Weak coupling between magnetically inequivalent spins: The deceptively simple, complicated spectrum of a ¹³C-labeled trimethylated amine

Magnetic inequivalence of nuclear spins is well known to cause additional splittings that complicate spectral analysis. Here, we present an extraordinary case of magnetic inequivalence, manifested in the 13-spin system of a ¹³C,¹⁵N-labeled trimethylated amine. All methyl group protons are chemically equivalent due to the molecular symmetry, but not all are magnetically equivalent as they have different ¹J_CH and ³J_CH couplings. In general, spectra of such a large spin system can be expected to be extremely complicated by the presence of hundreds if not thousands of extra lines, caused by the strong coupling between inequivalent nuclei. Surprisingly, the ¹H spectrum presented consists of very few lines, in a pattern of the utmost simplicity. Using sub-spectral analysis we show that this is due to weak coupling between the magnetically inequivalent nuclei, as a consequence of the particular combination of coupling constants. We find that the ⁴J_HH geminal methyl coupling constant is 0.43 Hz and ²J_CC is ∼0 Hz. In addition, we demonstrate that homo-decoupling can be used to transform the spin system to a set of fully equivalent spins, resulting in disappearance of ⁴J_HH-splittings. We believe this curious case is a highly instructive example of magnetic inequivalence. The spectra may be considered deceptively simple, as fewer lines are observed than one would anticipate. At the same time, the spectra are deceptively complicated, as they can very well be approximated by intuitive reasoning.