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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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At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree–Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localization in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localize are made. The density profiles we obtain emerge naturally when we minimize the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure, which has been predicted to be the ground-state structure of the two-dimensional Wigner crystal.

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Leptoquark models may explain deviations from the standard model observed in decay processes involving heavy quarks at high-energy colliders. Such models give rise to low-energy parity- and time-reversal-violating phenomena in atoms and molecules. One of the leading effects among these phenomena is the nucleon-electron tensor-pseudotensor interaction when the low-energy experimental probe uses a quantum state of an atom or molecule predominantly characterized by closed electron shells. In the present paper the molecular interaction constant for the nucleon-electron tensor-pseudotensor interaction in the thallium-fluoride molecule—used as such a sensitive probe by the CeNTREX collaboration [O. Grasdijk et al., Quantum Sci. Technol. 6, 044007 (2021)]—is calculated employing highly correlated relativistic many-body theory. Accounting for up to quintuple excitations in the wave-function expansion the final result is WT(Tl)=−6.25±0.31 (10−13⟨Σ⟩A a.u.) Interelectron correlation effects on the tensor-pseudotensor interaction are studied rigorously in a molecule.

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Sujets

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

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