Chem 781 Part 5

Multiple pulse- and double resonance experiments

Heteronuclear Decoupling

Why do we need decoupling ?

• In the 13C spectra of 13C-1Hn groups the signal will be split by large 1JCH.

• This splitting will reduce the sensitivity of signals which often are already naturally weak

• Such a large splitting can also cause severe overlap of lines and result in complex spectra.

• Therefore, in routine C-13 NMR spectra this coupling is removed by applying decoupling.

Basic idea of decoupling

• From the vector picture one can see that the dephasing of the doublet components can be reversed by interchanging the α and β states of the coupling partner (here proton):

• Such an exchange of α/β states can be achieved by application of a 180̊0 pulse on the protons (remember that an 180̊0 pulse inverts all spins). In the product operator formalism, that is equivalent to reversing the sign of the Ix

CIzH term:

πx

-IyC cos(JCHπτ) + Ix

CIzH sin(πJCHτ) ─────> -Iy

C cos(JCHπτ) - IxCIz

H sin(πJCHτ)

y

x

y

x

-I IC H

-I y

C

I IC H

exch

ang

e /

spi

ns

y

x

y

x

-I IC H

-I y

C

I IC H

t = 0̊ t = t = t = 2

Practical application of decoupling

• The ideal solution would therefore be to apply a 180̊0 proton pulse between each sampled data point during acquisition.

• In order to achieve 180̊0 pulse between every sampled data point many (320̊0̊0̊) strong pulses (τπ DW) would have to be applied in rapid succession. ≪

• In a typical 13C spectrum (220̊ ppm at 75 MHz) DW ≈30̊ μs or less. That is usually not achievable experimentally

1 3 C

1 H

1 H

t(acquisition)

/2(x) (y) / x /2(x) (y) / x

id e a ld eco u p lin g

C P D d ec o u p lin g w ith M L E V

0 2

Problems with achieving “ideal“ decoupling requirements

• duty cycle of amplifier

• damage to probe

• sample heating (too much energy absorbed)

Real life Decoupling sequences

• In practice the requirement for efficient decoupling is less demanding.• A more realistic requirement is that the dephasing from J coupling during/between

the 180̊0 pulses is small:

γB1/2π   J or τ≫ P180̊ ≪ 1/J

• As DW ≪ 1/J (JCH ≈ 150̊ Hz, 1/J = 6.7ms) dephasing from J coupling is small during DW, so inversion does not have to occur between every sampled point.

• Typically, decoupler pulses with τ90̊ = 10̊0̊ μs are used (γB1/2π = 2.5 kHz).

Problem of Bandwidth of decoupling

• Most basic decoupling scheme: continuous wave irradiation with a power of γB1/2π = 2.5 kHz (cw decoupling)

• However, for more many proton signals over a shift range of 10̊ ppm to be decoupled, another requirement is that γB1/2π needs to be strong enough to cover that range

• For 10̊ ppm at 30̊0̊ MHz that is 3 kHz, 5 kHz at 50̊0̊ MHz

• CW decoupling can often not performed with the power required to achieve the required bandwidth

Composite Pulse Decoupling• It is more efficient to use a series of pulses with variable phases (composite

pulses): => Composite Pulse Decoupling (CPD)

• MLEV (Malcom Levitts CPD-sequence): (90̊0x 180̊0y 90̊0x)n

• WALTZ (1x π/2, 2x π/2, 3x π/2 = 1,2,3)(90̊0x 180̊0-x 270̊0x)n

• other more complex schemes are also in use:

GARP (Globally Optimized Alternating Phase Rectangular Pulse)

Schematics of decoupling

Summary of decoupling techniques

Effect of decoupling on intensities

• In addition to removing couplings from the spectrum, decoupling will also effect the intensities of the signals

=> Nuclear Overhauser Effect (NOE)

• The effect is non trivial in origin, and will not treated fully from scratch here

Basic theory of NOE

• The observation of NOE enhancement is a special relaxation effect caused by the change in population of the proton levels during the decoupling.

• The details of how relaxation is induced will be discussed later.

• For now we accept that in the presence of through space (dipolar) spin-spin couplings, molecular motion induces random transitions between levels related by flipping one or both coupled spins.

Transitions in a two spin system

13C H

For an isolated 13C-1H pair these transitions can occur with the rates W1

C, W1H

, W2HC and

W0HC.

W1 are the observable NMR transitions of C and H with frequency ν0̊

H and ν0̊C.

W0 and W2 the two simultaneous flip transitions not observed in the NMR spectrum (cross relaxation), with the frequencies ν0

H-ν0C and ν0

H + ν0H.

