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.
(relative to 1H)
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 = 11.5times 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 bound 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.
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.