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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.

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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.

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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.

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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.

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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

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