Spin systems nuclear frequency spectra

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). 

If the molecule has dynamic motions on the timescale of the EPR experiment, this motion will lead to relaxation effects on the EPR line. Depending on the timescale and size of these motions, these effects may be observable directly in the cw-EPR spectrum or indirectly by pulsed EPR measurements of the relaxation times. In many cases, different dynamics may simultaneously contribute to the relaxation behavior of the electron spin system, as, for example, vibrational and rotational motion, conformational dynamics, phonon coupling to the frozen solvent, and nuclear spin dynamics. In these cases, it will be difficult to obtain specific information from these relaxation measurements. On the other hand, it is possible to highlight a specific time-scale window by the selection of pulse sequences and microwave frequencies that can lead, in favourable cases, to a direct relation between measured relaxation times and interesting molecular dynamics at the paramagnetic site. In these cases, very interesting molecular dynamical aspects of electron-transfer, catalytic, or photo-reactions, unobservable by other structural methods, can be studied directly by pulse-EPR techniques. 

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

The ID methods described above result in undistorted ESEEM spectra and thus can drastically improve resolution. However, in multinuclear spin systems having strongly coupled nuclei with small gyromagnetic ratios and weakly coupled nuclei with large gyromagnetic ratios, peaks may overlap and die spectrum can be complicated and difficult to analyze. The resolution can be further increased by implementing the HYSCORE experiment where times /] and 2 are ineremented independently [28]. As a consequence of the transfer of nuclear eoherence by the n pulse, this 2D experiment correlates nuclear frequencies from different manifolds. For an 5 = A, I = A spin system and ideal pulses the modulation formula for the HYSCORE experiment can be written as [29]... 

The data recorded as the laser frequency is scanned consists of the fluorscence signal from the PMT, a Doppler-free I2 spectrum and frequency markers from the etalon. The etalon provides a calibration of the frequency scan. The Doppler-free I2 spectra provides an absolute frequency reference used to correct for small laser frequency drifts, separator voltage drifts and to determine the absolute acceleration voltage of the separator for the Doppler shift corrections. We are thus able to record data over long periods of time, e.g. 3 hours, and maintain a reasonable resolution of 100 MHz. Some of the first online data recorded with this system is shown in Figure 2. The overall detection efficiency has been measured to be 1/1000, i.e. one detected photon per 1000 atoms, for the largest transition in the nuclear spin 1/2 isotopes. 

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