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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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In the realm of photochemistry, the significance of double excitations (also known as doubly-excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [http://dx.doi.org/10.1021/acs.jctc.8b01205; Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly-excited states where the transitions almost exclusively involve doubly-excited configurations and (ii) 19 "partial" doubly-excited states which exhibit a more balanced character between singly- and doubly-excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition ($\%T_1$) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

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We systematically study a set of strongly polar heteronuclear diatomic molecules composed of laser-coolable atoms for their suitability as sensitive probes of new charge-parity violation in the hadron sector of matter. Using relativistic general-excitation-rank configuration-interaction theory we single out the molecule francium-silver (FrAg) as the most promising system in this set and calculate its nuclear Schiff-moment interaction constant to WFrAgSM(Fr)=30168±2504a.u. for the target nucleus Fr. Our work includes the development of system-tailored atomic Gaussian basis sets for the target atom in each respective molecule.

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Sujets

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

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279