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Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron…
Ensemble Density Functional Theory (EDFT) is a generalization of ground-state Density Functional Theory (GS DFT), which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms…
The ground state of an homogeneous electron gas is a paradigmatic state that has been used to model and predict the electronic structure of matter at equilibrium for nearly a century. For half a century, it has been successfully used to…
Semi-local density functionals for the exchange-correlation energy of electrons are extensively used as it produce realistic and accurate results for finite and extended systems. The choice of techniques play crucial role in constructing…
Using a linear combination of atomic orbitals approach, we report a systematic comparison of various Density Functional Theory (DFT) and hybrid exchange-correlation functionals for the prediction of the electronic and structural properties…
Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band-gap materials. This promise is contingent upon the…
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…
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…
We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from…
Recently, Tao and Mo (TM) proposed an accurate all-purpose nonempirical meta-generalized gradient approximation (meta-GGA). The exchange part was derived from the density matrix approximation, while the correlation part is based on a…
The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by…
In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals,…
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…
Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations…
The effective g-factor ($g^{*}$) of a dilute interacting two-dimensional electron system is expected to increase with respect to its bare value as the density is lowered, and to eventually diverge as the system makes a transition to a…
Density-functional theory simplifies many-electron calculations by approximating the exchange and correlation interactions with a one-electron operator that is a functional of the density. Hybrid functionals incorporate some amount of exact…
The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc)…
We calculate the optical spectra of silicon and germanium in the adiabatic time-dependent density functional formalism, making use of kinetic energy density-dependent (meta-GGA) exchange-correlation functionals. We find excellent agreement…
We study numerically the strong-interaction limit of the exchange-correlation functional for neutral atoms and for Bohr atoms as the number of electrons increases. Using a compact representation, we analyse the second-order gradient…