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The ionization by photon or electron impact of the inner (2${a}$$_1$) and outer (1t$_2$) valence orbitals of the CH4 molecule is investigated theoretically. In spite of a number of approximations, including a monocentric approach and a rather simple distorting molecular potential, the calculated cross sections are overall similar to those of other theoretical methods, and in reasonable agreement with experimental data. The originality of the present approach stands in the way we evaluate the transition matrix elements. The key ingredient of the calculation scheme is that the continuum radial wave function of the ejected electron is represented by a finite sum of complex Gaussian type orbitals. This numerically expensive optimization task is then largely compensated by rather simple and rapid analytical calculations of the necessary integrals, and thus all ionization observables, including cross section angular distributions. The proposed and implemented Gaussian approach is proved to be numerically very reliable in all considered kinematical situations with ejected electron energy up to 2.7 a.u.. The analytical formulation of the scheme is provided here for bound molecular states described by monocentric Slater type orbitals; alternatively, one may also use monocentric Gaussian type orbitals for which the formulation is even simpler. In combination with complex Gaussian functions for the continuum states, an all Gaussian approach with multicentric bound states can be envisaged.

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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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Sujets

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

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