Challenging the weak cosmic censorship conjecture with charged quantum particles

Motivated by the recent attempts to violate the weak cosmic censorship conjecture for near-extreme black-holes, we consider the possibility of overcharging a near-extreme Reissner-Nordstr\"om black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-1/2 particles by the black hole in a unified framework and obtain analytically, for the first time, the pertinent reflection and transmission coefficients without any small charge approximation. Based on these results, we propose some gedanken experiments that could lead to the violation of the weak cosmic censorship conjecture due to the (classically forbidden) absorption of small energy charged particles by the black hole. As for the case of scattering in Kerr spacetimes, our results demonstrate explicitly that scalar fields are subject to (electrical) superradiance phenomenon, while spin-1/2 fields are not. Superradiance impose some limitations on the gedanken experiments involving spin-0 fields, favoring, in this way, the mechanisms for creation of a naked singularity by the quantum tunneling of spin-1/2 charged fermions. We also discuss the implications that vacuum polarization effects and quantum statistics might have on these gedanken experiments. In particular, we show that they are not enough to prevent the absorption of incident small energy particles and, consequently, the formation of a naked singularity.Comment: 9 pages; Final version to appear in PR

Reactivity studies of thienyl and (oligo)thienylpyrroles

Currently, a variety of synthetic approaches to substituted pyrroles exist, although their synthesis, in general, remains challenging. Often, the yields are rather low and a significant number of by-products, such as undesired regioisomers, are obtained. Furthermore, pyrroles are susceptible to chemical degradation as they are rather easily oxidized; this further hampers their synthesis and especially their isolation and purification.1 The chemistry of thienylpyrroles is a very recent field in the chemistry of heterocyclic compounds. In the last few years, synthetic 2-thienylpyrrole derivatives have come in focus. However, even more than 60 years since the first 2-thienylpyrrole: bis-2-[5-(2-thienyl)pyrrole]azametine dihydrochloride) has been reported by Edward Knott2 at Kodak, the synthesis of functionalized thienyl and (oligo)thienylpyrroles remains challenging. Often, the yields are low and the regioselectivity is only modest.3 Before our recent work,3-4 only a few papers were published concerning the regioselectivity studies of 1-(alkyl)aryl-2-thienylpyrrole systems. Following our interest in the chemistry and optical applications of new functionalized systems bearing thiophene and pyrrole rings we have used heterocyclic systems 1 bearing pyrrole and thiophene rings (1, 2 or 3) as precursors for the synthesis of functionalyzed pyrrole derivatives. Compounds 1 have proved to be versatile substrates in several reactions (aromatic electrophilic substitutions: azo coupling, direct tricyanovinylation reaction, Vilsmeier-Haack formylation) and metalation followed by reaction with DMF, allowing the preparation of interesting new donor-acceptor substituted heterocyclic systems, selectively functionalized on the pyrrole 2 or on the thiophene 3 rings. Precursors 1 were prepared through a palladium-catalyzed decarboxylative cross-coupling reaction. The structures of the new compounds were unambiguously confirmed by their analytical and spectral data. Acknowledgments Thanks are due to the Fundação para a Ciência e Tecnologia (Portugal) and FEDER-COMPETE for financial support through the Centro de Química - Universidade do Minho, Project PTDC/QUI/66251/2006 (FCOMP-01-0124-FEDER-007429), Project PEst-C/QUI/UI0686/2011 (F-COMP-01-0124-FEDER-022716) and a PhD grant to M. C. R. Castro (SFRH/BD/78037/2011). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re-equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT. References 1. Schmuch, C.; Rupprecht, D. Synthesis 2007, 3095. 2. Knott, E. B. J. Chem. Soc. 1947, 1196. 3. (a) Raposo, M. M. M. in Targets in Heterocyclic Systems: Chemistry and Properties, "Recent developments in the chemistry of 2-thienylpyrroles: synthesis, reactivity and applications", Attanasi, O. A.; Spinelli, D. Eds.; Royal Society of Chemistry: London, 2008, Vol. 11, pp 122-154. 4. (a) Raposo, M. M. M.; Sousa, A. M. R. C.; Fonseca, A. M. C.; Kirsch, G. Tetrahedron 2005, 61, 8249. (b) Raposo, M. M. M.; Sousa, A. M. R. C.; Kirsch, G.; Ferreira, F.; Belsley, M.; Matos Gomes, E.; Fonseca, A. M. C. Tetrahedron 2005, 61, 11991. (c) Raposo, M. M. M.; Sousa, A. M. R. C.; Fonseca, A. M. C.; Kirsch G. Tetrahedron 2006, 62, 3493. (d) Raposo, M. M. M.; Sousa, A. M. R. C.; Kirsch, G.; Cardoso, P.; Belsley, M.; Matos Gomes, E.; Fonseca, A. M. C. Org. Lett. 2006, 8, 3681. (e) Raposo, M. M. M.; Castro, M. C. R.; Schellenberg, P.; Fonseca, A. M. C.; Belsley, M. Tetrahedron 2011, 67, 5189

