Kβ X‑ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater–Condon reduction factors Fdd, Fpd, and Gpd, and crystal field splitting 10Dq. The algorithm produces significantly improved accuracy compared to current analysis methods, and probes inter-parameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3d transition metal valence shells, facilitating applications across various scientific fields.