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1. Manipulating valence and core electronic excitations of a transition-metal complex using UV/Vis and X-ray cavities

   https://doi.org/10.1039/d1sc01774h  

   Gu, Bing; Cavaletto, Stefano M.; Nascimento, Daniel R.; Khalil, Munira; Govind, Niranjan; Mukamel, Shaul (June 2021, Chemical Science)

   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. 

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2. Ab initio investigation of Br-3 d core-excited states in HBr and HBr+ toward XUV probing of photochemical dynamics

   https://doi.org/10.1063/1.5085011  

   Kobayashi, Yuki; Zeng, Tao; Neumark, Daniel_M; Leone, Stephen_R (January 2019, Structural Dynamics)

   Ultrafast X-ray/XUV transient absorption spectroscopy is a powerful tool for real-time probing of chemical dynamics. Interpretation of the transient absorption spectra requires knowledge of core-excited potentials, which necessitates assistance from high-level electronic-structure computations. In this study, we investigate Br-3d core-excited electronic structures of hydrogen bromide (HBr) using spin-orbit general multiconfigurational quasidegenerate perturbation theory (SO-GMC-QDPT). Potential energy curves and transition dipole moments are calculated from the Franck-Condon region to the asymptotic limit and used to construct core-to-valence absorption strengths for five electronic states of HBr (Σ10+, 3Π1, 1Π1, 3Π0+, 3Σ1) and two electronic states of HBr+ (2Π3∕2, 2Σ1∕2). The results illustrate the capabilities of Br-3d edge probing to capture transitions of the electronic-state symmetry as well as nonadiabatic dissociation processes that evolve across avoided crossings. Furthermore, core-to-valence absorption spectra are simulated from the neutral Σ10+ state and the ionic Π21/2,3/2 states by numerically solving the time-dependent Schrödinger equation and exhibit excellent agreement with the experimental spectrum. The comprehensive and quantitative picture of the core-excited states obtained in this work allows for transparent analysis of the core-to-valence absorption signals, filling gaps in the theoretical understanding of the Br-3d transient absorption spectra. 

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3. Slater transition methods for core-level electron binding energies

   https://doi.org/10.1063/5.0134459  

   Jana, Subrata; Herbert, John M. (March 2023, The Journal of Chemical Physics)

   Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a “full core hole” (or “ΔSCF”) approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater’s transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3–0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn–Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy. 

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4. Computing L- and M-edge spectra using the DFT/CIS method with spin–orbit coupling

   https://doi.org/10.1039/D5CP01656H  

   Mandal, Aniket; Herbert, John M (July 2025, Physical Chemistry Chemical Physics)

   Modeling L-edge spectra at X-ray wavelengths requires consideration of spin–orbit splitting of the 2p orbitals. We introduce a low-cost tool to compute core-level spectra that combines a spin–orbit mean-field description of the Breit–Pauli Hamiltonian with nonrelativistic excited states computed using the semi-empirical density-functional theory configuration-interaction singles (DFT/CIS) method, within the state-interaction approach. Our version of DFT/CIS was introduced recently for K-edge spectra and includes a semi-empirical correction to the core orbital energies, significantly reducing ad hoc shifts that are typically required when time-dependent (TD-)DFT is applied to core-level excitations. In combination with the core/valence separation approximation and spin–orbit couplings, the DFT/CIS method affords semiquantitative L-edge spectra at CIS cost. Spin–orbit coupling has a qualitative effect on the spectra, as demonstrated for a variety of 3d transition metal systems and main-group compounds. The use of different active orbital spaces helps to facilitate spectral assignments. We find that spin–orbit splitting has a negligible effect on M-edge spectra for 3d transition metal species. 

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5. Energy-specific Bethe–Salpeter equation implementation for efficient optical spectrum calculations

   https://doi.org/10.1063/5.0260895  

   Hillenbrand, Christopher; Li, Jiachen; Zhu, Tianyu (May 2025, The Journal of Chemical Physics)

   We present an energy-specific Bethe–Salpeter equation (BSE) implementation for efficient core and valence optical spectrum calculations. In the energy-specific BSE, high-lying excitation energies are obtained by constructing trial vectors and expanding the subspace targeting excitation energies above the predefined energy threshold in the Davidson algorithm. To calculate optical spectra over a wide energy range, energy-specific BSE can be applied to multiple consecutive small energy windows, where trial vectors for each subsequent energy window are made orthogonal to the subspace of preceding windows to accelerate the convergence of the Davidson algorithm. For seven small molecules, energy-specific BSE combined with G0W0 provides small errors around 0.8 eV for absolute and relative K-edge excitation energies when starting from a hybrid PBEh solution with 45% exact exchange. We further showcase the computational efficiency of this approach by simulating the N 1s K-edge excitation spectrum of the porphine molecule and the valence optical spectrum of silicon nanoclusters involving 6000 excited states using G0W0-BSE. This work expands the applicability of the GW-BSE formalism for investigating high-energy excited states of large systems. 

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