![]() However, there is insufficient experimental XES data with known ground truth to reliably train these ML models. This method requires a lot of training data because model parameters must be trained to enable accurate prediction. ML consists of numerical models that can predict output classes or values from input data. To address this challenge artificial intelligence (AI), such as machine learning (ML) including deep learning, has been applied to data analysis (Zheng et al., 2018 Timoshenko & Frenkel, 2019 Miyazato et al., 2019 Benmore et al., 2022 ). This problem occurs not only in XES but also in various fields trying to match theory and experimental data. However, data analysis remained challenging due to the tedious and difficult process of finding parameters in multiplet spectral simulations that match experimental data, leading to a trial-and-error method for determining them. Our group recently developed a program, Argonne X-ray Emission Analysis Package ( AXEAP) (Hwang et al., 2022 ), that was able to dramatically increase the processing speed of raw data by using unsupervised machine learning. Therefore, electron–electron interactions, the number of electrons and the spin state in the 3 d orbital all play crucial roles in determining the spectral shape. Usually, the high-spin (HS) spectrum has relatively prominent K β′ features compared with the low-spin (LS) spectrum, even if the number of 3 d electrons is the same. In the crystal field effect, the ligands and positively charged metal cation break the degeneracies of the 3 d electron orbital and separate them into energy levels such as t 2 g and e g, leading to differences in the number of pairing electrons and spin state. In 3 d transition metals, the Coulomb and exchange force of 3 d–3 d and 3 d–3 p electrons are considered, which cause the K β emission line to split into a K β 1,3 and a K β′ line. Atomic multiplet theory calculations are based on the interaction of two electrons and spin–orbital coupling in a many-body system. These characteristics are often collected as a complementary method to X-ray absorption spectroscopy (XAS) and are widely used to elucidate the unique structural and electronic information by comparing spectral shape with known standards samples (Bauer, 2014 Burkhardt et al., 2017 Agote-Arán et al., 2019 Lassalle-Kaiser et al., 2017 Glatzel & Bergmann, 2005 Gretarsson et al., 2013 Pelliciari et al., 2017 Chin et al., 2017 ).Ītomic multiplet theory and crystal field effects provide a solid theoretical foundation for explaining the XES spectra (Cowan, 1981 de Groot & Kotani, 2008 ). The XES shape is known to highly depend on spin state and oxidation state. The XES is a result of an electric-dipole-allowed 3 p → 1 s transition following an incident photon with sufficient energy to excite a 1 s electron through the absorption process. The non-resonant K β X-ray emission spectrum (XES) of 3 d transition metals is a widely used tool in the investigation of the electronic structure of materials of interest in condensed matter physics, coordination chemistry and catalysis (Vankó et al., 2006 Lafuerza et al., 2020 Kucheryavy et al., 2016 ). AXEAP2 is able to find a set of parameters that reproduce the experimental spectrum, and provide insights into the 3 d electron spin state, 3 d–3 p electron exchange force and K β emission core-hole lifetime. This approach is also implemented as a standalone application, Argonne X-ray Emission Analysis 2 ( AXEAP2), which finds a set of parameters that result in a high-quality fit of the experimental spectrum with minimal intervention. Here, a new XES data analysis method based on the genetic algorithm is demonstrated, applying it to Mn, Co and Ni oxides. Although the non-resonant K β XES of 3 d transition metals are known to provide electronic structure information such as oxidation and spin state, finding appropriate parameters to match experimental data is a time-consuming and labor-intensive process. ![]() However, the task of analyzing the processed spectra remains another challenge. Our previous work addressed the challenge of X-ray emission spectrum (XES) data processing by developing a standalone application using unsupervised machine learning. ![]() The processing and analysis of synchrotron data can be a complex task, requiring specialized expertise and knowledge.
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