Perturbative calculation of Franck-Condon integrals: new hints for a rational implementation

Perturbative approaches to the mode mixing effects in the calculation of Franck-Condon integrals are analyzed and discussed. The zero order multidimensional Franck-Condon integrals are factorized into products of one-dimensional ones, so that recurrence relations can be used without need of storing a huge number of data. Calculations on model systems show that at the second order of perturbation, the method gives results in very good agreement with the exact ones, even in the case of significantly large Duschinsky effect. The accuracy of the results can be substantially improved by grouping together all those modes which are strongly mixed with each other, usually a few ones, for which Franck-Condon integrals can be computed exactly, and using the perturbative approach for treating the smaller mixing between all the other modes.     

A Dual Photoredox- and Cp2TiCl2-Catalyzed Approach for the Direct Access to α-Vinyl-β-hydroxy Esters

For the first time, a dual photoredox- and titanocene-catalyzed methodology for the regioselective access to α-vinyl-β-hydroxy esters towards aldehyde allylation with 4-bromobut-2-enoate is reported. The protocol is based on the Barbier-type properties of the inexpensive and available Cp₂TiCl₂ in catalytic amount (5 mol%). The developed mild reaction conditions gave access to a library of differently functionalized α-vinyl-β-hydroxy esters in moderate diastereoselectivity, employing the commercially available ethyl 4-bromobut-2-enoate and both aromatic and aliphatic aldehydes. The reaction was realized under visible light irradiation, in the presence of an organophotocatalyst (3DPAFIPN, 2 mol%) combined with Hantzsch's ester as the sacrificial reductant. In contrast to other Barbier-type reactions employing ethyl 4-bromobut-2-enoate, the photoredox system ensures a better regioselectivity. Moreover, the use of preformed organometallic nucleophilic species (e. g., dienolborinates), and the need of metal reductants or stoichiometric amount of transition metals in low oxidation state for Barbier-type reactions, is avoided. To support the experimental evidence, a detailed photophysical study shed light on the mechanism of the reaction.     

Halogen Bonding Assembles Anion⋅⋅⋅Anion Architectures in Non-centrosymmetric Iodate and Bromate Crystals

Single crystal X-ray diffraction of iodate and bromate salts shows that the I and Br atoms in IO₃⁻ and BrO₃⁻ anions form short and linear O−I/Br ⋅⋅⋅ O contacts with the O atoms of nearby anions. Non-centrosymmetric systems are formed wherein anions are orderly aligned into supramolecular 1D and 2D networks. Theoretical evidences, namely the outcome of QTAIM and NCIplot studies, prove the attractive nature of these contacts and the ability of iodate and bromate anions to act as robust halogen bond (HaB) donors. The HaB is proposed as a general and effective assisting tool to control the architecture of acentric iodate salts.     

Structural Polymorphism and Thin Film Transistor Behavior in the Fullerene Framework Molecule 5,6;11,12‐di‐o‐Phenylenetetracene

The molecular structure of the hydrocarbon 5,6;11,12‐di‐o‐phenylenetetracene (DOPT), its material characterization and evaluation of electronic properties is reported for the first time. A single‐crystal X‐ray study reveals two different motifs of intramolecular overlap with herringbone‐type arrangement displaying either face‐to‐edge or co‐facial face‐to‐face packing depicting intensive π–π interactions. Density functional theory (DFT) calculations underpin that a favorable electronic transport mechanism occurs by a charge hopping process due to a π‐bond overlap in the DOPT polymorph with co‐facial arene orientation. The performance of polycrystalline DOPT films as active organic semiconducting layer in a state‐of‐the‐art organic field effect transistor (OFET) device was evaluated and proves to be film thickness dependent. For 40 nm layer thickness it displays a saturation hole mobility (μ_hole) of up to 0.01 cm² V^?1 s^?1 and an on/off‐ratio (I_on/I_off) of 1.5×10³.     

