Simulation of ESR spectra

Hyde, J. S. and W. K. Subczynski. 1984. Simulation of ESR spectra of the oxygen-sensitive spin-label probe CTPO. J. Magn. Reson. 56 125-130. 

For the simulation of ESR spectra one has to solve the spin Hamiltonian of Eq. (10). The easiest way to do this is to regard all the different terms in the spin Hamiltonian as small compared with the electron Zeeman interaction and to use perturbation theory of the first order. The Zeeman term can easily be solved within the eigensystem of the Sz operator (in the main axis system of the g-tensor or S 2=5 for isotropic cases), for instance in the isotropic case ... 

Note Answers can be formally obtained by using formulae in Appendix A4.1. The formulae apply also in the quantum mechanics treatment employed in the first general program for the simulation of ESR spectra of... 

Dolotov, S. V Roldughin, V. I. Simulation of ESR spectra of metal nanoparticle aggregates. Russ. Colloid J., 2007,69,9-12. 

In the latter case, the liquid-solution CW-ESR spectrum is very informative because its shape depends on several structural and dynamic parameters characterizing the double-labeled peptide. For this reason, recent theoretical studies have been focused on the development of effective and flexible computational approaches for the complete a priori simulation of ESR spectra of complex systems in solutions [93]. 

With ESR spectroscopy, open-shell species can be observed and characterized as long as their total spin differs from zero. With variable-temperature ESR spectroscopy, it is possible to deduce whether the observed multiplicity is a thermally populated excited state or is the ground state [69]. From such experiments, the T-S splittings of a variety of biscarbene and bisnitrenes have been determined. ESR spectroscopy is very sensitive to paramagnetic species, and because it does not see any singlet impurities or by-products, it is relatively easy to pick out the desired signals. At the same time, analysis of ESR spectra is not trivial and special simulations are required for their interpretation. 

Since identical ESR spectra were obtained on U.V. irradiation at liquid nitrogen temperature of PVC, copolymer of vinyl chloride with vinyl bromide and 3-chloropentane it is concluded that this radical is the "Radical I." This radical may play an important role in PVC degradation. To further firmly establish the identity of this radical, theoretical analysis of "Radical I" and computer simulations of ESR spectrum were performed. The polymer radical ESR spectra are very sensitive to the conformation of the chain. The characteristic chain conformation of vinyl syndiotactic sequences in solution has been shown (23) to consist chiefly of trans-trans groups, separated by gauche units . .. (TT)X (GG)i (TT)y (GG)y (TT)Z. .. 

In order to simulate the ESR spectra of these radicals twist had to be allowed for in the bonds to the phenyl groups. For 149, the 2(5)-phenyl twist is estimated at ca. 20° and the 3(4)-phenyl twist at ca. 60° for 150, coplanarity of the 2-phenyl and imidazole rings is indicated while the 4(5)-phenyl groups are twisted 30° from coplanar.492 Concordant results have been obtained for tetraarylpyrrolyl radicals by Broser et al. who studied the variation of the 0-factor with substituents.493... 

Many research groups have observed TR ESR spectra under photolysis of DAR, IRG651, TPO, and BAPO (Scheme 12.1) and of other Type 1 Pis. Analysis of ESR spectra of the primary radicals formed and their spin adducts allows determination of radical structure. Computer simulation with user-friendly software was used to elucidate the radical structure. 

Figure 7. ESR spectra of 5.4 x IQ- M (C6H5Cl)2Cr+ in DMSO at 22 °C. (a) No added (CeHsClljCfO. (c) Added ca. 0.04 M (CgHsClljCr". (e) Added ca. 0.08 M (C6H5Cl)2Cr . (g) added ca. 0.1 M (Cf H5Cl)2Cr . Panels (b), (d), (f), and (h) are computer simulations of the spectra immediately above them. Reprinted with permission from T, T.-T. Li and C. H. Brubaker, Jr., J. Organomet. Chem. 1981, 216, 223. Copyright 1981 Elsevier.

The experimental parameters that are fitted in the calculations are the 3 d-d transitions and the ESR parameters, g, g and A . is not fitted, because the accuracy of the experimental values is too low. The reason is that the computer program that we used to simulate the ESR spectra, does not include forbidden transitions, which are known to be important in the perpendicular region of the spectrum (12-14,25). 

Figure 6. Experimental (upper) and simulated (lower) ESR spectra of an aqueous solution of anion at pH 5...

Abstract The theoretical principles of the ESR technique and its application in the field of molecular sieve science are reviewed. The first part of this chapter focuses on the basic principles and instrumentation of the ESR, ENDOR, ESE and ESEEM techniques. Special attention will be given to spectral simulation and quantitative analysis of ESR spectra. In the second part, the general features of the ESR spectra of transition metal ions and paramagnetic clusters in molecular sieves are presented and discussed. In addition, some remarks will be made about the use of paramagnetic molecules, such as NO. 

