Proton Magnetic Resonance Spectra of a Three-Spin System: Oxalic Acid Dihydrate

Theoretical proton magnetic resonance spectra have been fitted to experimental room‐temperature spectra of a single crystal of oxalic acid dihydrate by least‐squares methods. The theoretical spectrum used is the seven‐line spectrum calculated by Andrew and Bersohn for a magnetic dipole–dipole coupled three‐spin system with each line in the spectrum broadened by a Gaussian function. The three‐spin system consists of two protons from a water molecule and one proton from a hydroxyl group. From the marked temperature dependence of the spectrum in certain orientations it is concluded that the water molecules are flipping fast at room temperature equalizing the coupling between the hydroxyl proton and each of the two protons in the water molecule. The theoretical line shapes are found to be in good agreement with the experimental spectra in crystal orientations where the fine structure is well resolved. From the analysis the interatomic distances and the orientation of the three‐spin triangle in the unit cell are determined. The intramolecular proton–proton distance is found to be 1.595 ± 0.004 Å, and the distances to the hydroxyl proton 2.046 ± 0.010 Å and 2.131 ± 0.017 Å. All distances are uncorrected for atomic vibration. The intramolecular distance is equal to the length as usually found in NMR studies of hydrates, and the other two distances are within the experimental uncertainty equal to the corresponding distances found in a neutron diffraction study. The broadening parameter $\beta$ , which is a measure of the coupling between the three‐spin systems, is found to be smaller than expected from the calculated Van Vleck second moment.