Time domain simulation of Gd³⁺-Gd³⁺ distance measurements by EPR

Gd³⁺-based spin labels are useful as an alternative to nitroxides for intramolecular distance measurements at high fields in biological systems. However, double electron-electron resonance (DEER) measurements using model Gd³⁺ complexes featured a low modulation depth and an unexpected broadening of the distance distribution for short Gd³⁺-Gd³⁺ distances, when analysed using the software designed for S = 1/2 pairs. It appears that these effects result from the different spectroscopic characteristics of Gd³⁺-the high spin, the zero field splitting (ZFS), and the flip-flop terms in the dipolar Hamiltonian that are often ignored for spin-1/2 systems. An understanding of the factors affecting the modulation frequency and amplitude is essential for the correct analysis of Gd³⁺-Gd³⁺ DEER data and for the educated choice of experimental settings, such as Gd³⁺ spin label type and the pulse parameters. This work uses time-domain simulations of Gd³⁺-Gd³⁺ DEER by explicit density matrix propagation to elucidate the factors shaping Gd³⁺ DEER traces. The simulations show that mixing between the |+½, -½〉 and |-½, +½〉 states of the two spins, caused by the flip-flop term in the dipolar Hamiltonian, leads to dampening of the dipolar modulation. This effect may be mitigated by a large ZFS or by pulse frequency settings allowing for a decreased contribution of the central transition and the one adjacent to it. The simulations reproduce both the experimental line shapes of the Fourier-transforms of the DEER time domain traces and the trends in the behaviour of the modulation depth, thus enabling a more systematic design and analysis of Gd³⁺ DEER experiments.