Related papers: Machine Learning Modeling of Wigner Intracule Func…
An outstanding challenge in chemical computation is the many-electron problem where computational methodologies scale prohibitively with system size. The energy of any molecule can be expressed as a weighted sum of the energies of…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
We perform unrestricted Hartree-Fock (HF) calculations for electrons in a parabolic quantum dot at zero magnetic field. The crossover from Fermi liquid to Wigner molecule behavior is studied for up to eight electrons and various spin…
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a…
Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted…
We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and…
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation…
We study the exchange coupling in small Wigner crystals confined to one-dimensional space. In particular we concentrate on the simplest nontrivial case of two electrons in a box potential and calculate analytically the energy splitting…
In one-channel, finite-size Luttinger one-dimensional quantum dots, both Friedel oscillations and Wigner correlations induce oscillations in the electron density with the same wavelength, pinned at the same position. Therefore, observing…
The capability of density-functional theory to deal with the ground-state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation…
We propose a descriptor for molecular electronic structure that is based solely on the one- and two-electron integrals but is translationally, rotationally, and unitarily invariant. Then, directly exploiting size consistency, we train and…
The linear term proportional to $|N-Z|$ in the nuclear symmetry energy (Wigner energy)is obtained in a model that uses isovector pairing on single particle levels from a deformed potential combined with a $\vec T^2$ interaction. The pairing…
We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential. This functional is extremely non-local, but…
The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a…
We present here a model of the exchange-correlation hole for strongly correlated systems using a simple nonlocal generalization of the Wigner--Seitz radius. The model behaves similarly to the strictly correlated electron approach, which…
We revisit the machine-learning (ML) approach to the universal density functional $F[\mathbf{n}]$ of the one-dimensional Hubbard model with a site-dependent random potential $\mathbf{v}=\{v_{i}\}$. We generate exact ground-state data via…
The ground state energy of the two--dimensional uniform electron gas has been calculated with fixed--node diffusion Monte Carlo, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We…
We present a machine learning (ML) method for predicting electronic structure correlation energies using Hartree-Fock input.The total correlation energy is expressed in terms of individual and pair contributions from occupied molecular…
Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…
The functional-renormalization-group aided density-functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius $…