Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Bridging the Green Gap: Metal–Organic Framework Heteromultilayers Assembled from Porphyrinic Linkers Identified by Using Computational Screening

In organic photovoltaics, porphyrins (PPs) are among the most promising compounds owing to their large absorption cross-section, wide spectral range, and stability. Nevertheless, a precise adjustment of absorption band positions to reach a full coverage of the so-called green gap has not been achieved yet. We demonstrate that a tuning of the PP Q- and Soret bands can be carried out by using a computational approach for which substitution patterns are optimized in silico. The most promising candidate structures were then synthesized. The experimental UV/Vis data for the solvated compounds were in excellent agreement with the theoretical predictions. By attaching further functionalities, which allow the use of PP chromophores as linkers for the assembly of metal-organic frameworks (MOFs), we were able to exploit packing effects resulting in pronounced redshifts, which allowed further optimization of the photophysical properties of PP assemblies. Finally, we use a layer-by-layer method to assemble the PP linkers into surface-mounted MOFs (SURMOFs), thus obtaining high optical quality, homogeneous and crystalline multilayer films. Experimental results are in full accord with the calculations, demonstrating the huge potential of computational screening methods in tailoring MOF and SURMOF photophysical properties.     

Solar Thermal Energy Storage in a Photochromic Macrocycle

The conversion and efficient storage of solar energy is recognized to hold significant potential with regard to future energy solutions. Molecular solar thermal batteries based on photochromic systems exemplify one possible technology able to harness and apply this potential. Herein is described the synthesis of a macrocycle based on a dimer of the dihydroazulene/vinylheptafulvene (DHA/VHF) photo/thermal couple. By taking advantage of conformational strain, this DHA–DHA macrocycle presents an improved ability to absorb and store incident light energy in chemical bonds (VHF–VHF). A stepwise energy release over two sequential ring‐closing reactions (VHF→DHA) combines the advantages of an initially fast discharge, hypothetically addressing immediate energy consumption needs, followed by a slow process for consistent, long‐term use. This exemplifies another step forward in the molecular engineering and design of functional organic materials towards solar thermal energy storage and release.     

Highly Functionalized Cyclopentane Derivatives by Tandem Michael Addition/Radical Cyclization/Oxygenation Reactions

Densely functionalized cyclopentane derivatives with up to four consecutive stereocenters are assembled by a tandem Michael addition/single‐electron transfer oxidation/radical cyclization/oxygenation strategy mediated by ferrocenium hexafluorophosphate, a recyclable, less toxic single‐electron transfer oxidant. Ester enolates were coupled with α‐benzylidene and α‐alkylidene β‐dicarbonyl compounds with switchable diastereoselectivity. This pivotal steering element subsequently controls the diastereoselectivity of the radical cyclization step. The substitution pattern of the radical cyclization acceptor enables a switch of the cyclization mode from a 5‐exo pattern for terminally substituted olefin units to a 6‐endo mode for internally substituted acceptors. The oxidative anionic/radical strategy also allows efficient termination by oxygenation with the free radical 2,2,6,6‐tetramethyl‐1‐piperidinoxyl, and two C?C bonds and one C?O bond are thus formed in the sequence. A stereochemical model is proposed that accounts for all of the experimental results and allows the prediction of the stereochemical outcome. Further transformations of the synthesized cyclopentanes are reported.