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ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [J. Chem. Theory Comput., 2022, 19(1): 109-121]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations, allowing for multi-GPU simulations of large systems. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals, which otherwise would not have fit on a single GPU. We also support GPU-accelerated multi-slater determinant trial wavefunctions [arXiv:2406.08314] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu$_2$O$_2$]$^{2+}$ and [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron-phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications.

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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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Sujets

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

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