Preprints
https://doi.org/10.5194/mr-2025-15
https://doi.org/10.5194/mr-2025-15
05 Dec 2025
 | 05 Dec 2025
Status: this preprint is currently under review for the journal MR.

The Origin of Mirror Symmetry in High-Resolution NMR Spectra

Dmitry A. Cheshkov and Dmitry O. Sinitsyn

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 (ν0), two conditions must be satisfied: the resonant frequencies of the spins must be symmetrically positioned about ν0, and the J‑coupling matrix must be symmetric about the secondary diagonal. The results were validated by calculating theoretical spectra for 3-, 4-, 5-, and 6-spin systems.

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Dmitry A. Cheshkov and Dmitry O. Sinitsyn

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Dmitry A. Cheshkov and Dmitry O. Sinitsyn
Dmitry A. Cheshkov and Dmitry O. Sinitsyn
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Latest update: 05 Dec 2025
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Short summary
This research reveals the hidden rules that connect the perfect mirror-image shape of a high-resolution nuclear magnetic resonance spectrum to the properties of a molecule's nuclear spin system. We found that this symmetry occurs only when specific, balanced conditions are met within the spin system. Testing these rules on various theoretical models confirmed their universal nature, providing a new framework for interpreting molecular symmetry from spectral patterns.
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