Conductive metal-organic frameworks and networks: fact or fantasy?

Electrical conduction is well understood in materials formed from inorganic or organic building blocks, but their combination to produce conductive hybrid frameworks and networks is an emerging and rapidly developing field of research. Self-assembling organic-inorganic compounds offer immense potential for functionalising material properties for a wide scope of applications including solar cells, light emitters, gas sensors and bipolar transparent conductors. The flexibility of combining two distinct material classes into a single solid-state system provides an almost infinite number of chemical and structural possibilities; however, there is currently no systematic approach established for designing new compositions and configurations with targeted electronic or optical properties. We review the current status in the field, in particular, the range of hybrid systems reported to date and the important role of materials modelling in the field. From theoretical arguments, the Mott insulator-to-metal transition should be possible in semiconducting metal-organic frameworks, but has yet to be observed. The question remains as to whether electro-active hybrid materials will evolve from chemical curiosities towards practical applications in the near term.     

Analytical evaluation of Fukui functions and real-space linear response function

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects.     

Structural and electronic properties of CuSbS2 and CuBiS2: potential absorber materials for thin-film solar cells

As the demand for photovoltaics rapidly increases, there is a pressing need for the identification of new visible light absorbing materials for thin-film solar cells that offer similar performance to the current technologies based on CdTe and Cu(In,Ga)Se(2). Metal sulphides are the ideal candidate materials, but their band gaps are usually too large to absorb significant fractions of visible light. However, by combining Cu(+) (low binding energy d(10) band) and Sb(3+)/Bi(3+) (low binding energy s(2) band), the ternary sulphides CuSbS(2) and CuBiS(2) are formed, which have been gathering recent interest for solar cell applications. Using a hybrid density functional theory approach, we calculate the structural and electronic properties of these two materials. Our results highlight the stereochemical activity of the Sb and Bi lone pair electrons, and predict that the formation of hole carriers will occur in the Cu d(10) band and hence will involve oxidation of Cu(I).     

The foundations of relativity

In a previous paper a stochastic foundation was proposed for microphysics: the nonrelativistic and relativistic domains were shown to be connected with two different approximations of diffusion theory; the relativistic features (Lorentz contraction for the coordinate standard deviation, covariant diffusion equation) were not derived from the relativistic formalism introduced at the start, but emerged from diffusion theory itself. In the present paper these results are given a new presentation, which aims at elucidating not the foundations of quantum mechanics, but those of relativity. This leads to a discussion of points still controversial in the interpretation of relativity. In particular two problems appear in a new light: the character of time and length alterations, and the privileged role of the velocityc. Besides, the question of a possible limitation of relativity (and more generally of the laws of mechanics) in the domain of particle substructure is raised and supported by exemples drawn from the hydrodynamical model of a spinned particle. Suggestions are presented for the possibility of a deeper conceptual unification of special and general relativity.     

Black Hole Thermodynamics and Lorentz Symmetry

Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.     

Zeros of Polynomials on Banach Spaces: The Real Story

Let E be a real Banach space. We show that either E admits a positive definite 2-homogeneous polynomial or every 2-homogeneous polynomial on E has an infinite dimensional subspace on which it is identically zero. Under addition assumptions, we show that such subspaces are non-separable. We examine analogous results for nuclear and absolutely (1,2)-summing 2-homogeneous polynomials and give necessary and sufficient conditions on a compact set K so that C(K) admits a positive definite 2-homogeneous polynomial or a positive definite nuclear 2-homogeneous polynomial.     

Dumbbells of Five-Connected Silicon Atoms and Superconductivity in the Binary Silicides MSi(3) (M = Ca, Y, Lu)

The new metastable binary silicides MSi(3) (M = Ca, Y, Lu) have been synthesized by high-pressure, high-temperature reactions at pressures between 12(2) and 15(2) GPa and temperatures from 900(100) to 1400(150) K. The atomic patterns comprise intricate silicon layers of condensed molecule-like Si(2) dimers. The alkaline-earth element adopts the oxidation state +2, while the rare-earth and transition metals realize +3. All of the compounds exhibit BCS-type superconductivity with weak electron-phonon coupling below critical temperatures of up to 7 K.     

Combinatorics of a certain ideal in the Segre coordinate ring

We focus on a ``fat' model of an ideal in the class of the canonical ideal of the Segre coordinate ring, looking at its Rees algebra and related arithmetical questions.