Heteronuclear correlation is used to assign the spectrum of another nucleus once the spectrum of one nucleus is known. It may also be of help in assigning the spectra of both nuclei even when a partial assignment of one or both is available. For small molecules, ¹H is usually correlated with ¹³C while for biomolecules, ¹H is also commonly correlated to ¹⁵N. Correlation to other nuclei such as ²⁹Si is also possible. The experiment may also provide chemical information which the spectra of neither nucleus can provide alone. In principle, heteronulcear correlation can be achieved using a two pulse sequence (fig. 1) and can be observed for the non-proton (X) nucleus. However, sensitivity is greatly improved by various methods including double INEPT, inverse detection, gradient selection and decoupling. As a result, one of a variety of pulse sequences that is best suited for a particular application is used instead of the two-pulse sequence in fig. 1.

Fig. 1. Pulse sequence for basic heteronuclear correlation

Here we discuss the class of experiment for large short-range heteronuclear couplings which usually arise from one-bond interactions, e.g., ¹H-¹³C or ¹H-¹⁵N. Long-range heteronuclear correlation is discussed elsewhere. There are seven common pulse sequences for this experiment that are best suited for different conditions: HSQC (Heteronculear Single Quantum Coherence), HSQCSI (Heteronuclear Single Quantum Coherence Sensitivity Improved), HSQCSIsp (HSQCSI with one additional shaped pulse), HSQCSIsp2 (HSQCSI with two additional shaped pulses), HMQC (Heteronuclear Multiple-Quantum Coherence), HMQCSIsp (Heteronuclear Multiple Quantum Coherence Sensitivity Improved with an additional shaped pulse) and short-range HMBC (Heteronuclear Multiple Bond Coherence adapted for one-bond correlations).

The best sequence for most small-molecule work is also the most complicated: the HSQCSIsp2 (fig. 2). This is based on the HSQC sequence with the addition of a second quantum pathway for sensitivity improvement (SI) and shaped pulses to improve the pureness of the phase but takes more time allowing signal loss due to relaxation and suppresses the 'useful artifact'. Therefore, the SI should only be applied if the ¹H line-width is less than 20 Hz for ¹H-¹³C and 12 Hz for ¹H-¹⁵N. Note that the ¹⁴NH line-width is usually broader than the ¹⁵NH line-width needed for deciding which technique to use. The ¹⁵NH line-width can be measured from the ¹⁵N satellites of the NH signal. If the ¹³C spectral width is less than 60 ppm or the ¹⁵N spectral width is less than 90 ppm or the ¹H line-width is greater than that suitable for SI, the addition of shaped pulses does not improve the spectrum enough to overcome the losses they cause in sensitivity. Only one pair of shaped pulses should be applied if ¹H line-width is greater than 10 Hz.

Fig. 2. Pulse sequence for HSQC variants

The sequence as drawn is that for HSQCSI. Omit the sky blue components for HSQC. Use shaped pulses for the first two 180°X pulses for HSQCSIsp and all the 180°X pulses for HSQCSIsp2. Parameters for the pulse sequence are listed in table 1.

Table 1. Gradient ratios and coupling constants for HSQC and HMQC

X nucleus	nHSQC	nHMQC	JAX
13C	3.98	1.2515	145 Hz
15N	9.86	1.1014	80 Hz

If the digital resolution without zero-filling of the spectrum in f₁ (¹³C, ¹⁵N, etc. direction) is coarser than 8 Hz then HMQC (fig. 3) gives greater sensitivity than HSQC. If the f₂ (¹H direction) resolution is less than 10 Hz for ¹H-¹³C or 6 Hz for ¹H-¹⁵N use HMQCSIsp variant.

Fig. 3. Pulse sequence for HMQC

Short-range HMBC should only be used as a last resort when ¹H line-widths are greater than 40 Hz for ¹H-¹³C and 30 Hz for ¹H-¹⁵N).

Δ should be 1/(4J_AX) where J_AX is the coupling constant. For ¹H-¹³C the coupling constant is approximately 125 Hz for sp₃ and 160 Hz for sp₂ (table 1). For ¹H-¹⁵N the coupling constant is approximately 80 Hz. The gradient strength m should not be a simple multiple of the other gradient strengths.

