DFT Simulations as Valuable Tool to Support NMR Characterization of Halide Perovskites: the Case of Pure and Mixed Halide Perovskites

Solid state NMR spectroscopy is swiftly emerging as useful tool to characterize the structure, composition and dynamic properties of lead halide perovskites. On the other hand, interpretation of solid state NMR signatures is often challenging, because of the potential presence of many overlapping signals in small range of chemical shifts, hence complicating the extraction of detailed structural features. Here, we demonstrate the reliability of periodic Density Functional Theory in providing theoretical support for the NMR characterization of halide perovskite compounds, considering nuclei with spin I=1/2. For light ¹H and ¹³C nuclei, we predict NMR chemical shifts in good agreement with experiment, further highlighting the effects of motional narrowing. Accurate prediction of the NMR response of ²⁰⁷Pb nuclei is comparably more challenging, but we successfully reproduce the downshift in frequency when changing the halide composition from pure iodine to pure bromine. Furthermore, we confirm NMR as ideal tool to study mixed halide perovskite compounds, currently at the limelight for tandem solar cells and color-tunable light emission.     

Non-linear optics in liquid-crystalline phases A 4 × 4 matrix formalism

The 4 × 4 matrix formalism of Berreman has been extended to include nonlinear optical terms. A non-linear source has to be added to the original homogeneous differential equation, giving an inhomogeneous equation that can be solved by standard procedures. The final expression can be given in a compact form by applying the Hamilton-Cayley theorem. The formalism is illustrated in the treatment of three-wave mixing in cholesteric phases.     

A numerical algorithm for pricing electricity derivatives for jump-diffusion processes based on continuous time lattices

We present a numerical algorithm for pricing derivatives on electricity prices. The algorithm is based on approximating the generator of the underlying price process on a lattice of prices, resulting in an approximation of the stochastic process by a continuous time Markov chain. We numerically study the rate of convergence of the algorithm for the case of the Merton jump-diffusion model and apply the algorithm to calculate prices and sensitivities of both European and Bermudan electricity derivatives when the underlying price follows a stochastic process which exhibits both fast mean-reversion and jumps of large magnitude.     

Crystallization of the mesomorphic form and control of the molecular structure for tailoring the mechanical properties of isotactic polypropylene

The combination of the control of the concentration of stereodefects in isotactic polypropylene using metallocene catalysts and the crystallization via the mesophase is a strategy to tailor the mechanical properties. Stiff materials, flexible materials, and thermoplastic elastomers can be produced depending only on the concentration of rr stereodefects. Modulus, ductility, and strength can be modulated through the crystallization of α and γ forms or of the mesophase. Different morphologies are observed depending on the stereoregularity and conditions of crystallization. Crystals of the mesomorphic form always exhibit a nodular morphology, accounting for the similar good deformability of all quenched samples, whatever the concentration of stereodefects. The mesophase transforms by thermal treatments into the α form preserving the nodular morphology, with increase of strength while maintaining the ductility typical of the mesophase. Annealing of the mesophase permits a precise adjustment of crystallinity and size of nodular crystals offering additional options to modify the mechanical properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 677–699     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Weak Intermolecular Hydrogen Bonds with Fluorine: Detection and Implications for Enzymatic/Chemical Reactions,Chemical Properties,and Ligand/Protein Fluorine NMR Screening

It is known that strong hydrogen‐bonding interactions play an important role in many chemical and biological systems. However, weak or very weak hydrogen bonds, which are often difficult to detect and characterize, may also be relevant in many recognition and reaction processes. Fluorine serving as a hydrogen‐bond acceptor has been the subject of many controversial discussions and there are different opinions about it. It now appears that there is compelling experimental evidence for the involvement of fluorine in weak intramolecular or intermolecular hydrogen bonds. Using established NMR methods, we have previously characterized and measured the strengths of intermolecular hydrogen‐bond complexes involving the fluorine moieties CH₂F, CHF₂, and CF₃, and have compared them with the well‐known hydrogen‐bond complex formed between acetophenone and the strong hydrogen‐bond donor p‐fluorophenol. We now report evidence for the formation of hydrogen bonds involving fluorine with significantly weaker donors, namely 5‐fluoroindole and water. A simple NMR method is proposed for the simultaneous measurement of the strengths of hydrogen bonds between an acceptor and a donor or water. Important implications of these results for enzymatic/chemical reactions involving fluorine, for chemical and physical properties, and for ligand/protein ¹⁹F NMR screening are analyzed through experiments and theoretical simulations.