Rate of NOE buildup

W W

W W W W

cross relaxa tion

sp in la ttice re laxa tionC H

T

2 0̊

1 1 0̊ 2

1

1

In general, the NOE enhancement η is given by relative rates of cross relaxation and total relaxation:

Nothing better than a picture

1 1 3H C

H C+

C

0̊

1H

1H

13C

13C

1 1 3H C

H C+

1H

1H

13C

13C

H C+

1 1 3H C

H C+

H C+

in itia l th e rm a l eq u ilib riu m

tu rn o n p ro to nd eco u p lin g

es tab lish n ew eq u ilib riu mu n d er d eco u p lin g co n d itio n s

P o p u la tio n d iffe ren ces :1H :

1 3C :

m = 2 : m = 0̊ :

s

s

}}

H

C

H + C

H - C

0̊

C

C C

(n o t lo n g e ra t eq u ilib riu m )

0̊

if W > > W : / + = [1 + /(2 )]

2 1 2

H C

1 H C

C

W 2

W 0̊

Effect of 1H decoupling on 13C population differences. The initial excess populations are denoted ΔH and ΔC, the spin function for ms = + ½ and - ½ are α and β, respectively.

Magnitude of NOE• For small molecules W2 is dominant over W0̊ (tumbling rate of molecules ω≫ 0̊ )

and under optimal conditions the enhancement will be ηmaxC{H} = γH/(2γC) ≈ 2

Thus the carbon signal will increase up to a factor of three in intensity upon

decoupling of protons:

M0̊C   ∼ ΔC MC

NOE   (∼ ΔC + ΔH/2) or MCNOE = MC

0̊ + η M0̊C

• In large molecules the situation will be different

• W0̊ and W2 depend only on dipolar interaction between 1H and 13C, whereas W1H

and W1C may also include other contributions to the relaxation (Chemical shift

anisotropy, paramagnetic impurities like oxygen), so the theoretical enhancement will not always be observed

• for tertiary carbons dipolar coupling to nearest protons is weak

• Note that dipolar coupling does not require a bond, but directly bound protons are also close in space.

Practical considerations of NOE for carbon NMR

• Distance dependence: Tertiary carbons like C=O and >C< show only very little enhancement and show up weaker than protonated carbons => intensities will not be proportional to number of C-atoms

• additional mechanisms of relaxation will only contribute to W1 and may reduce NOE (Chemical shift anisotropy, unpaired electrons from oxygen)

• Nuclei with negative g will exhibit a negative NOE, which in some cases may decrease signal (15N: gN-15 -1/10̊ gH, 113Cd)

• large molecules (M > 30̊0̊0̊): W2CH ≈ W0̊

CH and ήmax ≈ 0̊.25 (small NOE)

• NOE will depend on molecular size and will be close to zero for macromolecules.

• As NOE is a relaxation phenomenon it will take time to build up after turning the decoupler on.

Basic multiple pulse experiments

Quantitative 13C NMR• Goal: get decoupled spectrum without (or with minimum) NOE:• Solution: NOE takes time to build up (up to a few seconds). On the other hand

decoupling occurs instantaneously after turning on decoupling: • decouple only during aq, not during d1: “inverse gated decoupling” (zgig)

• aq needs to be kept to minimum to avoid NOE during acquisition

• d1 needs to be long enough to maintain M0̊H before each scan and ensure sufficient

relaxation of MzC

• This method is also used for 1D 15N, 113Cd NMR where NOE is undesired

Get spectrum with coupling to protons and with NOE:

• Goal: Obtain proton-coupling information, but retain sensitive advantage of NOE

• Solution: Decouple during d1, but not during aq:“gated decoupling” (zggd)

• This will not solve the problem of spreading signal intensity over many multiplet lines and potential overlap in crowded spectra, but it gives improved sensitivity over simple one pulse experiment.

CC

CCH 2

CH 3

O

H

H

H

1

2

3

4

5

1 23 4 5

Overview of different decoupling schemes

d 1

d ec o u p le

p 1

Regular decoupling

Gated Decoupling

Inverse Gated Decoupling

Simple Spetrum editing - APT (Attached Proton Test) experiment

• During decoupling information about coupling partners is lost.

• Goal: Reintroduce this information and still get decoupled spectrum Can we get the advantage of a decoupled spectrum and still retain some coupling information ?

