We study the electronic structure of black phosphorus by combining state-of-the-art density functional theory, multiple scattering calculations and electron energy loss spectroscopy. The hybrid functionals HSE03 and PBE0 are tested to investigate whether they give an improved description compared to the more traditional PZ-LDA and PBE-GGA functionals. These calculations are compared with invest...

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order objects, i.e. functionals are terms, computation is term rewriting. Œe idea explored in the paper is that functionals correspond to generic mechanisms for ma...

The difficulty of approximate density functionals in describing the energetics of Diels-Alder reactions and dimerization of aluminum complexes is analyzed. Both of these reaction classes involve formation of cyclic or bicyclic products, which are found to be underbound by the majority of functionals considered. We present a consistent view of these results from the perspective of delocalization...

This paper is concerned with the approximation of matrix functionals defined by a large, sparse or structured, symmetric definite matrix. These functionals are Stieltjes integrals with a measure supported on a compact real interval. Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may yield...

We present two new exchange-correlation functionals for hybrid Kohn-Sham electronic structure calculations based on the nonseparable functional form introduced recently in the N12 and MN12-L functionals but now with the addition of screened Hartree-Fock exchange. The first functional depends on the density and the density gradient and is called N12-SX; the second functional depends on the densi...

A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular scales, providing a crucial test of inflation. We propose Minkowski functionals as a calculational tool for testing Gaussianity and characterizing deviations ...

SIRS models with delay times (discrete or distributed) are studied. By means of Lyapunov functionals, we establish the global stability conditions of the equilibrium states. We will make ingenious linear combination of common quadratic, composite quadratic and Volterra-type functionals, for obtain a suitable Lyapunov functionals.

Density-functional theory requires ever better exchange-correlation (xc) functionals for the ever more precise description of many-body effects on electronic structure. Universal constraints on the xc energy are important ingredients in the construction of improved functionals. Here we investigate one such universal property of xc functionals: the Lieb-Oxford lower bound on the exchange-correla...