Heteronuclear shift correlation spectroscopy.

In the process of making a complete assignment of both the carbon and the proton spectrum of a
complicated system, it is often desirable to determine unambiguously which hydrogen is attached to
which carbon. Consequently on can then use information from the carbon spectrum to aid the
assignment of the proton spectrum and vice versa.

In addition heteronuclear correlation experiments can be designed to give correlations between
carbons and proton over several bonds, through multiple bond J couplings. Thus C-H pairs can be
pieces together using this information and information from COSY to obtain an assignment of the
whole system.

Traditionally heteronuclear correlation spectroscopy is performed between carbon and proton but
will work for any system containing to different types of nuclei, provided that at least one of which
is abundant.

Initially these experiments start with a single quantum coherence on proton and transfers it to carbon
and is then detected. This is performed by using and INEPT type transfer as seen in the HETCOR
experiment. Alternatively one could start with by exciting the carbon single quantum coherence,
transferring it to proton and detecting it as a proton single quantum coherence, gaining significant
sensitivity. These experiments are referred to as inverse experiments, such as HSQC and HMQC,
these make use of INEPT and DEPT like polarization transfers.
The Basic HETCOR Pulse Sequence
y
x
2
2
Evolution
H
t1
y
2
Acquire
C

t2
This pulse sequence starts with the two-spin heteronuclear equilibrium density matrix, which is
converted to a proton single quantum coherence by the 90ox pulse, which is allowed to evolve under
J for t1. Keeping track of only the first term, up to this point we get:
90 0
JI  I
x
z
z
I z  E 

 I y  E 


 I y  E cosJt1   2I x  S z sin Jt1 

Now considering evolution under the proton chemical shift term:
2v I E
 I y  E cosJt1   2I x  S z sin Jt1 

H 
z 




 I y  E cos( 2 H t1)  I x  E sin( 2 H t1) cosJt1   2I x  S z cos( 2 H t1)  2I y  S z sin( 2 H t1) sin Jt1 

Applying the 900y pulse in both channels:
 I y  E cos( 2 H t1 ) cosJt1   I z  E sin( 2 H t1 ) cosJt1 
 2I z  S x cos( 2 H t1 ) sin Jt1   2I y  S x sin( 2 H t1 ) sin Jt1 

Only the third term evolves into a detectable signal in the carbon channel thus only it will be
considered, which is the anti-phase term:
 2I z  S x cos( 2 H t1 ) sin Jt1 

These can be represented as:
I z  S x sin( 2 ( H  J / 2)t1 )  sin( 2 ( H  J / 2)t1 )

This evolves during the detection period as:
I z  S x cosJt2   0.5E  S y sin Jt2 sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
where only the second term is detectable:
0.5E  S y sin Jt 2 sin( 2 ( H  J / 2)t1 )  sin( 2 ( H  J / 2)t1 )
which evolves under the carbon chemical shift as:


0.5 E  S y cos(2C t2 )  E  S x sin( 2C t2 ) sin Jt2  
sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
which is equal to:


0.5 E  S y cos( 2C t2 ) sin Jt2   E  S x sin( 2C t2 ) sin Jt2  
sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
which can be simplified to:
 0.25E  S y sin( 2  C  J / 2t2 )  sin( 2  C  J / 2t2 )
sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
 0.25E  S x cos( 2  C  J / 2t2 )  cos( 2  C  J / 2t2 )
sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
detecting this with the receiver along the x-axis we get:
cos( 2  C  J / 2t2 )  i sin( 2  C  J / 2t2 ) 
 0.25

 cos( 2  C  J / 2t2 )  i sin( 2  C  J / 2t2 
sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
 0.25sin( 2 ( H  J / 2)t1)  sin( 2 ( H  J / 2)t1)
exp( i 2  C  J / 2t2 )  exp( i 2  C  J / 2t2 )
which represent an anti-phase doublet of anti-phase doublets just like the cross-peak in COSY.

