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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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The subject of the thesis focuses on new approximations studied in a formalism based on a perturbation theory allowing to describe the electronic properties of many-body systems in an approximate way. We excite a system with a small disturbance, by sending light on it or by applying a weak electric field to it, for example and the system "responds" to the disturbance, in the framework of linear response, which means that the response of the system is proportional to the disturbance. The goal is to determine what we call the neutral excitations or bound states of the system, and more particularly the single excitations. These correspond to the transitions from the ground state to an excited state. To do this, we describe in a simplified way the interactions of the particles of a many-body system using an effective interaction that we average over the whole system. The objective of such an approach is to be able to study a system without having to use the exact formalism which consists in diagonalizing the N-body Hamiltonian, which is not possible for systems with more than two particles.

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Sujets

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

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234

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278