Four-Pulse ELDOR Theory of the Spin ½ Label Pairs Extended to Overlapping EPR Spectra and to Overlapping Pump and Observer Excitation Bands

The current theory of the four-pulse electron double resonance (PELDOR) has been extended to take into account two effects: (1) overlapping of the electron paramagnetic resonance (EPR) spectra of paramagnetic spin ½ particles (spin labels) in pairs and (2) overlapping of the excitation bands by the pump and echo-forming pulses. It has been shown that the PELDOR signal contains additional terms in contrast to the situation considered in the current theory, when the EPR spectra of the spin labels in the pairs and the excitation bands do not overlap. All terms oscillate with the same frequency, which is the characteristic dipolar interaction frequency. The largest additional terms originate from the fact that both spins in pairs can be excited by the echo-forming pulses when the EPR spectra of the partners in pairs overlap essentially. The results of the numerical calculations, which illustrate the possible scale of the effect of these additional terms on the PELDOR signal, are presented.