This anti-phase peak structure makes it impossible to collect the signal while decoupling the proton
since the anti-phase peak will self can just like with INEPT.

In order to allow for decoupling during acquisition this anti phase double needs to be refocused just
like in the INEPT sequence. Consequently a refocusing delay is added at the end of the sequence
terminated by a 180o pulses in both the proton and carbon channels. To remove the coupling in the
proton domain the proton SQC is allowed to evolve in the evolution period under carbon decoupling.
After the evolution period the antiphase terms is allowed to build up optimally for a period 1/2J.
HETCOR Pulse Sequence Modified to Allow for Decoupling
x
2
H
x
x
Evolution
t1
Decoupling
x
x
C
1)
x
2
Decoupling
x
2
1/2J
Acquire
1/2J
t2
Start by considering the proton z-magnetization which is converted to a – y magnetization by
the first 90ox pulse,
90 0
x
I z  E 

 I y  E
2)
This proton single quantum coherence evolves under the proton chemical shift only since the
carbon nucleus is decoupled.
 I y  E cos2H t1   I x  E sin 2H t1 
3)
The decoupler is turned off after the evolution period and the system is allowed to evolve
over the scalar coupling term for a period 1/2J, allowing pure anti phase terms to evolve.
The 1800 pulse is applied in both channels remove the effects of further chemical shift
evolution, which can now be ignored.
2I x  S z cos  2 H t1   2I y  S z sin  2 H t1 
4)
Now a 900x pulse is applied in both channel allowing for polarization transfer from the proton
to the carbon as:
2I x  S y cos  2 H t1   2I z  S y sin  2 H t1 
The first term is undetectable and does not evolve into a a detectable signal later on and is
thus dropped.
5)
The now carbon anti-phase term is allowed to evolve under the scalar coupling interaction,
for a period of 1/2J, giving a pure in-phase carbon single quantum coherence. Again
chemical shift evolution is ignored, during this fixed delay.
E  S x sin 2H t1 
6)
This carbon SQC is allowed to evolve for a second evolution period giving only under the
carbon chemical shift term since proton decoupling is employed during acquisition:
E  Sx cos2Ct2   E  S y sin 2Ct2 sin 2H t1
this gives the sine modulated data set fot a C-H correlation spectroscopy without splitting due
to scalar coupling. The phase of the initial excitation pulse will have to be modifies in order
to obtain the cosine modulated data set, needed for both sign and phase sensitivity.
Indirectly detected heteronuclear correlation experiments

Heteronuclear correlation experiment can be performed using proton detection thereby greatly
increasing the sensitivity of the experiment. There are two basic approaches referred to as
Heteronuclear multiple quantum coherence, or HMQC, or the Heteronuclear signal quantum
coherence, or HSQC, both referring to the coherence order through which the magnetization passes
to establish the correlation between the heteronuclei.
The Heteronuclear Multiple Quantum Coherence Pulse sequence
x

2
Acquire
H
t2


2
C
2
Evolution
1/2J
1/2J
t1
Decoupling
1) The HMQC experiment, starts by exciting a proton SQC, which evolves into an anti-phase SCQ
after a period of 1/4J under scalar coupling evolution. (proton evolution is ignored)
90 0x (I )

I z I z
2 
I z  E  
 I y  E 
 2I x  S z
2) This anti-phase SQC is converted to a double quantum coherence a pulse in the carbon channel.
This DQC evolves under the both the chemical shift terms of H and C, but not the scalar
coupling term.
90 0 (S )
2I x  S z   2I x  S
where  = x, or y and where correspondingly = y or x.
3) The 1800 pulse in the proton channel right at the center of the sequence serve to refocus any
proton evolution up until the beginning of the detection period. Thus the DQC only acquires
dependence on the carbon chemical shift during the evolution period.
2 S t
C z 1
2I x  S  

 A( c , t1 )I x  S
4) At the end of the evolution period the DQC is converted back to the proton anti-phase SQC, by
the 900 pulse in the proton channel.
2
S t
H z 1
A( c , t1 )I x  S  
 A( c , t1 )I x  S z
5) This proton antiphase term is refocused to a in-phase SQC under the influence of the scalar
coupling term.

