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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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Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.

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In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection. Our methodology involves the use of a parameter-dependent potential dependent on a single parameter to facilitate practical computations. We analyze the energy errors and densities in a two-electron system (harmonium) under various conditions, employing different confinement potentials and interaction parameters. The study reveals that while the mean-field potential improves the expectation value of the physical Hamiltonian, it does not necessarily improve the energy of the system within the bounds of chemical accuracy. We also delve into the impact of density variations in adiabatic connections, challenging the common assumption that a mean field improves results. Our findings indicate that as long as energy errors remain within chemical accuracy, the mean field does not significantly outperform a bare potential. This observation is attributed to the effectiveness of corrections based on the short-range behavior of the wave function, a universal characteristic that diminishes the distinction between using a mean field or not.

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Sujets

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

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