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Chem 526Chem 526

NMR for Analytical Chemists

Lecture 7Lecture 7

(Chapter 3)

Homework 3 #1 (Due 9/20): Explain what the following operation or function means. What is the purpose for each item?

(1) Shimming

(2) Lock

(3) Spinning

(4) Window Function

(5) Fourier Transform( )

(6) Phasing

(7) Probe Tuning

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Homework 3 #2Q 1. Plot vs A() for = 100 and =10

Q 2. Plot f vs D() for = 100 and =10

)(

S

Q 3. Plot f vs A() for /2 = 200 and =10

Q 4. Plot f vs A() for /2 = 200 and =40

Q 5. Plot f vs D() for = 200 and =40

2222)(

iS

22)(

A

22

)(

D

Calculation of FT (p139-140)• S’(t) = exp(it)exp(-t)exp(i) ( =1/T2)

• [3.14b]

exp)()(0

titsdtS

Calculate FT of s’(t) in [3.14b] for = /2 as S’() and CalculateReal(S’()) and Imag(S’())

S() =

)(exp0

ttidt

0

)(exp1

ttii

=

=

2222

i

i

1

A() D()

3

0 04

0.06

0.08

0.1

0.12

A1(w)

-0.06

-0.04

-0.02

0

0.02

0.04

-200 -100 0 100 200 300 400

A1(w)

D2(w)

A5(w)

Q 1. Plot vs A() for = 100 and =10

Q 2. Plot f vs D() for = 100 and =10

Q 5. Plot f vs D() for = 200 and =40

Announcement 1• How is the preliminary analysis of the unknown

(1H & 13C NMR) for Homework 4 (Due 9/22)?

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Chemical Shifts• Electron near nuclei creates extra field –B0

–B0(1 + )

Higher Frequency Lower Frequency

7Lower Shielding Higher Shielding(Higher Field)(Lower Field)

Induction Effects in 1H shifts

1H chemical shifts of CHnCl4-n(ppm) CH 0 23CH4 0.23 CH3Cl 3.05CH2Cl2 5.3CHCl3 7.27

1H shifts of CH3X (ppm)

Cl C-H3

e-

8

3 (pp )

F OH NH2 H Me3Si

4.26 3.38 2.47 0.23 0.0

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Analysis Example: 13C and 1H NMR of

diethyl ether (CH3CH2)2O

Q1. 13C NMR: Which is CH3?

(ppm)(CH3CH2)2O( 3 2)2

(Ppm) = [Shift from TMS (Hz) ]/ [NMR Frequency (MHz)]

Q2. 1H NMR: Which is CH3?

13C Chemical shift additivity principle

• δ = -2.5 +Ajnj,

• Aj denotes a substituent parameter for• Aj denotes a substituent parameter for neighbouring chemical groups

Substituent parameters for C and CH, CH2, CH3,

α β γ

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9.1 9.4 -2.5

CH3-CH2-CH2-CH2-CH3CH3: -2.5 + 9.1 + 9.4 -2.5 = 13.4 (13.9)

Exp

CH2: -2.5 + 2x9.1 + 9.4 -2.5 = 22.6 (22.8)

CH2: -2.5 + 2x9.1+ 2x9.4 = 34.5 (34.7)

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13C aliphatic shifts of ethyl-ether• CH3-CH2-O-CH2-CH3

CH3 : -2.5+9.1+ 8 -2.5 = 12.1 ppmCH : 2 5 + 9 1 + 58 +9 4 2 5 = 71 5 ppmCH2 : -2.5 + 9.1 + 58 +9.4 -2.5 = 71.5 ppm

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13C aliphatic shifts of ethyl-ether• CO2H-CH2-NH2 (Glycine)CH2 : -2.5 + 29 + 21 =47.5 ppm

• CO2H-CH(CH3)-NH3 (Alanine)CH : -2.5 + 29 + 21 +9.1=56.6 ppm

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2D NMRA. 2D Heteronuclear Correlation NMR (HETCOR) The basic idea of 2D HETCOR NMR is to specify a peak with two frequencies I andS. The sequence is given as an extension of polarization The sequence is given as an extension of polarization transfer experiment, but there is the t1 period for indirectly detecting 1H signal.

Sxcos(It1)

+ Iysin(It1)Ixcos(It1)

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Array of FIDs are taken for different t1 period

Sxcos(St2)+Sysin(St2)cos(It1)

Ch4.1 (See p275)

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8

2D FT Processing

• So we obtained

s(t1, t2) = cos(It1)exp(iSt2).

