Related papers: Improved Lieb-Oxford exchange-correlation inequali…
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality.…
We prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller…
The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the…
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents…
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends…
We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with…
We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying…
In this manuscript we provide a family of lower bounds on the indirect Coulomb energy for atomic and molecular systems in two dimensions in terms of a functional of the single particle density with gradient correction terms.
We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching…
A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation…
Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less…
We improve the previous study of the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity parameter.…
An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the…
Coulomb drag experiments in which the inter-layer resistivity is measured are important as they provide information on the Coulomb interactions in bilayer systems. When the layer densities are low correlation effects become significant to…
The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both…
We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it…
The large-$Z$ asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading $Z…
By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be…