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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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The Bethe-Salpeter equation has been extensively employed to compute the two-body electron-hole propagator and its poles which correspond to the neutral excitation energies of the system. Through a different time-ordering, the two-body Green's function can also describe the propagation of two electrons or two holes. The corresponding poles are the double ionization potentials and double electron affinities of the system. In this work, a Bethe-Salpeter equation for the two-body particle-particle propagator is derived within the linear-response formalism using a pairing field and anomalous propagators. This framework allows us to compute kernels corresponding to different self-energy approximations ($GW$, $T$-matrix, and second-Born) as in the usual electron-hole case. The performance of these various kernels is gauged for singlet and triplet valence double ionization potentials using a set of 23 small molecules. The description of double core hole states is also analyzed.

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In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In particular we will discuss: 1) the derivation of the MCDE and the definition of the space in which it is to be solved; 2) the rationale of the approximation to the multichannel self-energy; 3) a diagrammatic analysis of the MCDE; 4) the recasting of the MCDE on an eigenvalue problem with an effective Hamiltonian that can be solved using standard numerical techniques. This work mainly focuses on the coupling between the one-body Green's function and the three-body Green's function to describe photoemission spectra, but the MCDE method can be generalized to the coupling of other many-body Green's functions and to other spectroscopies.

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Sujets

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

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