• First step is Complex FT on t2

s(t1, ω2) = cos(It1)A(ω2 -S)

• Second, Cosine FT on t1s(t ) A( )A( )

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s(t1, ω2) = A(ω1 -I)A(ω2 -S)

2D COSY for Coupled A-X system

A

1

X A

A

X

X 2

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COSY

TOCSY(total correlation spectroscopy)

Q1. Do you expect a cross peak between A and B if A and B form a dipeptide like A-B?

Q2. Do you expect a cross peak between A and B if A and B are a mixture of amino acids?

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Water Suppression

Rectangular Pre-saturation

Jump & Return

Jump & Return

3.7.1 Presaturation (p223)

• Irradiate weakly (1/2 ~ 50 Hz) for a long ti (1 2 ) Q Wh t ld h ?time (1-2 s) Q. What would happen?

• Advantage: Simple

• Disadvantage:

-Requires a good shimming

- Exchangeable 1H (such as amide 1H) may be also suppressed

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3.2 Data Acquisition

• FID Generated cos(0t)

Mixing to lower frequency (Real/Imag+Filter)

cos(0 - RF ) sin(0 - RF )

Digitization

Store to the computer

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Display

3.2.3 Quadrature Detection (p132)

cos(wRFt)cos(RFt)cos(0t)= cos(RF+ 0)t /2

+ cos (RF – 0)t/2

cos(w0t) Low pass

Low pass

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Q. Explain how the experimental scheme for data acquisition &detection (So called quadrature detection) works

sin(wRFt)

sin(RFt)cos(0t)= sin(RF+ 0)t/2

+ sin (RF – 0)t/2

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3.2.1 Sampling (p124)

After digitization, a time-domain signal is digitized ass(tn) = s(nt) A/D Conversion

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Nyquist frequency: fn = 1/(2t) defines the highest-frequency sinusoidal that can be reproduced from the digitized data. S(t) = s(kt)sinc[2fn(t-kt)],

where sinc(x)=sin(x)/x D/A Conversion

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What happens if the frequency is higher than fn?

• First note that 2π(2fn∆t) = 2πFrom this, cos[2π(2fnM+ ν0)k∆t] = cos[2π 2fnMk∆t+ 2π ν0k∆t] = cos[2πMk + 2π ν0k∆t] = cos[2π ν0k∆t] (k is an integer)

(2fnM+ ν0) and ν0 can’t be distinguished by the digital sampling

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sampling.

Hence, the signal shows up at νa

νa = (2fnM+ ν0), where -fn ≤ νa ≤ fn

-fn fn

Q. Where does the signal va show up?v0

Aliasing

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νa-fn fn

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3.2.3 Quadrature Detection (p132)

cos(wRFt)

cos(RFt)cos(0t)= cos(RF+ 0)t /2

+ cos (RF – 0)t/2

cos(w0t)

sin(w t)

Low pass RF Fileter+ Band Path Audio Filter

Low pass RF Filter + Band Path Audio Filter

Remove Aliasing of Noise

27Experimental Scheme for Data Acquisition &Detection (Quadrature detection)

sin(wRFt) sin(RFt)cos(0t)= sin(RF+ 0)t/2

+ sin (RF – 0)t/2

Digital resolution & Zero Filling

• Actual digital resolution in the obtained t ispectrum is

1/(N*∆t) = 1/tmax

∆t = sampling interval and N is data points in the FID

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the FID

Hence, the digital resolution can be enhanced by extending tmax.

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Ch 3.4 Pulse Effects

• We will cover – 1H Decoupling (3.4.3)

– Off-Resonance Effects (3.4.1)

– Composite Pulse (3.4.2)

– Selective Pulse (3.4.4)

– Water Suppression (3 4 5)

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Water Suppression (3.4.5)

1H decoupling

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13C spectrum of ethylbenzene

Q. Why are there no 1H-13C J splitting?

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J coupling

The local field that the S spin experiences due to a J coupling between I and S spins is denoted by

2πJIZ = 2πJmI.Z I

The energy due to the J coupling is

EJ = 2πJmISZ = 2πJIZSZ.

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What is 1H decoupling?

• The idea is to exchange and states rapidly for the I spin so that the splitting is averaged. p p g g

If <mI> = 0

<EJ> = 2πJ<IZ>SZ

= 2πJ<mI>SZ = 0

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• If you remember IZ – πIX -IZUnder continuous RF field matched at 1H frequency,

< IZ> = <mI> = 0

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Chemical Exchange (Ch5. p400)

A B

k

kA Bk

10 s-1

100s-1

450s-1

160 Hz

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450s

1000s-1

5000s-1

1H Spectrum of Leu-enkephalin in DMSO

(Tyr-Gly-Gly-Phe-Leu)Broadeningby chemical

D h i

yexchange

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Amide Phe

From “high-resolution NMR techniques in organic chemistry” by Claridge

Dephasing period

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How strong 1H decoupling must be?

