Ligand protons in a frozen solution of copper histidine relax via a $T1e$-driven three-spin mechanism

Davies electron-nuclear double resonance spectra can exhibit strong asymmetries for long mixing times, short repetition times, and large thermal polarizations. These asymmetries can be used to determine nuclear relaxation rates in paramagnetic systems. Measurements of frozen solutions of $copper(L-histidine)2$ reveal a strong field dependence of the relaxation rates of the protons in the histidine ligand, increasing from low $(g‖)$ to high $(g⊥)$ field. It is shown that this can be attributed to a concentration-dependent $T1e$-driven relaxation process involving strongly mixed states of three spins: the histidine proton, the Cu(II) electron spin of the same complex, and another distant electron spin with a resonance frequency differing from the spectrometer frequency approximately by the proton Larmor frequency. The protons relax more efficiently in the $g⊥$ region, since the number of distant electrons able to participate in this relaxation mechanism is higher than in the $g‖$ region. Analytical expressions for the associated nuclear polarization decay rate $Teen−1$ are developed and Monte Carlo simulations are carried out, reproducing both the field and the concentration dependences of the nuclear relaxation.