Porous and Water Stable 2D Hybrid Metal Halide with Broad Light Emission and Selective H2O Vapor Sorption

In this work we report a strategy for generating porosity in hybrid metal halide materials using molecular cages that serve as both structure-directing agents and counter-cations. Reaction of the [2.2.2] cryptand (DHS) linker with Pb^II in acidic media gave rise to the first porous and water-stable 2D metal halide semiconductor (DHS)₂Pb₅Br₁₄. The corresponding material is stable in water for a year, while gas and vapor-sorption studies revealed that it can selectively and reversibly adsorb H₂O and D₂O at room temperature (RT). Solid-state NMR measurements and DFT calculations verified the incorporation of H₂O and D₂O in the organic linker cavities and shed light on their molecular configuration. In addition to porosity, the material exhibits broad light emission centered at 617 nm with a full width at half-maximum (FWHM) of 284 nm (0.96 eV). The recorded water stability is unparalleled for hybrid metal halide and perovskite materials, while the generation of porosity opens new pathways towards unexplored applications (e.g. solid-state batteries) for this class of hybrid semiconductors.     

17O NMR studies of electronic and steric interactions of substituted quinoxaline-2(1H),3(4H)-diones

¹⁷O nmr studies, at natural abundance, of substituted quinoxaline-2(1H),3(4H)-diones demonstrate that the ¹⁷O chemical shift data can provide new insights into steric and electronic interactions due to long range substituent effects on the aromatic ring. The role of considerable “keto” character and torsion angle deformation of the diamide group in solution is emphasized.     

Excitonic Bands in the Spectra of Some Organic-Inorganic Hybrid Compounds Based on Metal Halide Units

 The optical absorption, photoluminescence, and photoconductivity spectra of some compounds of the formulas [R(CH₂) _n NH₃] _x M _y X _z , [R(CH₂) _n NH(CH₃)₂] _x M _y X _z , [R(CH₂) _n S(CH₃)₂] _x M _y X _z , [R(CH₂) _n SC(NH₂)₂] _x M _y X _z , and [R(CH₂) _n SeC(NH₂)₂] _x M _y X _z (R = organic residue; M = Bi(III), Pb(II), Sn(II), Cu(I), Ag(I) etc; X = I, Br, Cl; n, x, y, z = 0, 1, 2, 3, …) are briefly reviewed, and some new results are reported. The position, intensity, and shape of the excitonic bands depend on the dimensionality and size of the inorganic network as well as on the nature of the M, X, R, and onium moieties.     

Dodekahydro‐closo‐dodekaborate der schweren Erdalkalimetalle aus wäßriger Lösung: Ca(H2O)7[B12H12] · H2O,Sr(H2O)8[B12H12] und Ba(H2O)6[B12H12]

Dodecahydro‐ closo ‐dodecaborates of the Heavy Alkaline‐Earth Metals from Aqueous Solution: Ca(H₂O)₇[B₁₂H₁₂] · H₂O, Sr(H₂O)₈[B₁₂H₁₂], and Ba(H₂O)₆[B₁₂H₁₂] The crystalline hydrates of the heavy alkaline earth metal dodecahydro‐closo‐dodecaborates (M[B₁₂H₁₂] · n H₂O, n = 6–8; M = Ca, Sr, Ba) are easily accessible by reaction of an aqueous (H₃O)₂[B₁₂H₁₂] solution with an alkaline earth metal carbonate (MCO₃). By isothermic evaporation of the respective aqueous solution we obtained colourless single crystals which are characterized by X‐ray diffraction at room temperature. The three compounds Ca(H₂O)₇[B₁₂H₁₂] · H₂O (orthorhombic, P2₁2₁2₁; a = 1161.19(7), b = 1229.63(8), c = 1232.24(8) pm; Z = 4), Sr(H₂O)₈[B₁₂H₁₂] (trigonal, R3; a = 1012.71(6), c = 1462.94(9) pm; Z = 3) and Ba(H₂O)₆[B₁₂H₁₂] (orthorhombic, Cmcm; a = 1189.26(7) pm, b = 919.23(5) pm, c = 1403.54(9) pm; Z = 4) are neither formula‐equal nor isostructural. The structure of Sr(H₂O)₈[B₁₂H₁₂] is best described as a NaCl‐type arrangement, Ba(H₂O)₆[B₁₂H₁₂] rather forms a layer‐like and Ca(H₂O)₇[B₁₂H₁₂] · H₂O a channel‐like structure. In first sphere the alkaline earth metal cations Ca²⁺ and Sr²⁺ are coordinated by just seven and eight oxygen atoms from the surrounding water molecules, respectively. A direct coordinative influence of the quasi‐icosahedral [B₁₂H₁₂]^2– cluster anions becomes noticeable only for the Ba²⁺ cations (CN = 12) in Ba(H₂O)₆[B₁₂H₁₂]. The dehydratation of the alkaline earth metal dodecahydro‐closo‐dodecaborate hydrates has been shown to take place in several steps. Thermal treatment leads to the anhydrous compounds Ca[B₁₂H₁₂], Sr[B₁₂H₁₂] and Ba[B₁₂H₁₂] at 224, 164 and 116 °C, respectively.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

Two Characterizations of Optimality in Dynamic Programming

It holds in great generality that a plan is optimal for a dynamic programming problem, if and only if it is “thrifty” and “equalizing.” An alternative characterization of an optimal plan, that applies in many economic models, is that the plan must satisfy an appropriate Euler equation and a transversality condition. Here we explore the connections between these two characterizations.     

Complete description of invariant Einstein metrics on the generalized flag manifold SO(2n)/U(p)?× U(n ? p)

We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems. We also examine the isometric problem for these Einstein metrics.