• Consider an experiment where we add a time τ = 1/1JCH between the 13C excitation pulse and the start of acquisition with decoupling:

= /1

J

C P D

9 0̊ox

1 3C

1H

t = 7.15 ms for 1JCH= 140̊ Hz

Evolution of spins under coupling after a pulse:

C

C H

C H 3

C H 2

0 1/4 J

1/2 J1/Jt

Regard a C-Hx fragment: Evolution of 13C x,y -magnetization with 1H coupling after time tAfter τ = 1/J all spins will again be aligned, but their relative phases will depend on multiplicity.

J2

J

3 J2

J2

Obtaining multiplicity edited spectra in real samples

• On first sight such an experiment looks like a good multiplicity edited spectrum.• Why will this not work in a real experiment ?• Above experiment does not take into consideration rotation of spins due to

chemical shift, so it would only work for one spin exactly on resonance.• For many different spins, dephasing will occur during τ also for different Ω values

as Ω >> π∙J.• removal of chemical shift evolution necessary during τ:

APT (Attached Proton Test) Experiment

= /1

J

9 0̊ox

1 3C

1H

= /1

Jd 1

c re a te N O E d e fo c u s s p in sa c c o rd in g to m u ltip l ic ity

re fo c u s c h e m ic a ls h if t d iff e re n c e s ,s to p c o u p l in g

a c q u ire F ID

Vectors in APT with chemical shift

1/J

1/J

APT without refocusing APT with refocusing ofof chemical shift chemical shift

Notes on the APT experiment

• It is important to turn the decoupler on during the second τ period. With decoupling on the coupling will be “frozen” after the first τ and only chemical shift will refocus. With decoupling off during second τ also coupling will be refocused (it will also act as a decoupling pulse).

• Note that the condition τ = 1/1JCH can not perfectly achieved for all carbons as the coupling constants can vary (typically 125 - 160̊ Hz) and non-perfect editing will occur.

Note: Spectra can be phased arbitrarily, so it can be either CH, CH3 “up”, C, CH2 “down” or CH,CH3 “down”, C, CH2 “up”. The command apk can give you thus either result as the computer itself does not know or care whether a signal is CH or CH2.

220 200 180 160 140 120 100 80 60 40 20 ppm

11.3

7

131.

81

159.

71

193.

26

CC

CCH 2

CH 3

O

H

H

H

Acetone-CO

Acetone-C D 3

1

2

3

4

5

1 23

4

5

Typical use of 1805 pulses

9 0̊ox

1 3C

1H

1 8 0̊ox

9 0̊ox

1 3C

1H

1 8 0̊ox

9 0̊ox

1 3C

1H

1 8 0̊ox

1 8 0̊ox

rem o v e C -H co u p lin gk eep c h e m ica l sh ift

rem o v e C -H co u p lin gA N D c h em ica l sh ift

rem o v e ch em ica l sh iftk eep C H c o u p lin g

Combinations of 180̊0 pulses are frequently used in NMR experiments to remove one or more interactions for a period of time from the spectrum and allow for selective manipulation of magnetization.

Top: -IyC ───> -Iy

C cos(ΩC2τ) + IxC sin(ΩC2τ)

middle: -IyC ───> +Iy

C bottom: -Iy

C ───> -IyC cos(πJCH2τ) + Ix

CIzH sin(πJCH2τ)

Note that the last sequence offers an alternate way of doing APT.

Magnetization transfer through scalar coupling

• NOE is one way to transfer half the proton magnetization through a dipolar “through space” interactions

• Can we do better ?

• Magnetization can also be transferred by scalar “through bond” interactions

Selective Polarization Transfer (SPT)

1 1 3H C

H C+

C

0̊

1 1 3H C

H

C

C

H C+

H

C

H

C

H

C H-H

selec tiv e

-C -C

-H -H

1H 1 3C

1H 1 3C

H (C - )

-C

-C

-H

-H

Consider 13C-1H fragment:doublet split by 1JC-H

Applying a slective180̊0 pulse at proton frequency on one of the two lines of the doublet will invert the population along that transition. As a result the population difference of the corresponding 13C lines will also change

Result of the SPT experiment

☺The result is an enhancement of the carbon signal by | γH/γC |

☺Transfer is instantaneous, no need to wait for relaxation to take place

• The experiment works only in presence of a scalar coupling: SPT will work only one signal at a time.

• A selective 180̊0 pulse (γB1/2π << JCH ) is not easily implemented.

