Simulation of EPR spectra

In a system that enables rotational diffusion of paramagnetic species, the anisotropy of magnetic interactions is subject to a partial or complete averaging, and this results in changes of the EPR line shape. The correlation time of rotational movements, Tr, is related to the viscosity and temperature of the medium in the case of isotropic Brownian diffusion of a spherical molecule, it is given by the equation  

In general, to describe the EPR spectrum in a motional regime, a procedure based on the solution of the stochastic Liouville equation should be used [49-52]. However, in low-viscosity media, a very fast molecular tumbling leads to an averaging of the anisotropic part of the spin Hamiltonian to zero, and the spectrum is composed of narrow Lorentzian lines, and is characterized by 

The coefficient a includes broadening contributions resulting from other mechanisms (e.g., the presence of oxygen or instrumental factors), whereas and s are governed by the anisotropy of the g and A tensors, the viscosity of a medium and its temperature, and the resonance field Bq (thus the microwave frequency the broadening is different in X-band than for example in Q-band) [54]  

If the time dependence of the Hamiltonian H(t) is derived from the interaction of paramagnetic centers with the environment in such a way that the Hamiltonian is defined by a complete set of random parameters Q, and if the time dependence of 12 is a stationary Markov process, then  

Since this is a stationary process, the evolution operator Fq acting on random variables is independent of time and spin variables. When used to describe dynamically averaged EPR spectra, Fq is the operator of rotational diffusion motion, and random variables correspond to Euler angles (Q = a,p,Y). 

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One of the problems to extract structural information from EPR lies in the correct simulation of the experimental spectra. Misra536 reviewed spin Hamiltonians applicable to exchange-coupled Mn complexes, and described techniques for simulation of EPR spectra. Various structural models for the Mm-cluster in PS II were presented. 

Fig. 9.3. Structural parameters used for the simulation of EPR spectra involving weakly coupled S= 1/2/5 = 1/2 systems.

The MM-EPR approach has been used successfully in a number of recent studies [205,206 328 329]. The most novel is that of the solution structure refinement of a dicopper(II) compound of a cyclic octapeptide[205] which is only the second structure of a dicopper(II) compound of this type of biologically important ligand and the first of a metal compound of an artificial cyclic octapeptide. An important development in this area is a new method for the simulation of EPR spectra (SOPHE)[325,326], which allows the simulation of coupled EPR spectra of polynuclear species with more than two metal centers with any electron spin 0, based on sets of parameters similar to those discussed above. 

Electronic absorption and diffuse reflectance spectra (ESDR) were obtained with a "Specord M-40" spectrophotometer. IR spectra were recorded with a "Perkin Elmer FT-IR 1725X" spectrophotometer provided with diffuse reflectance accessory for solid samples. EPR spectra were recorded with a SE/X-2543 spectrometer at 77 K and 300 K. Primary treating and simulation of EPR spectra were carried out by special algorithms using IBM PC/XT type computers. 

Boyd, P.D.W., Smith, T.D., Price, J.H., Pilbrow, Theory and computer simulation of EPR spectra... 

Simulation of EPR spectra in glasses requires use of rather precise Mn(II) EPR lineshapes taking into account distribution of spin-Hamiltonian parameters [5], Only the parameter values restricted to Z) gllaS, gldsS, a will here be considered. The resonance magnetic fields for transitions between states M, m and M-1, m+i, denoted by... 

Figure 47. Computer simulation of EPR spectra of 1% Cr(III) doped into CsAl(S04) measured in the perpendicular and parallel modes of the ER4116 DM dual mode resonator (a) perpendicular mode showing the allowed transitions (b) parallel mode showing the forbidden resonances (c,d) conqmter simulation of (a) and (b), respectively. Computer simulation details are given in Figure 46. Reproduced with permission of Bruker Biospin.

Propagation of spin density matrix and simulation of EPR spectra... 

Simulation of EPR spectra exclusively from single truncated MD trajectories... 

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