To start I considered the theoretical sensitivity of an NMR signal. The size of an NMR signal generated by a spin ½ nucleus is proportional to Nγ3Bo2/T, where N is the number of spins in the sample, γ is the gyromagnetic ratio of the nucleus, Bo is the strength of the spectrometer magnet, and T is the temperature.
The gyromagnetic ratio is the magnetic strength of a nuclear spin and defines the rate at which a nucleus spins in a magnetic field. The signal intensity shows a cubed dependence on γ because it contributes in three ways. Firstly, the population difference between energy levels is proportional to γBo. Secondly, the intensity of the signal is proportional to the magnetic strength of the nucleus, γ. And thirdly, the intensity is proportional to the rate at which the spin precesses, which is γBo. Thus, γ is the major determinant of NMR signal intensity.
In real samples we have also to account for the fact that the isotopes that are measured do not compose all of the spins present in a sample. For example, while 1H makes up nearly all hydrogen atoms, 13C is only just over 1% of carbon atoms. To compare the sensitivity of different nuclei a term know as receptivity is calculated as the product of γ3 and the natural abundance. Receptivity is normally given relative to 1H or 13C. The table below lists γ, natural abundance and receptivity for 1H, 13C and 15N and shows 13C is about 6000 times less sensitive than 1H, and 15N is roughly 50 times less sensitive than 13C.
| Nucleus | γ (106 rad.s−1.T−1) |
Natural abundance (%) |
Receptivity (relative to 1H) |
|---|---|---|---|
| 1H | 267.522 | 99.9885 | 1.000 |
| 13C | 67.283 | 1.07 | 1.7x10-4 |
| 15N | -27.126 | 0.364 | 3.8x10-6 |
The receptivity listed above is a measure of the signal intensity we would expect for direct detection. The HMBC experiment, however uses polarization transfer to transfer the population difference of 1H to the heteronucleus. This eliminates one of the γ terms in the signal intensity expression leaving intensity proportional to γ2. Now in an experiment, signals are measured relative to noise so to determine sensitivity we have to account for noise intensity as well. In NMR, noise intensity approximates the square root of the detected frequency. Thus, the signal to noise ratio in the HMBC is proportional to γ2/√γ. If we use the γC / γN ratio in this expression and account for the difference in natural abundance we find the 15N HMBC should be
[(67.283/-27.126)2 / √(67.283/-27.126)] x 1.07/0.364 =
11.5
times less sensitive than the 13C HMBC.
For an experimental test I recorded 13C and 15N IMPACT-HMBC spectra of a saturated solution (~100mM) of strychnine in CDCl3. The same number of scans (16), t1 increments (256) and sweep widths (12 and 250 ppm) were used. Both experiments were optimized for 8 Hz long range coupling. The range for one bond coupling to filter out was set to 125-165 Hz in the 13C experiment and 50-150 Hz in the 15N. The total time for both experiments was 33 minutes. The spectra were processed identically and are shown below.
As expected there are a lot more correlations in the 13C spectrum than the 15N. In fact there are more correlations than expected in both spectra. The sample had degraded producing a mixture of compounds. Still, the 15N HMBC shows how one can easily determine the number of nitrogen atoms present by counting the number of different 15N resonances, in this case four.
To assess the sensitivity of the experiments I extracted rows from each spectrum through peaks that I could identify as belonging to the intact strychnine and measured the signal to noise using a 1000 Hz region for the noise. For the 15N HMBC there was only one such peak, N9-H11a, a three bond correlation. For the 13C HMBC I found five three bond correlations. The signal to noise of all six peaks is in the table below with the structure of strychnine beside it.
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The first two 13C correlations have about 12 times the sensitivity of the 15N correlation, matching well with the theoretical estimate. The other three 13C correlations are much weaker though. In hindsight, one might expect the intensities of HMBC correlations are likely to be significantly affected by electron density and bond orientation, making comparisons difficult. For HSQC spectra, though, there should be less variation and the theoretical estimate of a ten-fold difference in sensitivity between 13C and 15N indirectly detected experiments on natural abundance samples should hold.
I discovered your blog when I was searching for estimates of the relative sensitivities for 13C versus 15N HSQC and HMBC spectra. Your estimate sounds logical and is supported by some of Gary Martins work which has indicated that it takes about 100 times longer to get 1H-detectred 15N spectra than the corresponding 13C spectra (e.g. just under one hour versus 34 seconds).
ReplyDeleteHowever, my main reason for writing concerns HMBC spectra. I personally strongly prefer using mixed mode (absolute value along f2 but phase-sensitive along f1) for HMBC processing. As Ad Box first pointed out (JMR, Vol.78, 186 (1988)), mixed mode gives better S/N and f1 resolution, including fortuitous suppression of 1H-1H coupling along f1. I don’t have a copy of the figure on my home computer but, if there is a copy of my recent book (D. C. Burns and W. F. Reynolds, Optimizing NMR Methods for Structure Elucidation: Characterizing Natural Products and Other Organic Compound, Royal Society of Chemistry, 2018) available in the UCSD library, it is Figure 9.6. Mixed mode processing is standard for HMBC on Varian/Agilent spectrometers but apparently only an option on Bruker spectrometers.
Dear Professor Reynolds, thank you for your comment. Its nice to have the 15N sensitivity estimate confirmed from another source.
DeleteI was able to obtain access to your recent book and view the figure you mentioned. The processing scheme you describe and show there is how Bruker recommends processing HMBC spectra and how I have implemented the automated processing here. I agree that it seems to be the best option for processing HMBC spectra currently.
What about the 13C HSQC vs 15N HSQC? or 15N HSQC vs 15N HMBC? Additionally, in Freemans original paper and book he discusses that the sensitivity gains are much greater (in the base INEPT) for 15N than 13C, although it is true that since 15N is so much less abundant/receptive you will not reach the same overall sensitivity. Finally in practice, since small molecules have so many fewer nitrogens, we can set our t1 increments much lower for our 15N, thus saving time, and still access all the information we need.
ReplyDeleteThanks for your comment!
DeleteYou are correct that the lower occurrence of nitrogen compared to carbon means that less resolution is required and less increments can be acquired. I used the same number of increments here to get a fair comparison, but would not recommend doing that in practice.
As for HSQCs, the point of this post was to compare 13C and 15N sensitivity in the HMBC experiment, as this is the 15N spectrum that most of my users will run, but I do mention at the end of the post that the 15N HSQC is likely to be ten-fold less sensitive then the 13C version. In this post I am taking into account the natural abundance of the two isotopes as well as the enhancements due to the gyromagnetic ratios so that users can have an idea of what to expect when they attempt to run an 15N HMBC.
That makes sense! It is good to know, and I am glad this is out there as there is not much else that I have seen.
ReplyDelete