Heteronuclear Correlation Spectroscopy.PDF

5 Heteronuclear Correlation Spectroscopy

H,C-COSY

We will generally discuss heteronuclear correlation spectroscopy for X = 13 C (in natural

abundance!), since this is by far the most widely used application. However, all this can also be

applied to other heteronuclear spins, like 31 P, 15 N, 19 F, etc..

In the heteronuclear case, there are some important differences that allow to introduce additional

features into the NMR spectra:

- all heteronuclear coupling constants 1 J( 1 H- 13 C) are very similar, ranging from ca. 125 Hz

(methyl groups) up to ca. 160 Hz (aromatic groups) in contrast to the homonuclear couplings 2 J

( 1 H, 1 H) and 3 J( 1 H, 1 H), which can differ by more than an order of magnitude (ca. 1 Hz - 16 Hz).

This feature allows to adjust delays for coupling evolution to pretty much their optimum length

for all signals.

- r.f. pulses on 1 H and 13 C can (and actually must!) be applied separately, due to the very different

resonance frequencies for different isotopes. Thus, 1 H and 13 C spins can, e.g., be flipped

separately, resulting in refocussing of the heteronuclear coupling. For the same reason,

heteronuclear decoupling can also be applied during the acquisition time.

The basic COSY sequence can be readily extended to the heteronuclear case.

Again, during t 1 proton chemical shift W I evolves, as well as heteronuclear coupling J IS will evolve

(following the quite illogical convention, we will use I – insensitive – for the proton spins and S –

sensitive – for the heteronucleus, i.e., 13 C).

For the simplest case, an I–S two-spin system, we get the following evolution (only shown for the

relevant term that will undergo coherence transfer during the 90° pulse pair after t 1 , i.e., 2 I y S z ):

90° y (I) t 1

I z I x 2 I y S z cos (W I t 1 ) sin (p J IS t 1 )

90° x (I), 90° y (S) t 2

2 I z S x cos (W I t 1 ) sin (p J IS t 1 ) …

The transfer function is the same as for the 1 H, 1 H-COSY. We will get modulation in F1 (from the t 1 -

FT) with the proton chemical shift W I and the heteronuclear coupling J IS , and the coupling is

antiphase. Also, in F2 (from the data acquisition during

the t 2 period) we will get the carbon chemical shift (since

we do now have a carbon coherence, 2 I z S y ), and it is

also antiphase with respect to J IS . We will therefore get a

signal which is an antiphase dublet in both the 1 H and 13 C

dimensions, split with the 1 JHC coupling.

However, in the heteronuclear case, we can greatly improve the experiment by decoupling .

Depending on the presence or absence of 180° pulses, we can choose to refocus or evolve chemical

shift and/or heteronuclear coupling: chemical shift evolution is refocussed, whenever a 180° pulse is

centered in a delay. For the refocussing of heteronuclear coupling, the “relative orientation” of the

two coupling partners must change, i.e., a 180° pulse be performed on one of them (cf. table).

All these results can be verified by product operator calculations – a good exercise! By inserting a

180° pulse on 13 C in the middle of our t 1 period, we can decouple the protons from 13 C, so we won’t

get J IS evolution during t 1 , won’t get a sin (p J IS t 1 ) modulation and hence no antiphase splitting

in F1 after FT, but instead just a singulett at the proton chemical shift frequency.

d( 1 H) evolves

d( 13 C) evolves

J HC evolves

d( 1 H) is refocussed

d( 13 C) evolves

J HC is refocussed

d( 1 H) evolves

d( 13 C) is refocussed

J HC is refocussed

d( 1 H) is refocussed d( 13 C) is refocussed

J HC evolves

(of course, chemical shift evolution of 1 H or 13 C occurs only when this spin is in a coherent

state)

Heteronuclear decoupling can also be performed during the direct acquisition time. This is done by

constantly transmitting a B 1 field at the 1 H frequency. This causes transitions between the a and b

spinstates of 1 H (or, rotations from z to -z and back, about the axis of the B 1 field). If the rate of

these 1 H spin flips is faster than J IS , then heteronuclear coupling will be refocussed before it can

develop significantly, and no J IS coupling will be observed. In praxi, heteronuclear decoupling is

performed by using – instead of a continuous irradiation – composite pulse sequences optimized for

decoupling behaviour, which allow to effectively flip the 1 H spins over a wide range of chemical

shifts with minimum transmitter power, similar to the spinlock sequences used for TOCSY. Some

popular decoupling sequences are, e.g., WALTZ or GARP.