I z I z
2 
A(vc , t1 )I x  S z 
 A(vc , t1 )I y  E
6) The proton SQC is evolves only under the proton chemical shift term since carbon decoupling is
employed during the acquisition period, giving:
2v S t


H z 2
A(vc , t1 )I y  E  
 A(vc , t1 ) I y  E cos2v H t 2   I x  E sin 2v H t 2 
this term depends on the carbon chemical shift in t1 and the proton chemical shift in t2, which
means that in this experiment carbon is the indirect dimension and proton the direct dimension.
Again two-data set are required to be sensitive to sign and phase.

This experiment is used to correlate carbons to all local proton coupled to it, through several bond.
It is often referred to as the Heteronuclear Multiple Bond Correlation spectroscopy, and is one of the
main work horses in 2D NMR structural studies.
The Heteronuclear Single Quantum Coherence Experiment.

The Heteronuclear Single Quantum Coherence Spectroscopy, establishes correlation between carbon
and its directly bound protons. Longer range connection are not made with this experiment. Again
the cross peak do not contain fine structure due to the proton-carbon coupling since proton couplings
are refocused during the evolution period and carbon decoupling is employed during detection.

The experiment starts with a basic proton to carbon INEPT transfer, optimized to give a pure antiphase carbon SQC, which is allowed to evolve under the carbon chemical shift only during the
evolution period (Hence the name of the sequence). At the end of the evolution period, the proton
anti-phase SQC is converted to on observable carbon in-phase SQC by an carbon-proton INEPT
transfer.
The Heteronuclear Single Quantum Coherence Pulse Sequence
x
2
H

x
2

y
2
x
Acquire
1/2J
1/2J
x
1/2J


2
2
1/2J
t2
x
Evolution
C
Decouple
t1
1) INEPT transfer from proton to carbon giving pure anti-phase proton SQC:
H toC INEPT
I z  E    
 I z  S y
the phase of the carbon SQC is determined by the pulse phases, 1 and 

2) The Carbon anti-phase SQC evolves over only the carbon chemical shift. Evolution due to
carbon-proton J coupling is refocused by the 180o pulse in the proton channel in the center of the
evolution period.
2 S t
C z 1
 I z  S y 

 I z  S y cos2 C t1   I z  S x sin 2 C t1 
3) At the end of the evolution period the first term is converted to an anti-phase proton coherence,
whist the second into a double quantum coherence, by the simultaneous 90 0 pulses in the carbon
and proton channels:

(I x  S x )
2   I  S cos2 t   I  S sin 2 t 
 I z  S y cos2 C t1   I z  S x sin 2 C t1  
y
z
C1
y
x
C1
At this stage the second term is dropped from consideration since no observable signal arises
from it.
4) The anti-phase proton SQC is refocused into an in-phase proton SQC, by the remainder of the
sequence, which is just like the refocusing part in refocused INEPT sequence.
1 / 2 J  (I  S ) 1 / 2 J
x
I y  S z cos2 C t1  x 

 I y  E cos2 C t1 
5) Finally the proton evolves during the detection period under the influence of the proton chemical
shift only since it is decoupled from carbon.
2v I


H z
I y  E cos2 C t1  
 I y  E cos2 H t1   I x  E sin 2 H t1  cos2 C t1 
This is the cosine data set. A sequence with a different phase cycle provided the sine modulated
data set.
A Comparison Between Carbon Decoupled and Coupled HMQC Spectra.
A comparison between and HSQC and an HMQC spectrum showing the
difference in the cross peak structure.
Example – COSY spectrum of Camphor
13
C NMR spectrum with H decoupling
DEPT Spectra
HSQC spectrum of Camphor
HMBC Spectrum of Camphor