Related papers: Exact ground-state properties of one-dimensional e…
We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\"odinger perturbation theory to show that, in…
For the two-dimensional electron gas, the exact high-density limit of the correlation energy is evaluated here numerically for all values of the spin polarization. The result is spin-resolved into $\uparrow\uparrow$, $\uparrow\downarrow$,…
In this paper, we present the rigorous expression of the ground state energy and study the phase transition of the three-dimensional homogeneous electron gas by the eigenfunctional theory. The ground state energy is decided completely by…
We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum…
We use a recent approach [Phys. Rev. Letters, {\bf 84}, 959 (2000)] for including Coulomb interactions in quantum systems via a classical mapping of the pair-distribution functions (PDFs) for a study of the 2-D electron gas. As in the 3-D…
We present a new method for realizing the adiabatic connection approach in density functional theory, which is based on combining accurate variational quantum Monte Carlo calculations with a constrained optimization of the ground state…
Excitons in low-dimensional materials behave mathematically as confined hydrogen atoms. An appealing unified description of confinement in quantum wells or wires, etc., is found by restricting space to a fractional dimension 1 < D <= 3…
Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial `step' structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the…
Methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In one method, the electron density is…
The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…
Density functional theory at finite temperatures often relies on the zero-temperature approximation, which uses a ground-state exchange-correlation functional with thermalized densities. This approach, however, neglects the explicit…
In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schr\"odinger equation. Such an error in the different calculations is not…
In this work we have studied a new functional for the correlation energy obtained from the exact-exchange (EXX) approximation within time-dependent density functional theory (TDDFT). Correlation energies have been calculated for a number of…
Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose a…
The exchange-correlation hole density of the infinitely stretched (dissociated) hydrogen molecule can be cast into a closed analytical form by using its exact wave function. This permits to obtain an explicit exchange-correlation energy…
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly non-local density…
We have obtained an analytic expression for the ring diagrams contribution to the correlation energy of a two dimensional electron liquid as a function of the uniform fractional spin polarization. Our results can be used to improve on the…
We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit…
The complex ac-response of a quasi-one dimensional electron system in the one-band approximation with an interaction potential of finite range is investigated. It is shown that linear response is exact for this model. The influence of the…
Following a recent work [E. Fromager, J. Phys. Chem. A 2025, 129, 4, 1143-1155] on the ensemble density functional theory (DFT) of excited electronic energy levels, we derive in this paper the ensuing static linear response theory, thus…