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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

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

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