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Applications of EPR and ENDOR Spectrum Simulations in Radiation Research

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Applications of EPR in Radiation Research

Abstract

Applications of EPR and ENDOR simulations of relevance in radiation research involving free radicals, radical pairs, triplet states and to less extent metal complexes are treated. Early fundamental work involving in situ radiolysis of liquids and stickplot analysis of spectra is reviewed, while single crystal analysis is only briefly discussed. The analysis of data obtained with continuous wave methods of species trapped in disordered solid s, “powders” is emphasized. Simulations based on first and second order and exact theory are described and exemplified. Methods to obtain parameters for the dynamics of radicals in irradiated solids and for the simulation of spectra at microwave saturation are discussed. Procedures for the simulation of powder ENDOR spectra of radicals are described in detail, with special emphasis on the influence of nuclear quadrupole couplings due to nuclei with I ≥ 1. EPR and ENDOR simulation programs known to us are presented in an Appendix, including addresses for downloading when available.

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Notes

  1. 1.

    This is valid when the electron spin-spin cross relaxation rate is much slower than the electron spin-lattice relaxation rate, so that only the EPR transitions located at the field setting are brought into resonance by the microwaves, see further Sect. 19.6.1.

  2. 2.

    Note that there is a misprint in Table 1 of Ref. [172] in the order of the principal components of Q(14N-His).

  3. 3.

    Note that in [191] the vectors of the Q(14N)-tensor are not orthogonal, apparently due to a misprint in the sign of one of the direction cosines of the smallest nqc principal component 0.261 MHz; ( + 0.050 + 0.909 + 0.415). The vectors become orthogonal with a sign change to (− 0.050 + 0.909 + 0.415), which has been used in the simulations.

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  1. Department of Physics, Chemistry and Biology, Linköping University, 581 83, Linköping, Sweden

    Roland Erickson & Anders Lund

  2. Systems Development, SAAB Aeronautics, SAAB AB, 581 88, Linköping, Sweden

    Roland Erickson

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    Anders Lund

  2. Hiroshima University, Higashi-Hiroshima, Japan

    Masaru Shiotani

Appendix

Appendix

1.1 EPR and ENDOR Simulation Software

A large number of simulation methods has been presented during the last 50 years, the earlier ones, e.g. in [45, 46] being based on perturbation theory. Methods based on exact diagonalization of the spin Hamiltonian have been developed more recently and in many instances replaced the perturbation methods [43, 58–63]. The simulated CW-EPR spectra have traditionally been assumed to have the form (19.6), but a more recent method of calculation in frequency space [43] has been employed in several of the programs listed in Table 19.2. The programs of the general type are usually applicable both for EPR and ENDOR simulations of general spin systems. The fitting by visual inspection is not an objective method, and efforts were therefore made even at an early stage to make the final refinement by automatically optimising the coupling constants and the line width of the computed spectrum to the experimental one, see e.g. [38]. Optimised values of hfc constants can also be obtained with several of the recently developed programs. The references in Table 19.2 may be consulted for details. Hyperfine enhancement and angular selection effects are taken into account in the programs dedicated to the simulation of powder ENDOR spectra. Several commercial and free-ware program packages can be downloaded electronically, where updates are also reported. Some previously commonly used programs, e.g. in [45, 104] were excluded as it was not clear that they were still available or had been maintained. We refer to a literature survey [52] for programs dedicated to the powder spectrum simulation of free radicals and triplet state molecules.

Table 19.2 Programs for the simulation of EPR and ENDOR spectra
Full size table

1.1.1 Isotropic Spectra

Public electron spin resonance software tools from National Institute of Environmental Health Sciences are available electronically [41 ]. Software may also be available at the International EPR (ESR) Society, which also provides contact details with a number of EPR-groups [113, 114]. Codes primarily intended for calculations of powder spectra can as a rule also be employed, e.g. the following software.

EasySpin

The tools for isotropic CW-EPR in EasySpin apply to S = ½ species with arbitrary number of nuclei [60]. Resonance fields are calculated exactly. The magnetic field range is automatically determined. A least-squares fitting to an experimental spectrum can be made. Matlab must be installed on the computer and is not provided with EasySpin.

HRESOL

High resolution spectra are calculated of radicals in fluid isotropic media with hfc of several nuclei of any spin, taking into account the second order shift of resonance lines and the dependence of the line widths on the magnetic quantum number m I of the nucleus [49]. The program is written in APL, which must be obtained separately.

SimFonia

Spectra of radicals in fluid solution are calculated using up to third order perturbation theory for isotropic hfc constants [46]. Parameters for the simulation are given in an easy-to-use graphical interface. The software is a commercial product but one version might still be available free of charge.

1.1.2 Anisotropic Spectra

Definite simulation procedures were published already in 1965 for the analysis of the hfc structure of free radicals in amorphous solid samples [45]. Improved second order as well as exact methods have been implemented in the more recently developed free-ware and commercial software packages, presented in Table 19.2. The programs of the general type are usually applicable both for EPR and ENDOR simulations, and can handle complex spin systems. The references in the table may be consulted for details.

