Determination of the g-, hyperfine coupling- and zero-field splitting tensors in EPR and ENDOR using extended Matlab codes

Anders Lund,Freddy Callens,Einar Sagstuen

doi:10.1016/j.jmr.2021.106956

Anders Lund, Freddy Callens + Show 1 more

Open Access

https://doi.org/10.1016/j.jmr.2021.106956

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Abstract

The analysis of single crystal electron magnetic resonance (EMR) data has traditionally been performed using software in programming languages that are difficult to update, are not easily available, or are obsolete. By using a modern script-language with tools for the analysis and graphical display of the data, three MatLab® codes were prepared to compute the g, zero-field splitting (zfs) and hyperfine coupling (hfc) tensors from roadmaps obtained by EPR or ENDOR measurements in three crystal planes. Schonland’s original method was used to compute the g- and hfc -tensors by a least-squares fit to the experimental data in each plane. The modifications required for the analysis of the zfs of radical pairs with S = 1 were accounted for. A non-linear fit was employed in a second code to obtain the hfc -tensor from EPR measurements, taking the nuclear Zeeman interaction of an I = ½ nucleus into account. A previously developed method to calculate the g- and hfc -tensors by a simultaneous linear fit to all data was used in the third code. The validity of the methods was examined by comparison with results obtained experimentally, and by roadmaps computed by exact diagonalization. The probable errors were estimated using functions for regression analysis available in MatLab. The software will be published at https://doi.org/10.17632/ps24sw95gz.1, Input and output examples presented in this work can also be downloaded from https://old.liu.se/simarc/downloads?l=en.

Highlights

The structure and reactions of paramagnetic defects in solids have been extensively examined by electron magnetic resonance (EMR) methods for more than 60 years
Methods to extract the g- tensor by regular electron paramagnetic resonance (EPR) measurements on single crystals were presented in early work [1], and further developed in software containing error analyses and modifications to treat electron-nuclear double resonance (ENDOR) data [2,3,4,5]
The three Matlab functions presented in this work for the determination of the g, hfc- and zfs-tensors were prepared mainly for the analysis of data obtained by EPR and ENDOR measurements of organic free radicals and triplet molecules trapped in single crystal matrices

Summary

Introduction

The structure and reactions of paramagnetic defects in solids have been extensively examined by electron magnetic resonance (EMR) methods for more than 60 years. Methods to extract the g- tensor by regular electron paramagnetic resonance (EPR) measurements on single crystals were presented in early work [1], and further developed in software containing error analyses and modifications to treat electron-nuclear double resonance (ENDOR) data [2,3,4,5] These codes may no longer be available or maintained. The determination of the g and A ( g2 and A2) and D tensors in general requires EPR and/or ENDOR measurements with the magnetic field vector B in a set of 2–4 planes followed by fitting of the data to ellipsoidal surfaces A first possible practical procedure is described in more detail

The Schonland method

The Nelson method

Discussion

Summary

Source codes