Accessing distributions of exchange and dipolar couplings in stiff molecular rulers with Cu(II) centres

Determining distributed exchange couplings is important for understanding the properties of synthetic magnetic molecules. Such distributions can be determined from pulsed dipolar spectroscopy (PDS) data, but this is challenging due to the similar influence of both exchange and dipolar couplings on such data. In this work we introduce two models that aim to identify these two contributions to the spin-spin couplings from frequency-domain PDS data of shape-persistent molecules having either two Cu(ii) ions, or a Cu(ii) ion and a nitroxide radical as the paramagnetic moieties. The first model assumes correlated Lorentzian or Gaussian exchange and dipole-dipole coupling distributions whose parameters are the model's unknowns. The second model relies on prior knowledge of the distance distribution and by performing Tikhonov regularization along the exchange coupling dimension yields the latter distribution model-free. Both models were able to differentiate between the absence and the presence of exchange interaction, to determine the coupling regime (ferro- or antiferromagnetic) and to estimate the distribution shape. In contrast, calculations within the exchange resilient model of the neural network analysis implemented in DeerAnalysis2018 were not able for our data to identify exchange couplings and return correct distance distributions. However, the generic model was able to identify and separate the strongly curved intermolecular background in the relaxation-induced dipolar modulation enhancement (RIDME) experiments. Our analysis revealed that in such systems exchange coupling may be present up to at least 3.3 nm in π-conjugated systems involving Cu(ii)-PyMTA, while it is negligible for distances r ≥ 4.5 nm between Cu(ii) ions and r ≥ 3.8 nm between a Cu(ii) ion and an unpaired electron of a nitroxide radical. Disruption of the π-conjugation between the ligand of the Cu(ii) complex and the nitroxide leads to negligible exchange coupling at distances r ≥ 2.6 nm in the corresponding [Cu(ii)-TAHA]-nitroxide ruler. Overall, for cases with known distance distributions, the presented analysis techniques allow to determine distributions of exchange couplings from PDS data.