Two-pulse double quantum and five-pulse double-quantum modulation sequences in EPR: Coherence transfer and distance measurements

Abstract

Double-quantum (DQ) coherence transfers and signals in two-pulse DQ and five-pulse DQM (double quantum modulation) pulsed EPR sequences, utilized for orientation selectivity and distance measurements in biological systems using nitroxide biradicals, have been calculated here for X-band (9.26 GHz) pulsed EPR (electron paramagnetic resonance) using a rigorous numerical algorithm. It is shown, in general, that both, a finite (selective) pulse, rather than an infinite (non-selective) pulse, and the dipolar interaction between the two nitroxide radicals, are needed to produce non-zero coherence transfers in 0→2 and 2→-1 transitions. Furthermore, the simulations show that there exits orientational selectivity, as exhibited by the large value of the coherence transfer probability, T0→2, for those coupled nitroxides, whose dipolar axes, relative to the external magnetic field, are oriented symmetrically, within a small region, within about ±10° away from the magic angle θ = 54.74° and its supplementary angle θ = 125.26°. It increases monotonically as the amplitude of the irradiation field (B1) decreases. The magnitudes of the coherence transfers in the transitions 0→2 and 2→-1 are found to be about the same. They depend upon both, the amplitude of B1 and the duration of the pulse. As well, they increase significantly with increasing d, as found for d=10.0, 20.0, 30.0 MHz, where d=2D/3, with D being the dipolar-coupling constant. The numerical calculations, using Monte-Carlo averaging, reveal that the Pake doublets occur at ±3d/4$ and ±d for the two-pulse DQ and the five-pulse DQM sequences, respectively, as calculated for d=0.5, 7.0, 10.0, 20.0, 30.0, 40.0, 50.0 MHz. It is seen that for d = 0.5 MHz, considered here, for which the modulation depth can be measured within the dead-time, the dipolar depth of the modulation is ≈100%, which indicates that the DQ and DQM sequences are more efficient for distance measurements as compared to other techniques, e.g., DEER (double electron-electron resonance). The numerical algorithm for the five-pulse DQM sequence presented here is exploited to provide a good fit to the published experimental data. Simulations were also carried out at Ku-band (17.6 GHz), which showed that there occur no orientational selectivity at this band, unlike that at X-band. On the other hand, the signals and their Fourier transforms are found to be relatively more intense at Ku-band