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The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation (LDA), one of the most successful approximations in DFT. In this work, we extend the concept of UEG by introducing excited-state UEGs, systems characterized by a gap at the Fermi surface created by the excitation of electrons near the Fermi level. We report closed-form expressions of the reduced kinetic and exchange energies of these excited-state UEGs as functions of the density and the gap. Additionally, we derive the leading term of the correlation energy in the high-density limit. By incorporating an additional variable representing the degree of excitation into the UEG paradigm, the present work introduces a new framework for constructing local and semi-local state-specific functionals for excited states.

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In this work, we reexamine the Dailey–Townes model by systematically investigating the electric field gradient (EFG) in various chlorine compounds, dihalogens, and the uranyl ion (UO22+). Through the use of relativistic molecular calculations and projection analysis, we decompose the EFG expectation value in terms of atomic reference orbitals. We show how the Dailey–Townes model can be seen as an approximation to our projection analysis. Moreover, we observe for the chlorine compounds that, in general, the Dailey–Townes model deviates from the total EFG value. We show that the main reason for this is that the Dailey–Townes model does not account for contributions from the mixing of valence p-orbitals with subvalence ones. We also find a non-negligible contribution from core polarization. This can be interpreted as Sternheimer shielding, as discussed in an appendix. The predictions of the Dailey–Townes model are improved by replacing net populations with gross ones, but we have not found any theoretical justification for this. Subsequently, for the molecular systems X–Cl (where X = I, At, and Ts), we find that with the inclusion of spin–orbit interaction, the (electronic) EFG operator is no longer diagonal within an atomic shell, which is incompatible with the Dailey–Townes model. Finally, we examine the EFG at the uranium position in UO22+, where we find that about half the EFG comes from core polarization. The other half comes from the combination of the U≡O bonds and the U(6p) orbitals, the latter mostly nonbonding, in particular with spin–orbit interaction included. The analysis was carried out with molecular orbitals localized according to the Pipek–Mezey criterion. Surprisingly, we observed that core orbitals are also rotated during this localization procedure, even though they are fully localized. We show in an appendix that, using this localization criterion, it is actually allowed.

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Excited-state absorption (ESA) corresponds to the transition between two electronic excited states and is a fundamental process for probing and understanding light-matter interactions. Accurate modeling of ESA is indeed often required to interpret time-resolved experiments. In this contribution, we present a dataset of 53 ESA oscillator strengths in three different gauges and the associated vertical transition energies between 71 excited states of 23 small- and medium-sized molecules from the QUEST database. The reference values were obtained within the quadratic-response (QR) CC3 formalism using eight different Dunning basis sets. We found that the d-aug-cc-pVTZ basis set is always adequate while its more compact double-$\zeta$ counterpart, d-aug-cc-pVDZ, performs well in most applications. These QR-CC3 data allow us to assess the performance of QR-TDDFT, with and without applying the Tamm-Dancoff approximation, using a panel of global and range-separated hybrids (B3LYP, BH{\&}HLYP, CAM-B3LYP, LC-BLYP33, and LC-BLYP47), as well as several lower-order wavefunction methods, i.e., QR-CCSD, QR-CC2, EOM-CCSD, ISR-ADC(2), and ISR-ADC(3). We show that QR-TDDFT delivers acceptable errors for ESA oscillator strengths, with CAM-B3LYP showing particular promise, especially for the largest molecules of our set. We also find that ISR-ADC(3) exhibits excellent performance

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Building on our recent study [https://doi.org/10.1021/acs.jpclett.3c02052, J. Phys. Chem. Lett. 14, 8780 (2023)], we explore the generalization of the ground-state Kohn-Sham (KS) formalism of density-functional theory (DFT) to the (singlet) excited states of the asymmetric Hubbard dimer at half-filling. While we found that the KS-DFT framework can be straightforwardly generalized to the highest-lying doubly-excited state, the treatment of the first excited state presents significant challenges. Specifically, using a density-fixed adiabatic connection, we show that the density of the first excited state lacks non-interacting $v$-representability. However, by employing an analytic continuation of the adiabatic path, we demonstrate that the density of the first excited state can be generated by a complex-valued external potential in the non-interacting case. More practically, by performing state-specific KS calculations with exact and approximate correlation functionals -- each state possessing a distinct correlation functional -- we observe that spurious stationary solutions of the KS equations may arise due to the approximate nature of the functional.

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Sujets

3115bw Time-dependent density-functional theory Analytic gradient Argile Mécanique quantique relativiste Relativistic quantum chemistry Parity violation New physics Acrolein Ion 3315Fm Quantum Chemistry Coupled cluster calculations Time reversal violation Hyperfine structure Approximation GW Biodegradation Atom 3115aj BENZENE MOLECULE AB-INITIO Polarizabilities Atrazine-cations complexes Ab initio calculation Aimantation Pesticides Metabolites Clustering Molecular modeling Environmental fate Partial least squares Range separation Large systems Green's function Diatomic molecules Dispersion coefficients Xenon A priori Localization 3470+e Atomic charges Configuration interactions Anderson mechanism Anharmonic oscillator Perturbation theory Chemical concepts Carbon Nanotubes Configuration Interaction Electron electric moment Density functional theory Numerical calculations Ground states Fonction de Green Azide Anion Single-core optimization QSAR 3115ae Chimie quantique Excited states CP violation CIPSI Théorie des perturbations 3115am Atoms États excités Relativistic quantum mechanics Line formation Rydberg states Argon Molecular properties Pesticide Wave functions Corrélation électronique Parallel speedup Electron electric dipole moment Quantum chemistry X-ray spectroscopy Atomic and molecular structure and dynamics Coupled cluster Molecular descriptors Quantum Monte Carlo Adiabatic connection Atomic charges chemical concepts maximum probability domain population Relativistic corrections Path integral Dipole AB-INITIO CALCULATION Abiotic degradation ALGORITHM Atomic processes Auto-énergie AROMATIC-MOLECULES Diffusion Monte Carlo 3115vn BIOMOLECULAR HOMOCHIRALITY Dirac equation Atrazine Valence bond 3115ag Petascale 3115vj Electron correlation Atomic data A posteriori Localization Atomic and molecular collisions Spin-orbit interactions

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