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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

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

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