Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.Comment: 11 pages, 7 figure

Semilocal density functional theory with correct surface asymptotics

Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to the ones at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.Comment: 6 pages, 4 figure

Subsystem density functional theory with meta generalized gradient approximation exchange-correlation functionals

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes the problem and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.Comment: 14 pages, 3 figure

Semiclassical atom theory applied to solid-state physics

Using the semiclassical neutral atom theory, we extend to fourth order the modified gradient expansion of the exchange energy of density functional theory. This expansion can be applied both to large atoms and solid-state problems. Moreover, we show that it can be employed to construct a simple and non-empirical generalized gradient approximation (GGA) exchange-correlation functional competitive with state-of-the-art GGAs for solids, but also reasonably accurate for large atoms and ordinary chemistry.Comment: 10 pages, 7 figure

Assessment of the TCA functional in computational chemistry and solid-state physics

We assess the Tognetti-Cortona-Adamo (TCA) generalized gradient approximation correlation functional [J. Chem. Phys. 128:034101 (2008)] for a variety of electronic systems. We find that, even if the TCA functional is not exact for the uniform electron gas, it is very accurate for the jellium surface correlation energies and it gives a realistic description of the quantum oscillations and surface effects of various jellium clusters, that are important model systems in computational chemistry and solid-state physics. When the TCA correlation is combined with the non-empirical PBEint, Wu-Cohen, and PBEsol$_b$ exchange functionals, the resulting exchange-correlation approximations provide good performances for a broad palette of systems and properties, being reasonably accurate for thermochemistry and geometry of molecules, transition metal complexes, non-covalent interactions,equilibrium lattice constants, bulk moduli, and cohesive energies of solids.Comment: 14 pages, 6 figure

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure