Pulsed EPR simulations

The simulation of pulsed EPR spectra involves calculating the evolution of an observable (O Eq. (13)) during the microwave pulses, radiofrequency pulses, and free evolution periods that comprise the pulse sequence. The signal in an arbitrary pulsed EPR experiment can be simply described in superoperator notation [8,50]  

In most experiments fire initial density matrix (/od) is the equihbrium density matrix (p) with diagonal elements given by the Boltzmann population of the energy levels in the eigenbasis of the static Hamiltonian  

The transverse magnetization M, My) are proportional to Sx, Sy, respectively, and are determined by the g value in the x-y plane, the microwave power, and other experimental factors. 

Coherence transfer pathways provide a way of visualizing the transfer of magnetization during a pulse sequence and in general an element of the density matrix undergoes the following transformation  

In the eigenbasis of the static Hamiltonian the superpropagator for each free evolution period is diagonal. The time dependence of each element in the density matrix (p) is simply given by 

---

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... 

Observation of the stereoselective manner of chiral substrates binding to these asymmetric metal-salen complexes was not confined to [VO(l,3)] or chiral epoxides. Recently we showed how asymmetric copper salen complexes, [Cu(l)] and [Cu(4)] (Fig. 1), could also discriminate between chiral amines (R-IS-methylbenzylamine, MBA) as evidenced by multi-frequency CW and pulsed EPR, ENDOR, HYSCORE and DPT [45]. The discrimination of the MBA enantiomers was directly observed by W-band EPR. By simulating the W-band EPR spectra of the individual diastereomeric adduct pairs (i.e. R,R -[Cu(4)]+R-MBA and R,/ -[Cu(4)]-l-5-MBA), accurate spin-Hamiltonian parameters could be extracted for each adduct. The EPR spectmm of the racemic combinations (i.e. ra -[Cu(4)]+rac-MBA) was then simulated using a linear combination of the g/A parameters for the homochiral (R,R -[Cu(4)]+R-MBA) and heterochiral (R,R -[Cu... 

Representations in the Linewidth Parameter Form (Fig. 19) include orthorhombic, axial, and isotropic symmetries. Units inelude MHz, 10 em , and nanoseeonds (nsec), the latter being more appropriate for pulsed EPR speetra. For pulsed EPR spectra we also include the nuclear spin-spin relaxation time T. Addition of a more a generalized linewidth model involving a distribution of spin Hamiltonian parameters and positional coordinates (bond lengths and orientations) is forthcoming. The approach will be similar to that employed for the D- and. E-strain linewidth model in the XSophe-Sophe-XeprView computer simulation software suite. 

The SOPHE grid ( 3.1) is defined by the number of orientations between flic z and x global coordinate system. The number of gamma steps, used in flic simulation of pulsed EPR experiments, is used to calculate the transition probabilities of the echo intensities. 

Orientation-selective experiments involve performing a pulsed EPR experiment, such as HYSCORE, as a function of orientation (magnetic field). The orientation-selective HYSCORE Experiment will provide a four-dimensional dataset from which die complete hyperfine matrix for the remote nucleus can be determined. Subsequently the intemuclear distance and orientation of die nucleus from the electron spin can be determined from die anisotropic components of the hyperfine matrix. Computer simulation of an orientation-selective HYSCORE Experi-... 

The above approach to the simulation of pulsed EPR spectra allows the simulation of pulsed EPR spectra from not only isolated paramagnetic samples containing a single unpaired electron but also from samples containing multiple unpaired electrons, for example, high-spin Fe(III) centers found in cytochromes and nonheme iron proteins, and coupled centers, such as the type III copper-containing enzymes and the binuclear metallohydrolyases. 

In principle, the technique can also be extended to the fitting of pulsed EPR spectra using the frequency domain approach [62]. Each peak in the ESEEM spectrum is given by one or more frequencies, a complex intensity, and a linewidth. Derivatives of the ESEEM frequencies with respect to each of the spin Hamiltonian parameters can be calculated and utilized in an identical fashion to that used for CW spectra simulations. 

Spin-polarized mobile hydrogen and deuterium atoms were detected in silica glass containing 1200 ppm of OH or OD groups by the time-resolved pulsed EPR technique.The EPR spectra of the H/D atoms indicate the occurrence of CIDEP in reactions of H/D atoms with radiolytically induced metastable spin centres. The CIDEP effects in silica glass exhibit unusual polarization patterns, temperature dependence and dependence on hfs constants. A Monte Carlo lattice model is introduced to simulate the RPM spin polarization in amorphous silica. Although the model does not explain all the features observed, it indicates where peculiarities of CIDEP in disordered solids may originate. 

Most operations of the instrument are under computer control. The spectrum is recorded as a series of data points, along a linear axis of magnetic field. The signal-to-noise ratio can be improved by repetitive scanning and signal averaging. Fourier transform techniques are normally only used for analysis of pulsed EPR experiments. There is a range of different software for analysis of the spectroscopic data, in particular for simulation. 

Fig. 8 TREPR spectrum of a photo-generated radical pair in X. laevis cryptochrome-DASH. (a) Complete TREPR data set of X. laevis cryptochrome-DASH measured at 274 K [109]. (b) TREPR spectrum of wild type (solid blue curve) and W324F (solid green curve) X. laevis cryptochrome-DASH recorded 500 ns after pulsed laser excitation. The dashed curve shows a spectral simulation of the EPR data of the wild-type protein using parameters described in the text and in [109]. (c) The conserved tryptophan triad of X. laevis cryptochrome-DASH. Figure taken from [125]...

We expect significant advances in both CW and pulsed methods for determining distances between spins. Limitations of computer power available to most labs have inhibited using exact simulations of CW EPR spectra. There... 

For the MRI agents listed in Table 2 the values of D/gP are well within 100 mT. Therefore, the -1/2 o 1/2 EPR transition can be readily used for ENDOR measurements of these complexes at the. Bo > 3 T, which corresponds to the operational mw frequencies Vmw > 84 GHz (W-band). The analysis of the ENDOR spectra at such high-field conditions can be performed without taking account of the cfi. However, for most of the MRI agents even the Ka band (Bo 1 T, Dlg B < 0.1) pulsed ENDOR works reasonably well, although in this case it is better if the cfi corrections are taken explicitly into account in the numerical simulations. The... 

---