Strength of the [Z–I···Hal]− and [Z–Hal···I]− Halogen Bonds: Electron Density Properties and Halogen Bond Length as Estimators of Interaction Energy

Bond energy is the main characteristic of chemical bonds in general and of non-covalent interactions in particular. Simple methods of express estimates of the interaction energy, Eint, using relationships between Eint and a property which is easily accessible from experiment is of great importance for the characterization of non-covalent interactions. In this work, practically important relationships between Eint and electron density, its Laplacian, curvature, potential, kinetic, and total energy densities at the bond critical point as well as bond length were derived for the structures of the [Z–I···Hal]– and [Z–Hal···I]– types bearing halogen bonds and involving iodine as interacting atom(s) (totally 412 structures). The mean absolute deviations for the correlations found were 2.06–4.76 kcal/mol.

Bistable curvature potential at hyperbolic points of nematic shells

At hyperbolic points, where the Gaussian curvature is negative, nematic shells with unequal elastic constants can exhibit two preferred alignments.

Ten shades of black

The holographic principle has taught us that, as far as their entropy content is concerned, black holes in (3 + 1)-dimensional curved spacetimes behave as ordinary thermodynamic systems in flat (2 + 1)-dimensional spacetimes. In this paper, we point out that the opposite behavior can also be observed in black-hole physics. To show this we study the quantum Hawking evaporation of near-extremal Reissner–Nordström (RN) black holes. We first point out that the black-hole radiation spectrum departs from the familiar radiation spectrum of genuine (3 + 1)-dimensional perfect black-body emitters. In particular, the would be black-body thermal spectrum is distorted by the curvature potential which surrounds the black-hole and effectively blocks the emission of low-energy quanta. Taking into account the energy-dependent gray-body factors which quantify the imprint of passage of the emitted radiation quanta through the black-hole curvature potential, we reveal that the (3 + 1)-dimensional black holes effectively behave as perfect black-body emitters in a flat (9 + 1)-dimensional spacetime.

One gravitational potential or two? Forecasts and tests

The metric of a perturbed Robertson–Walker space–time is characterized by three functions: a scale-factor giving the expansion history and two potentials that generalize the single potential of Newtonian gravity. The Newtonian potential induces peculiar velocities and, from these, the growth of matter fluctuations. Massless particles respond equally to the Newtonian potential and to a curvature potential. The difference of the two potentials, called the gravitational slip, is predicted to be very small in general relativity, but can be substantial in modified gravity theories. The two potentials can be measured, and gravity tested on cosmological scales, by combining weak gravitational lensing or the integrated Sachs–Wolfe effect with galaxy peculiar velocities or clustering.