The decay of the refocused Hahn echo in double electron–electron resonance (DEER) experiments

Double electron–electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length [Formula: see text] , where [Formula: see text] and [Formula: see text] are the two time delays. In DEER, the value of [Formula: see text] is determined by the longest inter-spin distance that needs to be resolved, and [Formula: see text] is adjusted to maximize the echo amplitude and, thus, sensitivity. We show experimentally that, for typical spin centres (nitroxyl, trityl, and Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given [Formula: see text] is obtained neither at very short [Formula: see text] (which minimizes the pulse sequence length) nor at [Formula: see text] (which maximizes dynamic decoupling for a given total sequence length) but rather at [Formula: see text] values smaller than [Formula: see text] . Large-scale spin dynamics simulations based on the coupled cluster expansion (CCE), including the electron spin and several hundred neighbouring protons, reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.