This review deals with both the theoretical and practical aspects of the use of ESR spectroscopy in molecular sieve science. No attempt has been made to compile an exhaustive list of references to all the work that has been published so far. Rather, we have selected what, we feel, are the most important developments and also, where possible, we have drawn examples from our own work. In a first part, the ESR technique and its extensions such as ENDOR and ESEEM, will be highlighted with special emphasis on the principles of the techniques and the instrumental requirements. Attention will also be given to spectral simulation and to quantitative analysis. In a second part, the general features of ESR spectra of transition metal ions in molecular sieves are analyzed. In addition, some remarks will be made on paramagnetic metal clusters and on paramagnetic molecules. The chapter closes with general conclusions and an outlook into the future. For detailed explanations and discussions-in-depth, we refer to several excellent text books [1-9] and review papers [10-14]. 

Radical species during inclusion polymerization can readily be detected by ESR spectroscopy, indicating that the radicals are thermally stable in the channels. The reason is that the radicals in the channels do not meet with each other due to the host walls. y-Irradiation produces radicals of the host component as well as the monomers. Monomeric and propagating radicals were observed in the case of urea, while only the propagating radicals were observed in the case of perhydrotriphenylene, deoxycholic acid, and apocholic acid. Simulation of the spectra clarified that the propagating radicals do not rotate freely, indicating that mobilities of the radicals are constrained in the channels. 

Abstract The analysis of ESR, ENDOR, and ESEEM data to extract the resonance parameters is treated. Free radicals in solution are mainly identified by their hyper-fine couplings (hfc). The analysis of ESR and ENDOR spectra by visual inspection and by computer simulation is discussed. The Schonland method to obtain the principal values and directions of the anisotropic g- and hfc- tensors from single crystal ESR and ENDOR data is presented. The modifications needed when 5 > A or / > A to obtain zero-field splitting ( i) or nuclear quadrupole coupling (nqc) tensors are considered. Examples of simulations to extract g-, hfc-, Tfs-, and n c-tensors from ESR and ENDOR spectra of disordered systems are presented. Simulation methods in pulsed ESR (1- and 2-dimensional ESEEM) studies are exemplified. Internet addresses for down-loading software for the simulation of ESR, ENDOR, and ESEEM spectra are provided. Software for the analysis of single crystal data by the Schonland method is also available. 

Figure 7.26 shows the temperature dependence of ESR spectra of PE chain end type of propagating radical tethered to a PTFE surface [27]. The radicals were produced by ball-milling of PTFE with a large amount of ethylene monomer. The dotted spectra at 15 and 30 K were calculated using the site exchange rates of 10 and 56 MHz, respectively. The spectrum observed at 95 K could be simulated by the rotation of the chain end about the chain axis along with the site exchange motion. The oscillation amplitude was also estimated from the values of SPLIT A and B, shown in Fig. 7.26. The ESR spectra of the end type of scission radicals produced by the mechanical fracture of PE were also simulated by the site exchange model between the sites 1 and 2 as described in Fig. 7.50 (in Appendix A7.1). The reason...

ESR techniques use nitroxyl radicals either dispersed in polymer matrix (spin probe) or covalently bonded to polymer chain (spin label) which are sensitive to the environment allowing molecular motion and microstructure of polymers to be identified from spectra (103). Quantitative methods of heterogeneous ESR spectra are divided into (J) outer hyperfine etrema, (2) signal intensities related to the relative concentration of the probe in different phases, and (3) simulation of the spectra. The presence of two well-separated outer maxima above the glass-transition temperature could be ascribed to two phases in natural rubber (104), miscible blends (105), immiscible blends (106), cross-linked polymers (107), and polyurethanes (108). ESR has used the measurement of the oxidation product to monitor the consumption of stabilizer in polypropylene (109). 

The NMR data from Sect. 7,1 were used and the alkyl radicals were trapped by y-irradiation of UPEC in vacuo (1.3 x 10 Pa) up to 3 Mrad. Irradiated UPEC was heat treated so that only the alkyl radicals were trapped. Line widths of ESR spectra observed at various temperatures were determined by comparing the observed spectra and the best-fitted simulated spectra at various temperatures. The alkyl radicals show a sextet ESR spectrum as repeatedly shown (e.g., Fig. 5.1.). Since ESR spectra of alkyl radicals in powdered materials show a so-called amorphous pattern caused by the anisotropy of the hyperfine splitting due to a-protons (refer to Sect. 2), computer simulation is indispensable in order to determine the true line widths. Variations of line widths of NMR and ESR spectra with temperature are shown in Fig. 8.1., in which the temperature dependence of hyperfine splitting of the ESR spectrum is also shown by open rectangulars to be described at a later point. 

Fig. 5. Experimental (a) and simulated (b) ESR spectra of the propagating radical in polymerization of tBMA at 150°C. (From Ref. 22, with permission.)...

Further information on the dynamic behavior of the propagating radicals was obtained by simulating the temperature dependence of the ESR spectra." The average exchange time between the two conformers was calculated from the simulation of the spectra in Fig. 4. The activation energy for rotation of the terminal Cot-Cp bond was estimated to be 21.2 kJ mol. " ... 

Fig. 17. Experimental (a) and simulated b) ESR spectra of mid-chain radical generated by hydrogen abstraction from polyfBA by peroxide radicals b). The spectrum was reasonably simulated based on the structure shown in the figure.

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