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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

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

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