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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
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