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 n^th 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 n^th 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.

Keywords: F1-coupled HSQC; INEPT; Multiplets; Pascal’s triangle.