Electron spin echo envelope modulation amplitudes

Previous lower-frequency electron spin echo envelope modulation (ESEEM) studies showed a histidine nitrogen interaction with the Mn cluster in the S2 state, but the amplitude and resolution of the spectra were relatively poor at these low frequencies. With the intermediate frequency instruments we are much closer to the exact cancellation limit, which optimizes ESEEM spectra for hyperfine-coupled nuclei such as 14N and 15N. We will report the results on 14N and 15N labeled PSII at these two frequencies, along with simulations constrained by both isotope datasets at both frequencies, with a focus on high-resolution spectral determination of the histidine ligation to the cluster in the S2 state. 

Electron spin echo spectroscopy (ESE) monitors the spontaneous generation of microwave energy as a function of the timing of a specific excitation scheme, i.e. two or more short resonant microwave pulses. This is illustrated in Fig. 7. In a typical two-pulse excitation, the initial n/2 pulse places the spin system in a coherent state. Subsequently, the spin packets, each characterized by their own Larmor precession frequency m, start to dephase. A second rx-pulse at time r effectively reverses the time evolution of the spin packet magnetizations, i.e. the spin packets start to rephase, and an emission of microwave energy (the primary echo) occurs at time 2r. The echo ampHtude, as a fvmction of r, constitutes the ESE spectrum and relaxation processes lead to an irreversible loss of phase correlation. The characteristic time for the ampHtude decay is called the phase memory time T. This decay is often accompanied by a modulation of the echo amplitude, which is due to weak electron-nuclear hyperfine interactions. The analysis of the modulation frequencies and ampHtudes forms the basis of the electron spin echo envelope modulation spectroscopy (ESEEM). 

The magnetic moment of the unpaired electron spin of the spin-label interacts with magnetic moments of the nearby nuclear spins. In solids, these interactions result in the appearance of allowed and forbidden transitions for the electron spin. Because these transitions share the same energy levels, microwave pulses simultaneously excite both types of transition. This results in modulation of the echo amplitude when the time delay between pulses is varied. This phenomenon is called Electron Spin Echo Envelope Modulation, or ESEEM. 

Illustration of modulation of two pulse electron spin echo decay envelope. Microwave pulses 1 and 2 separated by the time x produce the echo signal at time x after pulse 2. As x is increased the echo amplitude changes and traces out an echo envelope which may be modulated. 

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

The physical origins of the effect can be illustrated from Figure 2, which shows the energy level scheme for an I = 1 nucleus, such as coupled to an S = 1/2 electron spin. In the case considered here (i.e., the electron-nuclear interaction, the nuclear Zeeman interaction, and the nuclear quadrupole interaction, all of the same order), microwaves can induce both allowed and semi-forbidden transitions between states in the Mj = 1/2 manifold (a) and the Ms = - 1/2 manifold (/ ). Simultaneous excitation of both kinds of transitions by the echo generating microwave pulses gives rise to interference effects, which manifest themselves as variations in the echo amplitude and thus cause the modulation of the echo envelope. Where a number of nuclei are coupled to the same electron spin, the level scheme becomes more complicated, but it is possible to factor out contributions due to coupling with each nucleus in the overall modulation pattern. If v(U l2>" n) is the modulation function due due to coupling with n nuclei, then... 

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