The use of decoupling sequences “freezes” spin states with respect to the heteronuclear coupling,

i.e., in-phase terms like S x will stay in-phase and induce a signal in the receiver coil corresponding

to a singulet (after FT). Antiphase terms like 2 I z S x will stay antiphase, won’t refocus to in-phase

terms and will not be detectable at all!

With this knowledge, we can remove the heteronuclear coupling from both the F1 and F2 dimension

of the H,C-COSY experiment, by decoupling during t 1 and t 2 :

Since heteronuclear coupling cannot evolve during t 1 , but we do need a heteronuclear antiphase term

for the coherence transfer, we have to insert an additional delay D 1 before the 90° pulse pair. Also,

we need to refocus the carbon antiphase term (after the coherence transfer) to in-phase coherence

before acquiring data under 1 H decoupling, which is done during D 2 .

This pulse sequence will give a singulet cross-peak in both dimensions. However, we will also have

chemical shift evolution during the two coupling evolution delays D 1 ( 1 H chemical shift) and D 2 ( 13 C

chemical shift), which will scramble our signal phases in both dimensions, so that we have to

process this spectrum in absolute value mode.

We can avoid this be introducing a pair of 180° pulses in the two coupling evolution delays. As

shown before, this will not interfere with the J IS evolution, but refocus chemical shift evolution:

In this version, the evolution of 1 H chemical shift (during t 1 ) and 13 C chemical shift (during t 2 ) are

completely separated from the evolution and refocussing of the heteronuclear coupling (during the

delays D 1 and D 2 ):

90° y (I) t 1 D 1

I z I x 2 I y S z cos (W I t 1 ) 2 I y S z cos (W I t 1 ) sin (p J IS D 1 )

90° x (I), 90° y (S) D 2

2 I z S x cos (W I t 1 ) sin (p J IS D 1 ) S y cos (W I t 1 ) sin (p J IS D 1 )

After FT, we get a 2D 1 H, 13 C correlation spectrum

with each cross-peak consisting of a single line, with

uniform phase. The factor sin (p J IS D 1 ) does not

contain a t 1 modulation (which would lead to a dublet

in F1), but merely a constant, which can be

maximized by setting D 1 = 1 / 2 J .

Actually, the sequence can be written more elegantly, by combining the two 13 C 180° pulses into a

single pulse. Instead of first refocussing the evolution during t 1 , and then during D 1 , one can

accomplish the same result with a single 180° pulse in the center of (t 1 + D 1 ):

This saves us one 180° pulse! No big deal? - well, no pulse is perfect, and this is not only due to

sloppy pulse calibration, but even inherent in the pulse: with limited power from the transmitter, our

pulse has a finite length (usually ‡ 20 ms for a 13 C 180° pulse). This means, however, that its

excitation bandwidth is also limited (cf. the F OURIER pairs), and that the effective flip angle for a

“180° pulse” (on resonance) will drop significantly at the edges of the spectral window! This causes

not only a decrease of sensitivity, but also an increase of artifacts.

Example: for a 20 ms 180° on-resonance pulse (i.e., 25 kHz B 1 field), one gets at –10,000 Hz

offset (= 80 ppm for 13 C at a 500 MHz spectrometer) an effective flip angle of ca. 135° – which

means that instead of going from z to -z (clean inversion), one gets equal amounts of -z and x,y

magnetization

The best pulse sequence for a H,C-COSY spectrum is therefore the following:

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