On the Connection of High-Resolution NMR Spectrum Mirror Symmetry With Spin System Properties

TL;DR

This paper establishes a link between high-resolution NMR spectrum mirror symmetry and specific properties of the underlying spin system, including frequency positioning and J coupling matrix symmetry.

Contribution

It identifies necessary conditions for spectrum symmetry related to spin resonances and J coupling matrix symmetry, validated through theoretical spectrum calculations.

Findings

Spectra symmetric about { u}0 require symmetric spin frequencies.

J coupling matrix must be symmetric about the secondary diagonal.

Theoretical spectra for 4-, 5-, and 6-spin systems confirm the correlation.

Abstract

A correlation between the symmetry of NMR spectra, including higher-order spectra, and the properties of the spin system has been established. It is shown that for a spectrum to be symmetric about the mid-resonance frequency ({\nu}0), two conditions must be satisfied: the resonant frequencies of the spins must be symmetrically positioned about {\nu}0, and the J coupling matrix must be symmetric about the secondary diagonal. The results were validated by calculating theoretical spectra for 4-, 5-, and 6-spin systems.