Simulations of HYSCORE spectra obtained with ideal and non-ideal pulses

Abstract

The two-dimensional hyperfine-sublevel correlation (HYSCORE) experiment provides correlations between nuclear frequencies belonging to different M _S manifolds. It is most useful for the assignment of electron spin echo envelope modulation (ESEEM) frequencies and for the detection of broad signals. A general expression for the echo intensity in the HYSCORE experiment, obtained under the conditions of ideal pulses exists for an S = 1/2 system. In this work it is extended to the case of non-ideal pulses in order to explore the possibility of generating correlations between nuclear frequencies belonging to the same M _s manifold, referred to as ‘forbidden’. For this purpose, an effective computer program that calculates the HYSCORE spectrum in the frequency domain under conditions of ideal and non-ideal pulses was developed. The program was used to simulate the HYSCORE spectrum of a frozen solution of a Cu(II) complex with a lipophilic bis-hydroxamate ion binder (Cu-RL252) which exhibits ¹⁴N modulations. It is shown that through HYSCORE simulations it is possible to disinguish between two sets of hyperfine parameters which were determined by earlier simulations of a series of orientation-selective ID ESEEM spectra and reproduced the experimental spectra equally well. The experimental HYSCORE spectrum exhibits weak cross-peaks at positions that can be interpreted as correlations within the same M _s manifold. The possibility that such ‘forbidden’ HYSCORE correlations are a consequence of non-ideal pulses and off-resonance effects is investigated, and it is shown that such cross-peaks may appear for relatively long pulses but their relative intensities are negligible. Therefore the features observed in the experimental spectra are due to accidental overlapping of nuclear frequencies in the two different M _s manifolds. Moreover, the simulations indicate that for hyperfine couplings obeying the cancellation condition at X band and for quadrupolar coupling constants up to ∼4 MHz, pulse durations of t _π/2 = t _π ≈ 20 ns, which usually are used under experimental conditions, can well be considered as ideal pulses.