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The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is…

A local approximation for dynamic polarizability leads to a nonlocal functional for the long-range dispersion interaction energy via an imaginary-frequency integral. We analyze several local polarizability approximations and argue that the…

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate…

The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional,…

A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…

We present an accurate local density-functional for electronic-structure calculations within the density functional theory (DFT). The functional is derived by analyzing the structure of the standard perturbative expansion of the correlation…

We use continuum mechanics [Tao \emph{et al}, PRL{\bf 103},086401] to approximate the dynamic density response of interacting many-electron systems. Thence we develop a numerically efficient exchange-correlation energy functional based on…

The effective central charge (denoted by $c_{\text{eff}}$) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient $c_{LR}$ of the two-point function of the energy-momentum…

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…

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. In this article, under some mild assumptions about both $X$ and the boundedness of the Hardy--Littlewood maximal operator on the associate space of the convexification of $X$, the…

The response of an infinite, periodic, insulating, solid to an infinitesimally small electric field is investigated in the framework of Density Functional Theory. We find that the applied perturbing potential is not a unique functional of…

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged…

By exploiting freedoms in the definitions of 'correlation', 'exchange' and 'Hartree' physics in ensemble systems we better generalise the notion of 'exact exchange' (EXX) to systems with fractional occupations functions of the frontier…

The discontinuous character of the exact exchange-correlation $(xc)$ energy functional of Density Functional Theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an \emph{ab-initio} $xc$…

This study investigates the impact of exchange-correlation functional choices on the predictive accuracy of multiscale models for charge transport in organic semiconductors (OSCs). A hybrid functional approach is applied to analyze…

In 1991 De Giorgi conjectured that, given $\lambda >0$, if $\mu_\varepsilon$ stands for the density of the Allen-Cahn energy and $v_\varepsilon$ represents its first variation, then $\int [v_\varepsilon^2 + \lambda] d\mu_\varepsilon$ should…

We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…

It is shown that the Hartree-plus-exchange-correlation density functional potential for an integer N-electron system differs by a constant form the corresponding potential for an (N-1)-electron system if the densities are determined from…

The on-shell self-energy of the homogeneous electron gas in second order of exchange, $\Sigma_{2{\rm x}}= {\rm Re} \Sigma_{2{\rm x}}(k_{\rm F},k_{\rm F}^2/2)$, is given by a certain integral. This integral is treated here in a similar way…

Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface.…