Weighted AnX multiplets

Abstract

That the NMR transition of a spin-1/2 nucleus is split into n evenly spaced lines by indirect dipole–dipole (J) coupling to n magnetically equivalent nuclei, whose successive amplitudes follow the nth row of Pascal’s triangle, is an elementary result in NMR. Described here are a family of less well known multiplet structures with different amplitudes for the evenly spaced lines. The amplitudes can be derived from the nth row of Pascal’s triangle by weighting the corresponding value of the row by z or z2, where z is related to the summed magnetic quantum number of the magnetically equivalent spins. z1-multiplets have been described in INEPT experiments. A z2-multiplet can be indirectly observed in HSQC experiments when the decoupling pulse during t1 is removed, i.e., an F1-coupled HSQC. While not difficult to generate and despite some reported usefulness, to the best of our knowledge, z2-multiplets have not been rigorously described in previous literature.