1/L. ) r1')n..I ~, ~..-

11(/1H

I (.

af}

IH11( .

Iy' -

., 90° . .iaOO. 900 1 .

o.( .,

:..J~.:...:r~~a b ( d (el f 9

f"

~

I

I

I

I

HS

90°,x

(121 -~--(+21

z

90°~.

~I.

Page 17 117 :I