Excitation Dynamics in Hetero‐bichromophoric Calixarene Systems

In this work, the dynamics of electronic energy transfer (EET) in bichromophoric donor–acceptor systems, obtained by functionalizing a calix[4]arene scaffold with two dyes, was experimentally and theoretically characterized. The investigated compounds are highly versatile, due to the possibility of linking the dye molecules to the cone or partial cone structure of the calix[4]arene, which directs the two active units to the same or opposite side of the scaffold, respectively. The dynamics and efficiency of the EET process between the donor and acceptor units was investigated and discussed through a combined experimental and theoretical approach, involving ultrafast pump–probe spectroscopy and density functional theory based characterization of the energetic and spectroscopic properties of the system. Our results suggest that the external medium strongly determines the particular conformation adopted by the bichromophores, with a direct effect on the extent of excitonic coupling between the dyes and hence on the dynamics of the EET process itself.     

Weighted $${{L^p}}$$-Liouville theorems for hypoelliptic partial differential operators on Lie groups

We prove weighted \({L^p}\)-Liouville theorems for a class of second-order hypoelliptic partial differential operators \({\mathcal{L}}\) on Lie groups \({\mathbb{G}}\) whose underlying manifold is \({n}\)-dimensional space. We show that a natural weight is the right-invariant measure \(\check{H}\) of \({\mathbb{G}}\). We also prove Liouville-type theorems for \({C^{2}}\) subsolutions in \({L^{p}(\mathbb{G},\check{H})}\). We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator \({\mathcal{L}-\partial_{t}}\).     

Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case

We study the ODE/IM correspondence for ODE associated to \({\widehat{\mathfrak{g}}}\)-valued connections, for a simply-laced Lie algebra \({\mathfrak{g}}\). We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called \({\Psi}\)-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.     

A primal algorithm for the weighted minimum covering ball problem in $$\mathbb {R}^n$$

The nonlinear programming problem of finding the minimum covering ball of a finite set of points in \(\mathbb {R}^n\), with a positive weight corresponding to each point, is solved by a directional search method. At each iteration, the search path is either a ray or the arc of a circle and is determined by bisectors of points. Each step size along the search path is determined explicitly. The primal algorithm is shown to search along the farthest point Voronoi diagram of the given points. We provide computational results that show the efficiency of the algorithm when compared to general convex nonlinear optimization solvers.     

Laminar-turbulent reactive flows in porous media

We state some recent results concerning liquid-vapor phase transitions for a fluid flow through a porousmedium. The focus is on the friction exerted by the porous medium, which is modeled in such a way to include both laminar and turbulent flows. In this way we obtain a hyperbolic system of three balance laws with a forcing term that is discontinuous in the state variables. Existence, uniqueness and qualitative behavior of traveling waves is proved by a novel regularization technique.     

Discovery of novel polyamine analogs with anti-protozoal activity by computer guided drug repositioning

Chagas disease is a parasitic infection caused by the protozoa Trypanosoma cruzi that affects about 6 million people in Latin America. Despite its sanitary importance, there are currently only two drugs available for treatment: benznidazole and nifurtimox, both exhibiting serious adverse effects and limited efficacy in the chronic stage of the disease. Polyamines are ubiquitous to all living organisms where they participate in multiple basic functions such as biosynthesis of nucleic acids and proteins, proliferation and cell differentiation. T. cruzi is auxotroph for polyamines, which are taken up from the extracellular medium by efficient transporters and, to a large extent, incorporated into trypanothione (bis-glutathionylspermidine), the major redox cosubstrate of trypanosomatids. From a 268-compound database containing polyamine analogs with and without inhibitory effect on T. cruzi we have inferred classificatory models that were later applied in a virtual screening campaign to identify anti-trypanosomal compounds among drugs already used for other therapeutic indications (i.e. computer-guided drug repositioning) compiled in the DrugBank and Sweetlead databases. Five of the candidates identified with this strategy were evaluated in cellular models from different pathogenic trypanosomatids (T. cruzi wt, T. cruzi PAT12, T. brucei and Leishmania infantum), and in vitro models of aminoacid/polyamine transport assays and trypanothione synthetase inhibition assay. Triclabendazole, sertaconazole and paroxetine displayed inhibitory effects on the proliferation of T. cruzi (epimastigotes) and the uptake of putrescine by the parasite. They also interfered with the uptake of others aminoacids and the proliferation of infective T. brucei and L. infantum (promastigotes). Trypanothione synthetase was ruled out as molecular target for the anti-parasitic activity of these compounds.