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The Bethe–Salpeter equation (BSE) is the key equation in many-body perturbation theory based on Green's functions to access response properties. Within the GW approximation to the exchange-correlation kernel, the BSE has been successfully applied to several finite and infinite systems. However, it also shows some failures, such as underestimated triplet excitation energies, lack of double excitations, ground-state energy instabilities in the dissociation limit, etc. In this work, we study the performance of the BSE within the GW approximation as well as the T-matrix approximation for the excitation energies of the exactly solvable asymmetric Hubbard dimer. This model allows one to study various correlation regimes by varying the on-site Coulomb interaction U as well as the degree of the asymmetry of the system by varying the difference of potential Δv between the two sites. We show that, overall, the GW approximation gives more accurate excitation energies than GT over a wide range of U and Δv. However, the strongly correlated (i.e., large U) regime still remains a challenge.
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.
Sujets
3115vn
CIPSI
Fonction de Green
Chemical concepts
Relativistic corrections
Electron electric dipole moment
Configuration Interaction
Pesticide
Atomic charges chemical concepts maximum probability domain population
Configuration interactions
Argon
Coupled cluster calculations
Polarizabilities
QSAR
Perturbation theory
Rydberg states
Atrazine
Argile
Green's function
Electron correlation
Atrazine-cations complexes
Quantum Monte Carlo
Xenon
3115ag
Basis set requirements
Mécanique quantique relativiste
Molecular descriptors
Configuration interaction
Parallel speedup
Atomic charges
3115ae
Dirac equation
3315Fm
Auto-énergie
Analytic gradient
AB-INITIO
Single-core optimization
Dipole
Adiabatic connection
États excités
Quantum chemistry
BENZENE MOLECULE
Diatomic molecules
Pesticides Metabolites Clustering Molecular modeling Environmental fate Partial least squares
Atomic and molecular structure and dynamics
Valence bond
Atomic processes
CP violation
Time-dependent density-functional theory
Excited states
3470+e
X-ray spectroscopy
A posteriori Localization
Atomic and molecular collisions
Acrolein
Relativistic quantum mechanics
Large systems
Spin-orbit interactions
3115vj
Ground states
Biodegradation
Molecular properties
Corrélation électronique
Ion
Wave functions
Anderson mechanism
Diffusion Monte Carlo
New physics
Approximation GW
AROMATIC-MOLECULES
Numerical calculations
Electron electric moment
Coupled cluster
AB-INITIO CALCULATION
Petascale
3115bw
Aimantation
Quantum Chemistry
Chimie quantique
Parity violation
Atom
3115aj
Atoms
Range separation
3115am
BIOMOLECULAR HOMOCHIRALITY
Time reversal violation
Atomic data
Ab initio calculation
Dispersion coefficients
ALGORITHM
BSM physics
Line formation
Carbon Nanotubes
Hyperfine structure
Azide Anion
A priori Localization
Density functional theory
Abiotic degradation
Relativistic quantum chemistry