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