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