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Spectroscopic techniques based on core-level excitations offer powerful tools for probing molecular and electronic structures with high spatial resolution. However, accurately calculating spectral features at the L or M edges is challenging due to the significant influence of spin–orbit and multiplet effects. While scalar-relativistic effects can be incorporated with minimal computational cost, accounting for spin–orbit interactions requires complex frameworks that can be computationally expensive. In this work, we develop a reduced-cost state-interaction approach for simulating near-edge soft x-ray absorption spectra of closed-shell transition metal complexes with relativistic effects incorporated using the ZORA-Kohn–Sham Hamiltonian. The computed spectra closely agree with those obtained with state-of-the-art approaches. This methodology provides a practical and cost-effective alternative to more rigorous two-component methods, making it particularly valuable for large-scale calculations and applications such as resonant inelastic x-ray scattering simulations, where capturing a large number of excited states is essential. 

We report a comprehensive computational study of unsupervised machine learning for extraction of chemically relevant information in X-ray absorption near edge structure (XANES) and in valence-to-core X-ray emission spectra (VtC-XES) for classification of a broad ensemble of sulphorganic molecules. By progressively decreasing the constraining assumptions of the unsupervised machine learning algorithm, moving from principal component analysis (PCA) to a variational autoencoder (VAE) to t-distributed stochastic neighbour embedding (t-SNE), we find improved sensitivity to steadily more refined chemical information. Surprisingly, when embedding the ensemble of spectra in merely two dimensions, t-SNE distinguishes not just oxidation state and general sulphur bonding environment but also the aromaticity of the bonding radical group with 87% accuracy as well as identifying even finer details in electronic structure within aromatic or aliphatic sub-classes. We find that the chemical information in XANES and VtC-XES is very similar in character and content, although they unexpectedly have different sensitivity within a given molecular class. We also discuss likely benefits from further effort with unsupervised machine learning and from the interplay between supervised and unsupervised machine learning for X-ray spectroscopies. Our overall results, i.e. , the ability to reliably classify without user bias and to discover unexpected chemical signatures for XANES and VtC-XES, likely generalize to other systems as well as to other one-dimensional chemical spectroscopies. 

We demonstrate how optical cavities can be exploited to control both valence- and core-excitations in a prototypical model transition metal complex, ferricyanide ([Fe( iii )(CN) 6 ] 3− ), in an aqueous environment. The spectroscopic signatures of hybrid light-matter polariton states are revealed in UV/Vis and X-ray absorption, and stimulated X-ray Raman signals. In an UV/Vis cavity, the absorption spectrum exhibits the single-polariton states arising from the cavity photon mode coupling to both resonant and off-resonant valence-excited states. We further show that nonlinear stimulated X-ray Raman signals can selectively probe the bipolariton states via cavity-modified Fe core-excited states. This unveils the correlation between valence polaritons and dressed core-excitations. In an X-ray cavity, core-polaritons are generated and their correlations with the bare valence-excitations appear in the linear and nonlinear X-ray spectra.