EPR simulation

In powder EPR simulators we use the orientation of the static-field vector B with respect to the molecular xyz-axes system as the definition of molecular orientation. The orientation is defined in terms of the polar angles 0, direction cosines as defined previously in Equation 5.3. To solve Equation 8.17 we have to define the direction cosines k, of B, in terms of the direction cosines li of B. 

A combination of the two techniques was shown to be a useful method for the determination of solution structures of weakly coupled dicopper(II) complexes (Fig. 9.4)[119]. The MM-EPR approach involves a conformational analysis of the dimeric structure, the simulation of the EPR spectrum with the geometric parameters resulting from the calculated structures and spin hamiltonian parameters derived from similar complexes, and the refinement of the structure by successive molecular mechanics calculation and EPR simulation cycles. This method was successfully tested with two dinuclear complexes with known X-ray structures and applied to the determination of a copper(II) dimer with unknown structure (Fig. 9.5 and Table 9.9)[119]. 

Another disadvantage of the small, hydrophilic agents is that they tumble very rapidly in the extracellular fluid. In water at 25 °C, for example, Gd-DTPA has a rotational correlation time (rR) of 58 ps as determined by the fitting of NMRD data [3], and 105 ps by EPR simulation in the VO++-DTPA analog [4]. This very rapid motion dominates the relaxivity of the PCA in the frequency range of typical clinical interest (42-63 MHz). The reasons for this dominance of rR can be traced to the fact that small Gd3+ chelates like Gd-DTPA have a relaxivity at clinical frequencies that is determined predominantly by an inner sphere process for Gd-DTPA at 50 MHz, Chen et al. calculate that the relaxivity in water is 43 % inner sphere, 25 % second sphere, and 32 % outer sphere [4]. In turn, the inner sphere contribution to relaxivity is often modeled by the Solomon-Bloem-bergen equations [5,6]... 

Fig. 6. EPR simulation of an octahedrally co-ordinated copper(II) centre in the field range 0.1-12 T, calculated with the following parameters 7ww = 70cm-1, Af = —200 cm-1, Af = — 2.3 cm-1, A = — 50 cm-1 lODq = 10 000 cm-1,...

Figure 3 Energy-level diagram and corresponding EPR signals at 9.6 GHz (X-band) with maximized resolution for an unpaired electron in an imposed magnetic field that interacts with a) a proton (nuclear spin / = 1/2), b) a nucleus (/= ), and c) a nucleus in which the energy levels are additionally split by a nearby proton. The spectra were produced by the EPR simulation program SimFonia for illustration of the hyperfine splitting purpose.

Simfonia EPR simulation programme, www.bruker-biospin.com/epr software.html... 

This work was supported by grants from the Swedish Natural Science Research Council, the A. and M. Ax son Johnson Foundation, and fellowships to A. Haddy from the American-Scandinavian Foundation and the University of Michigan. We would like to thank 0. Hansson for use of the EPR simulation program, and R. H. Sands and W. R. Dunham for helpful discussion. 

Derived from EPR simulations using the ENDOR data. 

From EPR simulations in connection with the ENDOR and ELDOR data [69Hydl]. 

The Sophe tab (Fig. 29) allows the user to input various parameters required for the computational calculation, definition of the SOPHE Grid ( 3.1), and determination of the transition probability (selection rules to be used). In the Calculation Panel, matrix diagonalization is currently the only method available for performing continuous wave and pulsed EPR simulations. The field segmentation algorithm... 

The basic CW EPR simulation involves the search for the resonant field position, Bi, for each transition, i. The intensity, and linewidth, o) are calculated and with the resonant field define the peak Bj, Ij, crj. The simulated spectrum is then generated by adding each peak to the spectrum using an appropriate lineshape function. 

The eft parameters obtained this way in D-band experiments were quite close to those later obtained by CW-EPR at 240 GHz (see Table 2) [35]. The latter work, however, did not introduce any physical model to relate the eft parameters with the stracture of the complexes, and the EPR simulations were based, as we already mentioned, on formal separate Gaussian distributions of D and E. 

The SLE approach was developed further and adapted for EPR simulations by Freed and co-workers. The FP-SLE equation describes a quantum mechanical spin system S embedded in a classical lattice where the degrees of freedom are described by a FP equation. The SLE is defined as ... 

The seeond so-called trajectory based approach, that has been employed for EPR simulations, is based on the Liouville von Neumann equation (LvN) in the semi-classical approximation, often called the Langevin form of SLE. This method was first introdueed for EPR simulations by Robinson and co-workers in 1992. In this approach the SLE is transformed into a system of coupled stoehastie differential equations with explieit time dependence in the spin-lattiee coupling of the Liouvillian ... 

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