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Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections.
The Bethe–Salpeter equation (BSE) is the key equation in many-body perturbation theory based on Green's functions to access response properties. Within the GW approximation to the exchange-correlation kernel, the BSE has been successfully applied to several finite and infinite systems. However, it also shows some failures, such as underestimated triplet excitation energies, lack of double excitations, ground-state energy instabilities in the dissociation limit, etc. In this work, we study the performance of the BSE within the GW approximation as well as the T-matrix approximation for the excitation energies of the exactly solvable asymmetric Hubbard dimer. This model allows one to study various correlation regimes by varying the on-site Coulomb interaction U as well as the degree of the asymmetry of the system by varying the difference of potential Δv between the two sites. We show that, overall, the GW approximation gives more accurate excitation energies than GT over a wide range of U and Δv. However, the strongly correlated (i.e., large U) regime still remains a challenge.
We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost. The main advantage of this algorithm is that it allows for the calculation to be stopped at any time, providing an unbiased estimate, with a statistical error that goes to zero as the exact calculation is approached. We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods. Specifically, we demonstrate that a precision of 0.5 millihartree can be attained with only 10\% of the computational effort required by the full calculation. This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive.
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently the singlet and triplet component of the repulsion between electrons not present in the model (its short-range part). The scaling factors depend uniquely on the parameter used in defining the model interaction, and are constructed using only exact properties. We show results for the ground states and low-lying excited states of Harmonium with two to six electrons. We obtain important improvements for the estimation of the exact energy, not only over the model energy, but also over the expectation value of the Hamiltonian.
Sujets
Acrolein
Argile
Electron electric dipole moment
Green's function
Coupled cluster
Petascale
New physics
Atom
3115bw
Diatomic molecules
Dipole
Ion
X-ray spectroscopy
AB-INITIO
Fonction de Green
Chimie quantique
Line formation
Configuration interaction
Single-core optimization
Adiabatic connection
BIOMOLECULAR HOMOCHIRALITY
Electron correlation
Configuration Interaction
Analytic gradient
Time-dependent density-functional theory
Dirac equation
3115vj
QSAR
Atomic charges chemical concepts maximum probability domain population
3115aj
Coupled cluster calculations
Atomic and molecular structure and dynamics
Auto-énergie
Large systems
3315Fm
Dispersion coefficients
Atrazine
Basis set requirements
Configuration interactions
Diffusion Monte Carlo
Range separation
Polarizabilities
Atomic and molecular collisions
Quantum chemistry
3470+e
Approximation GW
Chemical concepts
Wave functions
AROMATIC-MOLECULES
CIPSI
Atrazine-cations complexes
Xenon
Electron electric moment
Time reversal violation
Relativistic quantum mechanics
Rydberg states
Atoms
3115ag
Spin-orbit interactions
Azide Anion
Relativistic quantum chemistry
Abiotic degradation
BSM physics
Perturbation theory
Density functional theory
BENZENE MOLECULE
A priori Localization
États excités
Pesticide
ALGORITHM
Numerical calculations
Mécanique quantique relativiste
Valence bond
Biodegradation
Aimantation
Carbon Nanotubes
Hyperfine structure
3115vn
Molecular descriptors
Ground states
Quantum Chemistry
Atomic processes
CP violation
Atomic data
Ab initio calculation
Argon
Pesticides Metabolites Clustering Molecular modeling Environmental fate Partial least squares
Excited states
Parity violation
Quantum Monte Carlo
Relativistic corrections
AB-INITIO CALCULATION
Anderson mechanism
A posteriori Localization
Corrélation électronique
Molecular properties
Atomic charges
Parallel speedup
3115am
3115ae