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