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