Abstract
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 2(τ1+τ2)2(τ1+τ2)<math><mrow><mn>2</mn><mo>(</mo><msub><mi>τ</mi><mn>1</mn></msub><mo>+</mo><msub><mi>τ</mi><mn>2</mn></msub><mo>)</mo></mrow></math>, where τ1τ1<math><mrow><msub><mi>τ</mi><mn>1</mn></msub></mrow></math> and τ2τ2<math><mrow><msub><mi>τ</mi><mn>2</mn></msub></mrow></math> are the two time delays. In DEER, the value of τ2τ2<math><mrow><msub><mi>τ</mi><mn>2</mn></msub></mrow></math> is determined by the longest inter-spin distance that needs to be resolved, and τ1τ1<math><mrow><msub><mi>τ</mi><mn>1</mn></msub></mrow></math> 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 τ2τ2<math><mrow><msub><mi>τ</mi><mn>2</mn></msub></mrow></math> is obtained neither at very short τ1τ1<math><mrow><msub><mi>τ</mi><mn>1</mn></msub></mrow></math> (which minimizes the pulse sequence length) nor at τ1=τ2τ1=τ2<math><mrow><msub><mi>τ</mi><mn>1</mn></msub><mo>=</mo><msub><mi>τ</mi><mn>2</mn></msub></mrow></math> (which maximizes dynamic decoupling for a given total sequence length) but rather at τ1τ1<math><mrow><msub><mi>τ</mi><mn>1</mn></msub></mrow></math> values smaller than τ2τ2<math><mrow><msub><mi>τ</mi><mn>2</mn></msub></mrow></math>. 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.