EasySpin Tools are included for CW and pulse EPR and ENDOR spectra of solid samples [60, 183, 184]. An arbitrary number of electron and nuclear spins can be treated taking all interactions, including high-order operators and nuclear quadrupole couplings into account by exact and second order treatments. Line broadening by g, A and D strain and unresolved hfc splittings are considered as well as non-equilibrium populations. Spectra with perpendicular and parallel detection modes can be analysed. EasySpin is available free of charge. Matlab version 7.5 or later must, however, be installed on the computer and is not provided with EasySpin.

EPR-NMR

This program was written primarily for the handling of magnetic resonance spectra of single crystals and powders, but spectra of liquids can also be dealt with [116]. The number of spins included is arbitrary, as is their assignment as either electronic or nuclear. The program sets up spin-Hamiltonian matrices, and determines their eigenvalues using “exact” diagonalization. A variety of applications can be treated as energy-level calculation, spectrum simulation, comparison with observed data, and parameter optimization. EPR-NMR contains capabilities for NMR as well as EPR calculations and for handling of several unpaired electronic spins. Boltzmann factors are also available. The program, including the source code and utilities, runs on any computer capable of running 32-bit FORTRAN 77.

Sim

Software for simulation and fitting of EPR spectra has been developed during long time at the University of Copenhagen. Simulations are performed by diagonalization of the spin Hamiltonian used to model the complex under study. General Hamiltonians can be treated like exchange-coupled complexes of transition metal ions. Single crystal and powder spectra can be analysed. Fits to experimental spectra are obtained by the least squares method. The software was developed by Dr Høgni Weihe, Department of Chemistry, University of Copenhagen.

HRESOL, RIGMAT, MULTIP, HMLT

A suite of EPR simulation programs prepared by Dr C. Chachaty are available free of charge [49]. Simulation can be made for radicals or metal ions of electron spin S = ½, and of triplet states, of biradicals, radical or ion pairs in rigid matrices for Δm S = 1 and Δm S = 2 transitions. The second order treatment in [55] was utilized. Diagonalization of the spin Hamiltonian matrix can also be applied to free radicals in liquid phase and to triplet states, biradicals or ion pairs in rigid matrices.

SOPHE

The XSophe-Sophe-XeprView computer simulation software suite is applicable for the analysis of isotropic, randomly oriented, and single crystal CW and pulse EPR spectra from isolated and clusters of paramagnetic centres [62]. XSophe provides a graphical user interface to the Sophe computer simulation software programme. The simulations available include CW-EPR spectra, orientation dependent CW-EPR spectra , energy level diagrams and transition surfaces diagrams. Spectra are simulated based on full matrix diagonalization. Superhyperfine interactions may be treated with up to third order perturbation theory. Isolated systems, magnetically coupled systems for unlimited electron and nuclear spins including multiple nuclear isotopes can be treated. Details are given in [115].

Xemr

Xemr is an EPR, ENDOR, and TRIPLE (electron-nuclear-nuclear triple resonance) spectrum manipulation and simulation package written for Linux systems [59]. First order simulation is restricted to S = ½ and to electron Zeeman and hyperfine interaction whereas a numerical method can handle electron and nuclear Zeeman, hyperfine, electron-electron, and nuclear quadrupole interactions exactly in simulations of both EPR and ENDOR spectra. Absorption, first derivative and second derivative spectra can be generated. The powder spectrum integrator can be added on top of these methods. The parameters for the simulations are provided interactively. The program is distributed free of charge under the GNU general public license.

ENDORF2

ENDORF2 is an ENDOR simulation program for S = ½, treating hfc-, nqc-, and nuclear Zeeman interactions as a joint perturbation. Numerical diagonalisation of the perturbation matrix is used for nuclei with I = 2 and higher, but for I = 1 and 3/2 species the eigen-energies and -waveforms can be obtained by the analytical formulas in [192]. These are implemented in ENDORF2, together with the simple case of species with I = 1/2. The program is written in FORTRAN77 and is distributed free of charge. Details are given in [52, 172, 186], see also http://www.liu.se/simarc/downloads/?l=en?l=en.

1.1.3 Motional Effects

Procedures for the analysis in the slow motional region are well documented, while computer programs for the simulation of intramolecular motion are not always publically available or are in obsolete code.

Slow Motion

Several programs for the CW spectrum simulation of reorienting nitroxide radicals used as spin labels described in [118–120] are freely available. The software packages include the original PC version of the CW spectrum simulation programs, and the least squares version of the program described in [119]. CW- EPR spectra of a slow tumbling nitroxide radical can also be simulated in the EasySpin package, see [120] for details of the algorithm. The EasySpin program runs with Matlab 7.5 or later.

Chemical Exchange

The program ESREXN [142, 143] simulates multiline exchange- broadened EPR spectra from the coupling constants, the line widths, and the populations of the different chemical configurations. The original program might not be available. Heinzer’s intramolecular exchange model is, however, implemented in the XEMR spectrum manipulation and simulation package written for Linux systems. A slightly modified stand-alone version was used in the works [144–146]. We are not aware of publically available software for the treatment of chemical exchange in anisotropic systems.

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Erickson, R., Lund, A. (2014). Applications of EPR and ENDOR Spectrum Simulations in Radiation Research. In: Lund, A., Shiotani, M. (eds) Applications of EPR in Radiation Research. Springer, Cham. https://doi.org/10.1007/978-3-319-09216-4_19

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