Transfer using non selective pulses (INEPT)

• However, the effect of selective 180̊0 pulse can be achieved for all signals by applying two 90̊0 pulses separated by τ = 1/2JCH :

yx y

xyx

z

a b c

d

( /2 ) x ( /2 ) y

( /2 ) y

1H

1 3 C

-M I0̊ y

H H

= 1 /(2 J )C H

a b c

-M I I0̊ x z

H H C -M I I0̊ z z

H H C

dzz

yx

z

-M 0̊

H I Iy z

C H

-M I0̊ z

C C -M I0̊ z

C C -M I0̊ y

C C -M I0̊ y

C C

-I Ix

C H

I Iz

C H

I Ix

C H

I Iz

C H

Accounting for chemical shift dispersion

• This sequence will work for one C-H if pulses are applied on resonance (ΩC and ΩH = 0̊).

• In real life however many peaks will be present and additional rotation by ΩH will occur during τ = 1/2 J . Thus the vectors will not be aligned along x at point b.

• However, insertion of two 180̊0 pulses in the center of τ will remove the chemical shift dephasing but keep the coupling evolution:

INEPT experiment (Insensitive Nucleus Enhancement by Polarization Transfer)

Result of INEPT experiment• Enhancement by factor |γH/γX|X = 13C: ≈4 X = 15N: ≈ 10̊

• One disadvantage of the basic INEPT is that the multiplets appear in anti phase

• No decoupling possible: positive and negative component will cancel. In vector picture, the magnetization will remain anti phase and will not develop x,y magnetization (Ix

CIzH is not observable)

• The multiplets are asymmetric due to natural C-13 magnetization

CH CH2 CH3

| | | | | | | | J | J J | J | J J))))))) )))) )))|))))))) )))))))))))))))))

| | | || | | ||

| | | | | | | | J | J J | J | J J))))))) )))) )))|))))))) )))))))))))))))))

| | | || | | ||

Refocused INEPT

• In order to obtain decoupled spectra, add another delay Δ to refocus IyCIz

H to IxC

before turning on decoupler and acquiring data:

• Note that during τ one considers a proton coupled to one carbon, while during Δ one has to consider a carbon coupled to one, two or three protons

( /2 ) x ( /2 ) y

( /2 ) y

1H

1 3 C

2

2

t 22

2

C P D

Editing using INEPT• The situation in INEPT during the second refocusing is similar, but not identical to

APT (one starts with anti phase magnetization at the beginning of Δ)

APT: IyC ± I⇒ y

C

refocused INEPT: Iy

CIzH ⇒

± IxC

=> the length of Δ can be used for multiplicity editing

Editing with INEPT

refocu sed IN E P T :

ed itin g w ith d e lay J : C H o n ly

= 3 /(4 J): C H ,C H u p , C H d o w n 3 2

= 1 /(4 J): C H , C h 2 , C h 3 p o sitiv e

c)-M I I0̊ z z

H H C d)-M 0̊

H I Iy z

C Ha)-M I0̊ y

H Hb)-M I I0̊ x z

H H C e) s in ( J ) (C H ) C HM 0̊

H I x

C

s in ( J )c o s( J ) (C H ) C H C H 2

s in ( J )c o s ( J ) (C H ) C H C H 3

2

d iffe ren ce s in J v a lu e s e ffe c t p h ases o f s ig n a ls

1H

1 3 C

--- 2

--- 2

yx

C P D

deco up lin g d uring a cq u isition

a b c

d e

Editing using DEPT

• Disadvantage of editing with refocussed INEPT: As in APT it works perfect only if all coupling constants 1JCH are the same. Typical values vary from 125 Hz - 150̊ Hz (up to 20̊0̊ Hz in some cases)

Better way: DEPT experiment (Distortionless Enhancement by Polarization Transfer):

Pulse angle θ takes role of Δ :

θ = π/2 (90̊0): DEPT-90̊ CH only

θ = 3π/4 (1350): DEPT-135CH, CH3 up, CH2 down (or vice verca)

θ = π/4 (450):DEPT-45 CH, CH2, CH3 positive

Editing with DEPT

• The DEPT experiment can not easily visualized by using the vector model but requires quantum mechanical operator description.

• The problem is the effect of the first 13C π/2 pulse which converts IxHIz

C into -IxHIy

C. This is called a double/zero quantum coherence.

• The quality of editing in the DEPT does not depend on the accuracy of matching the delay τ to the coupling constant but is determined by the pulse width β and depends on the different operators generated by different numbers of protons coupled to the 13C.

Editing with INEPT/DEPT: Dependence on delay/pulse

• There is no delay/pulse that is optimal for all multiplicities. • N > possible if experiment gets optimized for couplings over more than one

bond

Example of editing with DEPT

INEPT vs NOE

Example for NOE vs. INEPT

29Si INEPT

31P to 103Rh INEPT