• The idea is to exchange and states rapidly for the I spin so that the splitting israpidly for the I spin so that the splitting is averaged.

From the chemical exchange example,

IZ – πIX -IZ IZ πIX IZ

must be faster than J coupling

However, there is a problem in 1H decoupling Heating by rf

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1H spectrum of L tryptophan in 400 MHz

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Off-resonance Effects & Effective Field

= - BHow is the magnetization evolved by the effective field ?

eff = - Beff the effective field ?

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eff = (2 + 12)1/2

eff = - Beff Near On-Resonance

eff = - Beff Off-Resonance

eff = (2 + 12)1/2

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3.4.1 Off-Resonance Effects Excitation by /2-pulsefor different offsets

R ( ) R () R ( )R ()Ry(,) ~ Rz() Ry()Rz()

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Iz after pulse

|IX|2 + |Iy|21/2 after pulse

Excitation by -pulsefor different offsets

Off-resonance Effects in 1H Decoupling

• Scaled coupling is J c,where = Ω/Ω2 + (γB1)21/2where c Ω/Ω + (γB1)

c = 0 for the on-resonance case Ω=0.However, when Ω~γB1, c = 0.707.

On the other hand, if you use a strong B1 field, you can bake your sample because of theyou can bake your sample because of the heat generated by a decoupling RF field. (W B1

2)

What is solution ?

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Resonance Offset Dependence of Effective Coupling

Resonance-Offset Dependence

0 91

0 20.30.40.50.60.70.80.9

lc c

DecouplingNot Effective

00.10.2

0 0.5 1 1.5 2 2.5 3omega/gB1

DecouplingEffective

3.4.3 Composite Pulse (p174)

• Composite pulse compensates non-ideal ff t f ff d RFeffects of off-resonance and RF-

inhomogeneity over sample i.e. B1(1±).

• One idea is to add an extra pulse that does not function in the ideal case butdoes not function in the ideal case, but compensates for the non-ideal effects.

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Off-resonance dependence of composite rotation

β = 90º β’ = 240º

From “Principles of NMR in one and two dimension” by Ernst et al.

3.5.2 Super cycle for Composite Pulse Decoupling (p204)

• R = 90x180-x270x

• R = 90-x180x270-xR 90 x180x270 x

• If 90 = 1, R = 1x2-x3x

RRRR WALTZ4

RRRRRRRR WALTZ8RRRRRRRR WALTZ8

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Offset (Ω) dependence of effective coupling constants

Fig. 3.28

Effects of Super cycle

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Computer optimized sequence Garp-1

3.4.4 Selective Pulse (p179)Ideal Selective /2-pulse

0.2

0.4

0.6

0.8

1

0

-1-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8

1

1.5

Ideal Selective -pulse

-1.5

-1

-0.5

0

0.5

-1-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8

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Typical Shaped Pulse for Selective Excitation

Gaussian Sinc

Hermitian

Selective 90° PulseMX MY MZ

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Water Suppression

Rectangular Pre-saturation

Jump & Return

Jump & Return

3.7.1 Presaturation (p223)

• Irradiate weakly (1/2 ~ 50 Hz) for a long ti (1 2 ) Q Wh t ld h ?time (1-2 s) Q. What would happen?

• Advantage: Simple

• Disadvantage:

-Requires a good shimming

- Exchangeable 1H (such as amide 1H) may be also suppressed

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3.7.2 Jump-Return

90y ------ ------ 90-y

In case of on-resonance (H2O signal)

IZ – 90y IX – IZ – 90-y IZ

In case of some-what off-resonance (Other signals)

Water Signal Undetected!

IZ – 90y IX – Ixcos + Iysin

– 90-y IZcos + Iysin

Other Signals Detected!

Spin Lock & Field Gradient for Water Suppression

SLy

Water /2x

Non-selective /2X

SLy

Non-selective /2X Non-selective X

FG FG

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H exchange rate kex (p 224)From “NMR of Proteins and Nucleic Acids” By K. Wuthrich

Lo

g(k

ex )

(m

in-1

)

Indole

pH and Temperature dependence of kex

(min)

From:http://www.hxms.com/

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pH = 4.1 25 º C

H/D Exchange of BPTI

Use of DMSO

2D 1H/15N HSQC spectrum of β2m amyloid fibril in 95 % DMSO/5 % D2O Goto et al. Nature Structural Biology 2002

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Dissolved into DMSOAfter 8 days incubation of amyloid In D2O

D2O DMSO

HH

H

D2O

DD

H

D

DH

T

H/D Exchange Pattern

Amyloid Fibril Native

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Fast 2D NMR and Real-time Monitoring of H/D exchange in protein folding

PNAS 2007PNAS 2007Brutscher et al.