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

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.本研究基于成熟理论与一阶微扰方法，开发了三款MATLAB代码，用于从含捕获自由基（电子自旋S=½）或三重态分子（S=1）的晶体的电子顺磁共振（Electron Paramagnetic Resonance, EPR）或电子核双共振（Electron Nuclear Double Resonance, ENDOR）测量得到的角度依赖谱图中，计算g张量、零场分裂（zero-field splitting, ZFS）与超精细耦合（hyperfine coupling, HFC）张量。 代码I采用肖恩兰德原始方法（Schonland’s original method），通过对每个晶面的实验数据进行最小二乘拟合，计算g张量与HFC张量；该方法已适配S=1的自由基对的零场分裂分析需求。代码II采用非线性拟合方法，从自由基的EPR测量数据中提取HFC张量，同时纳入核自旋I=½的核塞曼相互作用项。代码III则对已有的有机自由基g张量与HFC张量计算方法进行拓展，可用于三重态顺磁物种的分析，该方法通过同时拟合所有实验数据来获取目标张量。 三款方法的有效性均通过与实验测量结果、精确对角化方法计算得到的角度依赖谱图进行对比得到验证。用户可下载示例输入文件与源代码。本软件借助现成的回归与误差分析函数，将代码行数压缩至约200行，相较于旧版软件减少了一个数量级。 旧版程序的源代码与可执行文件要么无法获取，要么采用了过时的代码格式，这意味着传统语言编写的软件可能已不再维护。专业实验室开发的代码往往难以公开获取。因此，本研究提供的软件可用于EPR与ENDOR单晶数据的分析，尤其适用于S=½与S=1态的有机顺磁物种。 代码III具备通用适用性，而代码I与代码II仅针对代码文档中描述的特定场景开发。测试用谱图数据集gALA_x,y,z、Laspexp_a,b,c与RPmT_X,Y,Z用于代码I与代码III的功能验证，ALFAMTHX,Y,Z则用于代码II的测试。所有测试用谱图数据集需存储至本地计算机，所有数据均通过响应屏幕上的各项提示交互式输入。使用本软件需单独安装MATLAB与Easyspin软件。