Abstract

This dissertation is devoted to the subject of computations for pulse EPR by solving the Liouville von Neumann equation in Liouville space in the presence of relaxation, providing a comprehensive theoretical treatment, including a detailed description of relaxation processes.
The algorithm is illustrated here to simulate SECSY and echo-ELDOR signals for an electron-nuclear spin coupled system (electron spin S=1/2; nuclear spin I=1/2) in an irradiated malonic-acid crystal, taking into account spin-phonon modulation. The simulated results so obtained are compared with the experimental results of Lee et al. (1993). The experimental and simulated spectra are found to be in reasonably good agreement.
In addition, the developed algorithm is used to simulate the spectra for a specific case of the electron-electron dipolar interaction of two nitroxide radicals, each with electron spin S=1/2, nuclear spin I=1/2, for a proposed experiment, intended for distance measurements. The Pake doublets in the Fourier transform of both the signals calculated with and without relaxation correctly indicate the spacing of 10 MHz of dipolar coupling as assumed in the simulation.
This algorithm is also extended to calculate the effect of relaxation due to fluctuation of spin-Hamiltonian parameters by phonon modulation (Freed and Fraenkel, 1963; Slichter, 2013). From a comparison of the Figures showing the simulated SECSY and echo-ELDOR signals for an electron-nuclear spin-coupled system (S = I = ½) in an irradiated malonic acid crystal as calculated for τ_c=〖10〗^(-5),〖10〗^(-6),〖10〗^(-7) and the fluctuation ∆(SHP)=〖10〗^ %,1%,0.1% of their static values as fitting parameters with the experimental results of Lee et al. (1993), it is seen that for the two cases considered (SECSY and echo-ELDOR) the best agreement is obtained for the following ranges: τ_c=〖10〗^(-6) s - 〖10〗^(-7) s and ∆(SHP)=0.1 % - 1.0 %. The value of τ_c~〖10〗^(-7) s as calculated by Freed (1965) is found to be in the range of values found here that provide a good agreement of the calculated spectra with the experimental ones. In the light of these observations, it appears that the fluctuation model considered here, may indeed be refined further to reproduce the simulations to be in satisfactory agreement with the experiment.