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.     

Correlating Charge-Carrier Dynamics with Efficiency in Quantum-Dot Solar Cells: Can Excitonics Lead to Highly Efficient Devices?

The photovoltaic performance of quantum-dot solar cells strongly depends on the charge-carrier relaxation and recombination processes, which need to be modulated in a favorable way to obtain maximum efficiency. Recently, significant efforts have been devoted to investigate the carrier dynamics of nanocrystal sensitizers, both in solution and deposited on TiO₂ photoanodes, with the aim to correlate the excitonics with solar-energy conversion efficiency. This Minireview summarizes some proof of the concepts that efficiency can be directly correlated to the exciton dynamics of quantum-dot solar cells. The presented findings are based on CdSeS alloy, CdSe/CdS core/shell, Au/CdSe nanohybrids, and Mn-doped CdZnSSe nanocrystals, where the favourable excitonic processes are optimized to enhance the efficiency. Future prospects and limitations are addressed as well.     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Multifold factorizations of cyclic groups into subsets

Let $(G,+)$ be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset $A+B:=\{a+b:a\in A,b\in B\}$. In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact value or an upper bound of the minimum multiplicity λ of a factorization of G can be given by introducing a concept of ‘lcm-closure’. Furthermore, a couple of properties on a given factor A will be shown when A has a prime or prime power order (cardinality). A relation to multifold factorizations of the set of integers will be also glanced at a general perspective.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Conformational Changes and Redox Properties of Bimetallic Single Helicates of Hexapyrrole-α,ω-dicarbaldehydes

The hexapyrrole-α,ω-dicarbaldehydes 1 a and 1 b were metallated with Cu^II, Ni^II, and Pd^II to give bimetallic complexes where a pair of 3 N+O four-coordinate metal planes are helically distorted and the central 2,2′-bipyrrole subunit adopts a cis or trans conformation. X-ray crystallographic analysis of the bisCu complex revealed a closed form with a cis-2,2′-bipyrrole subunit and an open form with a trans-2,2′-bipyrrole subunit. The bisPd complexes took a closed form both in the solid state and in solution. They are regarded as single helicates of two turns and the energy barrier for the interchange between an M helix and a P helix was remarkably influenced by the bulky 3,3′-substituent of the central 2,2′-bipyrrole subunit. Although the bisNi complexes adopt a closed form in the solid state, they exist as a homohelical open C₂-symmetric form or a heterohelical open C_i-symmetric form in solution. A theoretical study suggested that the closed form of 1 a Pd was stabilized by the Pd–Pd interaction. Compound 1 a Pd was reversibly oxidized by one electron at 0.14 V versus ferrocene/ferrocenium (Fc/Fc⁺) and this oxidized species showed Vis/NIR absorption bands at λ=767 and 1408 nm.