Contribution to excitonic linewidth from free carrier–exciton scattering in layered materials: the example of hBN

Scattering of excitons by free carriers is a phenomenon, which is especially important when considering moderately to heavily doped semiconductors in low-temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal boron nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova–Keldysh potential. Making the distinction between elastic and inelastic scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence.M.F.C.M.Q. acknowledges the International Nanotechnology Laboratory (INL) and the Portuguese Foundation for Science and Technology (FCT) for the Quantum Portugal Initiative (QPI) grant SFRH/BD/151114/2021. N.M.R.P. acknowledges support by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020, COMPETE 2020, PORTUGAL 2020, FEDER, and FCT through projects PTDC/FIS-MAC/2045/2021, EXPL/FIS-MAC/0953/ 2021, and from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3)

A colloquium on the variational method applied to excitons in 2D materials

In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the connections between experimental and theoretical results. In particular, we focus our review of the literature on the absorption spectrum and polarizability, as well as the Stark shift and the dissociation rate. Afterwards, we begin the discussion of the use of variational methods in the study of excitons. We initially model the electron-hole interaction as a soft-Coulomb potential, which can be used to describe interlayer excitons. Using an \emph{ansatz}, based on the solution for the two-dimensional quantum harmonic oscillator, we study the Rytova-Keldysh potential, which is appropriate to describe intralayer excitons in two-dimensional (2D) materials. These variational energies are then recalculated with a different \emph{ansatz}, based on the exact wavefunction of the 2D hydrogen atom, and the obtained energy curves are compared. Afterwards, we discuss the Wannier-Mott exciton model, reviewing it briefly before focusing on an application of this model to obtain both the exciton absorption spectrum and the binding energies for certain values of the physical parameters of the materials. Finally, we briefly discuss an approximation of the electron-hole interaction in interlayer excitons as an harmonic potential and the comparison of the obtained results with the existing values from both first--principles calculations and experimental measurements.The authors thank Eduardo Castro and Joao Lopes dos Santos for comments on a preliminary version of this work, and Bruno Amorim for outlining the derivation in the Appendix A. N.M.R.P. acknowledges support from the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 881603 - core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. In addition, funding from the projects POCI-01-0145-FEDER-028114, and POCI01-0145-FEDER-029265, and PTDC/NAN-OPT/29265/2017, and POCI-01-0145-FEDER-02888 is acknowledged

Synthesis of π-conjugated systems bearing thiophene and pyrrole heterocycles through palladium-catalyzed decarboxylative cross-coupling reaction

