Calculation of pulsed EPR DEER signal for two coupled Gd3+ ions by dipolar interaction using rotating frames

Abstract

A method, based on the use of rotating frames, to either consider only the rotating frame of the observer spin, which is the main rotating frame, or to consider only the rotating frame of the pump spin, used only during the application of the pump pulse, has been exploited to calculate accurately the four-pulse EPR (Electron Paramagnetic Resonance) DEER (Double Electron-Electron Resonance) signal for two Gd3+ ions, coupled by the dipolar interaction in a biradical in a biological system, including the zero-field splitting of each Gd3+ ion. It has been illustrated here by calculating the four-pulse DEER signals at W-band for three values of the dipolar constant: ωdd=0.63MHz, ωdd=0.49MHz and ωdd=0.39MHz, corresponding to the range of typical Gd3+−Gd3+ distance (r) values, r=4.36 nm, 4.73 nm, 5.10 nm, respectively, in a sample of Gd-DOTA.