Sensitivity of 13C-NMR and indirect measurement

Measurement of 13C-NMR is essential for characterisation of compounds in organic synthesis, however, sensitivity can often be an issue, especially as molecules get larger and quantities get smaller, due to the low natural abundance of the NMR active 13C nuclei.

Standard carbon NMR is ran using a single pulsed experiment with heteronuclear decoupling for the 1H nuclei. This decoupling improves sensitivity by focusing the multiplets into a single sharp peak, with added sensitivity gained due to the nOe. Even with this enhancement, it can still often be difficult to obtain satisfactory spectra without resorting to using a stronger magnet (500 MHz/600 MHz is standard, the use of the 800 MHz spectrometer is prohibitively expensive for routine work) or running thousands of scans (there's a limit to how well this works anyway due to natural drift leading to peak broadening over time).

Unlike the standard 13C-NMR experiment, many 2D experiments such as HSQC are able to record data for 13C by observing the 1H nuclei (this is a huge oversimplification, I realise). This does, of course, lose the data for quaternary carbons, but I believe there are ways to get this data back (DEPTQ and various 2D experiments for example).

Why then are we unable to record 1D heteronuclear NMR using a similar technique?

• I'm not sure I understand the question. If you detect 1H in a 1D experiment, you'll get proton chemical shifts out of it. This doesn't help you if you're interested in 13C shifts, then you have to measure a 2D and we're at the HSQC/HMQC again. – Mad Scientist Jan 7 '17 at 20:18
• Well, yes and no. I'm talking about using/exploiting the 1H, not actually just measuring a proton spectrum. – NotEvans. Jan 7 '17 at 20:20

We are able to record 1D heteronuclear experiments using these techniques, and absolutely do make use of this behaviour as a commonplace method for measuring 1D spectra of low sensitivity nuclei, such as $\ce{^13C, ^15N}$ and $\ce{^29Si}$. However, in order to get frequency information for the insensitive nucleus, we still need to use what is called a direct-detect method, where the nucleus of interest is actually the acquisition nucleus.

The most common method for sensitivity enhancement uses the general class of experiments called INEPT experiments; Insensitive nuclei enhanced by polarization transfer. The DEPT series (DEPT45, DEPT90 and DEPT135) are a sub-class of the INEPT experiment.

The signal of some nuclei can be improved by taking advantage of low power 1H decoupling during the relaxation period to allow nOe transfer to occur. This, as you mention, is typically how $\ce{^13C}$ spectra are recorded, and is why the $\ce{CH3}$ peaks ar much bigger than quaternary peaks. This method cannot be used for nuclei that have a negative magnetogyric ratio, such as $\ce{^15N}$ and $\ce{^29Si}$, as the nOe will actually generate a diminished signal. For these nuclei, the INEPT method is the preferred experiment for acquisition.

The INEPT magnetisation transfer step is at the core of most common 2D sequences, such as the HSQC. It provides a much greater signal enhancement than the nOe, although is strongly dependent on correct calibration of pulses.

• The theoretical maximum sensitivity gain for nOe is $\displaystyle1+\frac{\gamma_\mathrm{S}}{2\gamma_\mathrm{I}}$
• The theoretical maximum sensitivity gain for INEPT is $\displaystyle\left|\frac{\gamma_\mathrm{S}}{\gamma_\mathrm{I}}\right|$

For $\ce{^13C}$, this equates to $\approx 3x$ for nOe and $\approx 4x$ for INEPT. For $\ce{^15N}$, it is $\approx -4x$ for nOe (yep, negative) and $\approx 25x$ for INEPT

Glenn Facey at University of Ottowa has a couple of nice examples of INEPT and DEPT that are well worth looking at.

Both of these classes of experiment (nOE and INEPT) typically rely on interaction with nearby $\ce{^1H}$ signals: nOe is a through space interaction, and INEPT is a through bond interaction. Other nuclear pairs can be used, and many examples such as INEPT using $\ce{^19F-^29Si}$ have been published. The detection of insenstive nucleus environments with no directly attached sensitive nucleus (such as $\ce{^13C}$ quaternary centres) still requires long range coupling, and there are many published long-range INEPT methods.

The 2D HSQC method is an indirect detection method — we get information about the insensitive nucleus by acquiring another nucleus. Equivalent 1D variants of these 2D experiments do exist (so, a 1D HSQC), but they will only give you information about those $\ce{^1H}$ signals that have coupling to $\ce{^13C}$ — they don't provide any information about the $\ce{^13C}$ frequencies, unless you do a selective variant. So, a sel-HSQC will only irradiate a small band of the $\ce{^13C}$ frequency window, and therefore only give $\ce{^1H}$ signals that correlate to a $\ce{^13C}$ nucleus in this band. This is sometimes useful to probe a specfic question of structure, but a very tedious method of stepping through frequency bands of the $\ce{^13C}$ region (which is what a 2D experiment does for you).

For what it is worth, there are a number of cost-effective ways to improve sensitivity without having to fork out the big bucks for an 800. Choice of probe (X-observe, cryoprobe, microprobe) will offer improvements over increase in magnetic field at a fraction of the cost, and Shigemi tubes and micro cell tubes will also provide significant boosts in sensitivity.

You are asking for a free lunch, i'm afraid.

HSQC gives you a carbon spectrum via 1H-detection, but it is only gained mathematically afterwards, and you have to record many 1H spectra (with incremented INEPT mixing time) for it.

If you do it fast, with too few mixing time increment steps, you get a carbon spectrum with a lousy resolution, instead of lousy S/N if you measure too few scans in direct detection.

The point about HSQC is that you get a correlated heteronuclear 2D spectrum in a reasonable amount of time, much faster than C-H COSY.