Thiophene and pyrrole moieties play important roles in synthetic and medicinal chemistry, as they are present in a large number of natural products and biologically active compounds. For this reason, amongst all five-membered aromatic heterocycles, molecules containing the pyrrole nucleus have attracted the greatest attention of researchers and have been studied in most detail. Especially, 2-aryl- and 2-heteroaryl-substituted pyrroles are of great interest to the pharmaceutical industry, for instance, as precursors in the synthesis of chemotherapeutics.1 Furthermore, synthetic pyrrole -containing derivatives (e.g. functionalized thienylpyrroles and 2,5-dithienylpyrroles) and -conjugated oligo- and polypyrrolic systems are of growing relevance in materials science, supramolecular chemistry, and nanotechnology. For example, they have found application in anion binding and cation coordination, conducting organic polymers, liquid crystals, and nonlinear optics.2 The wide array of interesting properties has inspired the development of several procedures for the preparation of differently substituted pyrroles. On the other hand, methods for the construction of 2-(2´-thienyl)pyrroles and (oligo)thienylpyrroles remains limited. Therefore the development of efficient methods for the synthesis of these compounds has become an important and topical area of heterocyclic chemistry. In our laboratories we have developed a convenient method for the syntheis of 1-alkyl(aryl)-2-thienylpyrroles, through the combination of the Friedel-Crafts and Lawesson reactions.3 The transition-metal-catalyzed decarboxylative cross-coupling has been recently utilized as a new synthetically useful tool for the preparation of heterocyclic systems.4 Having in mind our recent work and also our interest in the development of synthetic methodologies for the synthesis of novel heterocyclic systems we report in this communication the synthesis and the characterization of new -conjugated systems 1 bearing thiophene and pyrrole rings through palladium-catalyzed decarboxylative cross-coupling reaction between 1-methyl-1H-pyrrole-2-carboxylic acid 1 and thienyl bromides 2. Several reaction conditions (catalyst, solvent, additive, base, stoichiometry and temperature) were studied in order to obtain better yields for compounds 3. Some of the precursor thienyl bromides 2 were prepared through Suzuki coupling reaction. The new compounds were completely characterized by the usual spectroscopic techniques. Acknowledgments Thanks are due to the Fundação para a Ciência e Tecnologia (Portugal) and FEDER-COMPETE for financial support through the Centro de Química - Universidade do Minho, Project PTDC/QUI/66251/2006 (FCOMP-01-0124-FEDER-007429), Project PEst-C/QUI/UI0686/2011 (F-COMP-01-0124-FEDER-022716) and a PhD grant to M. C. R. Castro (SFRH/BD/78037/2011). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re-equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT. References 1. Bellina, F.; Rossi, R. Tetrahedron 2006, 62, 7213. 2. (a) Raposo, M. M. M. in Targets in Heterocyclic Systems: Chemistry and Properties, "Recent developments in the chemistry of 2-thienylpyrroles: synthesis, reactivity and applications", Attanasi, O. A.; Spinelli, D. Eds.; Royal Society of Chemistry: London, 2008, Vol. 11, pp 122-154. (b) Raposo, M. M. M.; Sousa, A. M. R. C.; Kirsch, G.; Cardoso, P.; Belsley, M.; Matos Gomes, E.; Fonseca, A. M. C. Org. Lett. 2006, 8, 3681. (c) Raposo, M. M. M.; Castro, M. C. R.; Schellenberg, P.; Fonseca, A. M. C.; Belsley, M. Tetrahedron 2011, 67, 5189. 3. (a) Raposo, M. M. M.; Sampaio, A. M. B. A.; Kirsch, G. Synthesis 2005, 2, 199. (b) Raposo, M. M. M.; Sousa, A. M. R. C.; Fonseca, A. M. C.; Kirsch G. Tetrahedron 2006, 62, 3493. 4. Zhao, D.; You, J.; Hu, C. Chem. Eur. J. 2011, 17, 5466

Highly efficient and thermally stable NLO organic materials based on pyrrole and thiophene heterocycles

A series of novel donor-acceptor chromophores designed to have good second order nonlinear optical responses has been synthesized and characterized. This series of compounds was designed to explore the consequence of using different electron accepting moieties which were linked through an arylthiophene bridge to a pyrrole heterocycle that plays the role of an auxiliary donor group. These new push-pull chromophores have been extensively characterized using cyclic voltammetry, thermogravimetric analysis and hyper-Rayleigh scattering (HRS) in solution. The measured molecular first hyperpolarizabilities and the observed electrochemical behavior showed that they were very sensitive to the acceptor strength of the acceptor moieties. Moreover, the combination of their good nonlinearity and high thermal stability make them good candidates for potential device applicationsThanks are due to the Fundacao para a Ciencia e Tecnologia (Portugal) and FEDER for financial support through the Centro de Quimica and Centro de Fisica-Universidade do Minho, Project PTDC/QUI/66251/2006 (FCOMP-01-0124-FEDER-007429), Project PTDC/CTM/105597/2008 with funding from COMPETE/FEDER and a research grant to M.C. R. Castro (UMINHO/BI/142/2009). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re-equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT

Synthesis, redox and quadratic nonlinear optical properties of novel thienylpyrrole derivatives containing pyridinium electron-acceptor group

