Weighted AnX multiplets

Brennan J Walder; Keith J Fritzsching

doi:10.1016/j.jmr.2022.107353

Weighted A_nX multiplets

J Magn Reson. 2023 Feb:347:107353. doi: 10.1016/j.jmr.2022.107353. Epub 2022 Dec 14.

Authors

Brennan J Walder¹, Keith J Fritzsching²

Affiliations

¹ Sandia National Laboratories, 1611 Innovation Pkwy SE, 87123 Albuquerque, NM, USA. Electronic address: bwalder@sandia.gov.
² Sandia National Laboratories, 1611 Innovation Pkwy SE, 87123 Albuquerque, NM, USA. Electronic address: kjfritz@sandia.gov.

PMID: 36571906
DOI: 10.1016/j.jmr.2022.107353

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.