Quantitative analysis of Earth's field NMR spectra of strongly-coupled heteronuclear systems

In the Earth's magnetic field, it is possible to observe spin systems consisting of unlike spins that exhibit strongly coupled second-order NMR spectra. Such spectra result when the J-coupling between two unlike spins is of the same order of magnitude as the difference in their Larmor precession frequencies. Although the analysis of second-order spectra involving only spin-(1/2) nuclei has been discussed since the early days of NMR spectroscopy, NMR spectra involving spin-(1/2) nuclei and quadrupolar (I>(1/2)) nuclei have rarely been treated. Two examples are presented here, the tetrahydroborate anion, BH4-, and the ammonium cation, NH4+. For the tetrahydroborate anion, (1)J((11)B,(1)H)=80.9Hz, and in an Earth's field of 53.3microT, nu((1)H)=2269Hz and nu((11)B)=728Hz. The (1)H NMR spectra exhibit features that both first- and second-order perturbation theory are unable to reproduce. On the other hand, second-order perturbation theory adequately describes (1)H NMR spectra of the ammonium anion, (14)NH4+, where (1)J((14)N,(1)H)=52.75Hz when nu((1)H)=2269Hz and nu((14)N)=164Hz. Contrary to an early report, we find that the (1)H NMR spectra are independent of the sign of (1)J((14)N,(1)H). Exact analysis of two-spin systems consisting of quadrupolar nuclei and spin-(1/2) nuclei are also discussed.