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

## Description

Three MatLab codes based on established theory and first-order perturbation methods were prepared to compute the g, zero-field splitting (zfs) and hyperfine coupling (hfc) tensors from roadmaps obtained by Electron Paramagnetic Resonance (EPR) or Electron Nuclear Double Resonance (ENDOR) measurements on crystals containing trapped free radicals (electron spin S=½) or triplet state molecules (S=1). Schonland’s original method (I) was used to compute the g- and hfc -tensors by a least-squares fit to the experimental data in each crystal 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 (II) to obtain the hfc -tensor from EPR measurements on free radicals, taking the nuclear Zeeman interaction of nuclear spin with I = ½ into account. A previously developed method to calculate the g- and hfc -tensors of organic radicals was extended in the third code (III) to allow analysis of triplet state species. A simultaneous fit to all data was employed to obtain the tensors. The validity of all three methods was examined by comparison with results obtained experimentally, and by comparing with roadmaps computed by exact diagonalization methods. Input examples and source codes can be downloaded. By using the available functions for regression and error analysis the number of program lines was reduced to ca 200, i.e. by an order of magnitude in comparison with older software. The source and executables of the old programs are either unavailable or in obsolete code, indicating that software in traditional languages may no longer be maintained. Codes developed in specialized laboratories are not easily available. The software presented in this work might therefore be of interest for the analysis of EPR and ENDOR single crystal data, particularly for organic paramagnetic species with S=½ and S=1 states. Code (III) is generally applicable, codes (I) and (II) are developed for special cases described in the computer codes. The roadmaps gALA_x, y, z, Laspexp_a, b, c, RPmT_X, Y, Z are intended for testing of the codes (I) and (III), ALFAMTHX, Y, Z for code (II). The roadmaps should be stored on the computer. All data are entered interactively by responding to each issue on the screen. MatLab and Easyspin software must be installed separately.