Quaternized pyridine derivatives have attracted interest for many years from various perspectives, especially for potential applications in electronic/optical devices.1 Pyridinium salts are readily synthesized, highly stable, and often combine intense visible absorptions with reversible electrochemistry. Notable recently proposed applications of these compounds range from advanced telecommunications to fluorescent probes for bioimaging.2 As part of an ongoing program to develop strong charge transfer donor-acceptor thienylpyrrole systems with enhanced nonlinear optical (NLO) properties3 we have explored the potential of pyrrole 4 and thienylpyrrole-based chromophores 5-6 as efficient π-electron donor moieties functionalized with N-methylpyridinium acceptor group substituted at thiophene or pyrrole rings (Figure). Compounds 4-6 were prepared, in good yields, through Knoevenagel condensation of the precursor pyrrole 1 or thienylpyrrole 2-34 aldehydes with 1-methylpyridinium salt. On the other hand, formyl-pyrroles 1 were prepared through Paal-Knorr synthesis followed by Vilsmeier formylation. The molecular structure, especially the degree of planarity and the relative orientations of the auxiliary donor and acceptor entities, is found to strongly influence their electrochemical and NLO properties. In this communication we report on the synthesis, redox properties, thermal stability and first order nonlinear optical hyperpolarizabilities for the novel cationic chomophores 4-6. These results indicate that these compounds have goo

Synthesis and evaluation of NLO properties of π-conjugated donor‐acceptor systems bearing pyrrole and thiophene heterocycles

Two series of novel push-pull heterocyclic azo dyes have been synthesized and characterized. The two series of compounds were based on different combinations of π-conjugated bridges (bithiophene and thienylpyrrole) which also act simultaneously as donor groups, together with diazo(benzo)thiazolyl as acceptor moieties. Their thermal stability and electrochemical behavior were characterized, while hyper-Rayleigh scattering (HRS) was employed to evaluate their second-order nonlinear optical properties. The results of these studies have been critically analyzed together with several thienylpyrrole azo dyes reported earlier from our laboratories in which the thienylpyrrole system was used as the donor group functionalized with aryl and (benzo)thiazolyldiazene as acceptor moiety. The measured molecular first hyperpolarizabilities and the observed linear optical and redox behavior showed strong variations in function of the heterocyclic spacers used (bithiophene or thienylpyrrole) and were also sensitive to the acceptor strength of the diazenehetero(aryl) moiety.Thanks are due to the Fundacao para a Ciencia e Tecnologia (Portugal) and FEDER for financial support through the Centro de Quimica and Centro de Fisica-Universidade do Minho, Project PTDC/QUI/66251/2006 (FCOMP-01-0124-FEDER-007429), Project PTDC/CTM/105597/2008 with funding from COMPETE/FEDER and a research grant to M. C. R. Castro (UMINHO/BI/142/2009). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT

Push-pull bithiophene azo-chromophores bearing thiazole and benzothiazole acceptor moieties: synthesis and evaluation of their redox and nonlinear optical properties

Three series of bithiophene azo dyes functionalized with thiazol-2-yl or benzothiazol-2-yl-diazene acceptor moieties were synthesized through azo coupling reaction using 2,2´-bithiophene, 5-alkoxy-2,2´-bithiophenes, 5-N,N-dialkylamino-2,2´-bithiophenes and thiazolyl and benzothiazolyl diazonium salts as coupling components. The 5-alkoxy-2,2´-bithiophene precursors yielded the 5-thiazolylazo-5´-alkoxy-2,2´-bithiophenes, while the azo coupling reaction of 5-N,N-dialkylamino-2,2´-bithiophenes with the thiazolyldiazonium salt gave 4-thiazolyl-azo-5-N,N-dialkylamino-2,2´-bithiophenes. A different reactivity behavior was observed for 2,2-bithiophene with thiazolyl diazonium salts which gave rise to the expected azo dyes together with several arylation products. The redox behavior, thermal stability, and the first hyperpolarizability of the novel chromophores were evaluated through cyclic voltammetry, thermogravimetric analysis (TGA) and hyper-Rayleight scattering (HRS) respectively. By varying the position of the thiazolyldiazene acceptor group on the bithiophene system, the electrochemical behavior as well as the optical (linear and nonlinear) properties of the donor-acceptor -conjugated systems can readily be tuned. Push-pull 5-thiazolylazo-5´-alkoxy-2,2´-bithiophenes exhibit the most promising redox and the solvatochromic properties and second order nonlinear optical response. The redox and the optical properties also show notable variations for the different heterocyclic spacers and were also sensitive to the electronic acceptor strength of the (benzo)thiazolyldiazene moieties.Thanks are due to the Fundacao para a Ciencia e Tecnologia (Portugal) and FEDER for financial support through the Centro de Quimica and Centro de Fisica-Universidade do Minho, Project PTDC/QUI/66251/2006 (FCOMP-01-0124-FEDER-007429), Project PTDC/CTM/105597/2008 with funding from COMPETE/FEDER and a research grant to M. C. R. Castro (UMINHO/BI/142/2009). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re-equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT