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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

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

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274