The peaks for short-range (one-bond) correlation are pure phase and positive for all the experiments except short-range HMBC (see figure for long-range correlation) that has a complex phase structure in f₂ and is best process as a magnitude spectrum in that direction.

The correlation experiment does not contain a diagonal, unlike most homonulcear experiments. Each proton signal is correlated with a carbon signal. For example in the spectrum (fig. 4) H2' of ethylbenzene (fig. 5) at 1.24 ppm correlates with C2' at 15.69 ppm and H1' at 2.65 ppm correlates with C1' at 28.97 ppm. Those signals in the 1D spectrum that do not correlate do not appear in the 2D spectrum.

Fig. 4. 2D HSQCSI spectrum of ethylbenzene

Fig. 5. Structure of ethylbenzene

The heteronuclear correlation experiments suffer from t₁ noise artifacts that appear as vertical streaks in the spectrum. In addition HSQCSI suffers from a 'useful artifact' (fig. 6) where weak correlations are seen to protons coupled to the proton attached to the carbon. This can be useful when there is strong overlap in the proton spectrum allowing advantage to be taken of the dispersion of the ¹³C chemical shift. The use of shaped pulses suppresses the 'useful artifact' so hard pulses should be used if one wishes to observe the 'useful artifact'. For an example of the use of the 'useful artifact' see the assignment of cholseteryl acetate.

Fig. 6. 2D HSQCSI spectrum of ethylbenzene showing the 'useful artifact'

The ¹H-¹³C coupling constant can be measured by not using coupling (fig. 7). This has the advantage over the 1D carbon coupled spectrum in that the doublets do not overlap.

Fig. 7. Coupled 2D HSQCSI spectrum of ethylbenzene

The HQSCSI correlation spectrum (fig. 8) for 12,14-di^tbutylbenzo[g]chrysene (fig. 9) clearly separates the aliphatic and aromatic regions. From the ¹H spectrum, the proton attached carbons in the ¹³C spectrum are assigned, starting with the ^tbutyls. Their assignment confirms the assumption that ^tbu14 yields a wider peak than ^tbu12. The HMQC spectrum (fig. 10) gives the same result but is slightly weaker because the f₁ resolution is not low.

Fig. 8. 2D HSQCSI spectrum of 12,14-di^tbutylbenzo[g]chrysene

Fig. 9. 12,14-di^tbutylbenzo[g]chrysene

Fig. 10. 2D HMQC spectrum of 12,14-di^tbutylbenzo[g]chrysene

The ¹³C resolution is a limiting factor in the two spectra above. This can be resolved by acquiring the spectrum over a restricted ¹³C range (fig. 11). However, signals falling outside the region of interest fold, are out of phase, may not be completely decoupled in the horizontal direction and have reduced sensitivity. Nonetheless, the resolution in the vertical (f₁) direction is dramatically improved without increasing the acquisition time.

Fig. 11. 2D HSQCSI spectrum over a restricted range of 12,14-di^tbutylbenzo[g]chrysene

The aromatic region (fig. 12) can then be used to assign all the proton-attached carbons.

Fig. 12. 2D HSQCSI spectrum of the aromatic region of 12,14-di^tbutylbenzo[g]chrysene

The heteronuclear coupling constants can be measured from the coupled HSQCSI spectrum (fig. 13).

Fig. 13. Coupled 2D HSQCSI spectrum of 12,14-di^tbutylbenzo[g]chrysene

Short-range HMBC is used for broad signals that would otherwise decay into the noise during the pulse sequence. The spectrum is not phase-sensitive and not decoupled in f₂. Fig. 14 shows the short-range HMBC of gramicidin (fig. 15) even though, its signals are narrow enough to use regular HSQCSIsp2.

Fig. 14. Short-range HMBC spectrum of gramicidin

Fig. 15. Sturcture of gramicidin

HSQC is applied to ¹H-¹⁵N in the same way as shown above for ¹H-¹³C. Fig. 16 shows the ¹H-¹⁵N HSQCSIsp2 spectrum of gramicidin.

Fig. 16. ¹H-¹⁵N HSQCSIsp2 spectrum of gramicidin