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1. 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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2. The millimeter-wave spectrum of the SiP radical (X ² Π _i ): Rotational perturbations and hyperfine structure

   https://doi.org/10.1063/5.0118939  

   Burton, M. A.; Sheridan, P. M.; Ziurys, L. M. (November 2022, The Journal of Chemical Physics)

   The millimeter/submillimeter-wave spectrum of the SiP radical (X 2 Π i ) has been recorded using direct absorption spectroscopy in the frequency range of 151–532 GHz. SiP was synthesized in an AC discharge from the reaction of SiH 4 and gas-phase phosphorus, in argon carrier gas. Both spin–orbit ladders were observed. Fifteen rotational transitions were measured originating in the Ω = 3/2 ladder, and twelve in the Ω = 1/2 substate, each exhibiting lambda doubling and, at lower frequencies, hyperfine interactions from the phosphorus nuclear spin of I = 1/2. The lambda-doublets in the Ω = 1/2 levels appeared to be perturbed at higher J, with the f component deviating from the predicted pattern, likely due to interactions with the nearby excited A 2 Σ + electronic state, where ΔE Π-Σ ∼ 430 cm −1 . The data were analyzed using a Hund’s case a β Hamiltonian and rotational, spin–orbit, lambda-doubling, and hyperfine parameters were determined. A 2 Π/ 2 Σ deperturbation analysis was also performed, considering spin–orbit, spin-electronic, and L-uncoupling interactions. Although SiP is clearly not a hydride, the deperturbed parameters derived suggest that the pure precession hypothesis may be useful in assessing the 2 Π/ 2 Σ interaction. Interpretation of the Fermi contact term, b F , the spin-dipolar constant, c, and the nuclear spin-orbital parameter, a, indicates that the orbital of the unpaired electron is chiefly p π in character. The bond length in the v = 0 level was found to be r 0 = 2.076 Å, suggestive of a double bond between the silicon and phosphorus atoms. 

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3. Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

   https://doi.org/10.1039/d2sc01022d  

   Zhou, Chen; Hermes, Matthew R.; Wu, Dihua; Bao, Jie J.; Pandharkar, Riddhish; King, Daniel S.; Zhang, Dayou; Scott, Thais R.; Lykhin, Aleksandr O.; Gagliardi, Laura; et al (July 2022, Chemical Science)

   Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals. 

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4. Low-energy effective theory and anomalous Hall effect in monolayer $$\mathrm{WTe}_2$$

   https://doi.org/10.21468/SciPostPhys.12.4.120  

   Nandy, Snehasish; Pesin, Dima (January 2022, SciPost Physics)

   We develop a symmetry-based low-energy theory for monolayer \mathrm{WTe}_2 W T e 2 in its 1T ^{\prime} ′ phase, which includes eight bands (four orbitals, two spins). This modelreduces to the conventional four-band spin-degenerate Dirac model nearthe Dirac points of the material. We show that measurements of the spinsusceptibility, and of the magnitude and time dependence of theanomalous Hall conductivity induced by injected or equilibrium spinpolarization can be used to determine the magnitude and form of thespin-orbit coupling Hamiltonian, as well as the dimensionless tilt ofthe Dirac bands. 

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5. Quadruple bonds in MoC: Accurate calculations and precise measurement of the dissociation energy of low-lying states of MoC

   https://doi.org/10.1063/5.0211422  

   Androutsopoulos, Alexandros; Tzeli, Demeter; Tomchak, Kimberly H; Morse, Michael D (June 2024, The Journal of Chemical Physics)

   Lian, Tianquan (Ed.)

   In the present work, the electronic structure and chemical bonding of the MoC X3Σ− ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ−, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas–Kroll–Hess approximation, while spin–orbit coupling has also been calculated. Five of the investigated states, X3Σ−, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23 eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm−1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm−1, respectively. 

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