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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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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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Subjets

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

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