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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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Reduced density matrix functional theory (RDMFT) and coupled cluster theory restricted to paired double excitations (pCCD) are emerging as efficient methodologies for accounting for the so-called non-dynamic electronic correlation effects. Up to now, molecular calculations have been performed with real-valued orbitals. However, before extending the applicability of these methodologies to extended systems, where Bloch states are employed, the subtleties of working with complex-valued orbitals and the consequences of imposing time-reversal symmetry must be carefully addressed. In this work, we describe the theoretical and practical implications of adopting time-reversal symmetry in RDMFT and pCCD when allowing for complex-valued orbital coefficients. The theoretical considerations primarily affect the optimization algorithms, while the practical implications raise fundamental questions about the stability of solutions. Specifically, we find that complex solutions lower the energy when non-dynamic electronic correlation effects are pronounced. We present numerical examples to illustrate and discuss these instabilities and possible problems introduced by N-representability violations.

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Sujets

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

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256

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274