Small D–π–A Systems with o‐Phenylene‐Bridged Accepting Units as Active Materials for Organic Photovoltaics

Donor–acceptor (D–π–A) systems that combine triarylamine donor blocks and dicyanovinyl (DCV) acceptor groups have been synthesized. Starting from the triphenylamine (TPA)? thiophene? DCV compound ( 1 ) as a reference system, various synthetic approaches have been developed for controlling the light‐harvesting properties and energy levels of the frontier orbitals in this molecule. Thus, the introduction of methoxy groups onto TPA, the replacement of one phenyl ring of TPA by a thiophene ring, or the extension of the π‐conjugating spacer group lead to the modulation of the HOMO level. On the other hand, the fusion of the DCV group onto the vicinal thiophene ring by an ortho‐phenylene bridge allows for a specific fine‐tuning of the LUMO level. The electronic properties of the molecules were analyzed by using UV/Vis spectroscopy and cyclic voltammetry and the compounds were evaluated as donor materials in basic bilayer planar heterojunction solar cells by using C₆₀ as acceptor material. The relationships between the electronic properties of the donors and the performance of the corresponding photovoltaic devices are discussed. Bilayer planar heterojunction solar cells that used reference compound 1 and C₇₀ afforded power‐conversion efficiencies of up to 3.7 %.     

Theoretical study of the photophysical processes of a styryl-bodipy derivative eliciting an AND molecular logic gate response

We study, via density functional theory and time dependent DFT calculations, the photophysical processes of a styryl-bodipy derivative, which acts as a three metal-cation-receptor fluorophore in order to (a) gain information on the appropriate computational approach for successful prediction of molecular logic gate candidates, (b) rationalize the available experimental data and (c) understand how the given combination of three different receptors with the BODIPY fluorophore presents such interesting optoelectronic responses. The fluorophore ( 1 ), its monometallic complexes ( 1-Ca ²⁺ , 1-Zn ²⁺ , and 1-Hg ²⁺ ), and its trimetallic complex ( 2 ) are studied. The calculated λ_max values for absorption and emission are in excellent agreement with experimental data. It was found that the observed quenching of emission of 1 and of the monometallic complexes is attributed to the fact that their first excited state is a charge-transfer state whereas this does not happen for the complex 2 . It should be noted that for the correct ordering of the excited states, the inclusion of corrections to the excitation energies for nonequilibrium solvent effects is required; while in the case of 1-Ca ²⁺ , the additional explicit inclusion of the solvent is necessary for the quenching of the emission spectra.     

Splitting of the Cr 2p ions states in some ternary sulphides and selenides

X-ray photoelectron spectroscopy was used to investigate ACr₂S₄ (, Zn, Mn, Fe, Fe:Cu) and BCr₂Se₄ (, Cu, Hg, Hg:Cu) single crystals. Well defined splitting of the Cr 2p core level has been found. The local magnetic moments of the Cr ions are responsible for the observed effect. Received 2 November 1999     

A theory of generally invariant lagrangians for the metric fields. II

The second-order generally invariant Lagrangians for the metric fields on anyn-dimensional manifold are studied as certain special coordinate functions on a space of jets. The number of independent Lagrangians of this type is determined. The dimensionsn=3 andn=4 are examined in detail with the help of a computer.     

Explorations on the multidimensional potential energy surface of a chiral stationary phase

The multidimensional potential energy surface for a soluble analog of a chiral phase is computed with MM2 and MNDO. Minimum energy conformations are located. The minimum energy reaction pathway between these forms is located, and the templating ability of these phases is described.     

On generalized invariant transformations

The notion of generalized invariant transformations of variational problems in Lagrangian formulation is discussed in the framework of the variational theory in fibred manifolds. Necessary and sufficient conditions for generators of one-parameter groups of such transformations are derived, completing thus some previous results of A. Trautman on the theory of transformations.     

Endpoint Bounds for the Quartile Operator

It is a result by Lacey and Thiele (Ann. of Math. (2) 146(3):693–724, 1997; ibid. 149(2):475–496, 1999) that the bilinear Hilbert transform maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{p_{3}}(\mathbb{R})$ whenever (p ₁,p ₂,p ₃) is a Hölder tuple with p ₁,p ₂>1 and $p_{3}>\frac{2}{3}$ . We study the behavior of the quartile operator, which is the Walsh model for the bilinear Hilbert transform, when $p_{3}=\frac{2}{3}$ . We show that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ when p ₁,p ₂>1 and one component is restricted to subindicator functions. As a corollary, we derive that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2},\frac{2}{3}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ . We also provide weak type estimates and boundedness on Orlicz-Lorentz spaces near p ₁=1,p ₂=2 which improve, in the Walsh case, the results of Bilyk and Grafakos (J. Geom. Anal. 16 (4):563–584, 2006) and Carro et al. (J. Math. Anal. Appl. 357(2):479–497, 2009). Our main tool is the multi-frequency Calderón-Zygmund decomposition from (Nazarov et al. in Math. Res. Lett. 17(3):529–545, 2010).     

Variational Sequences in Mechanics on Grassmann Fibrations

Extension of the variational sequence theory in mechanics to the first order Grassmann fibrations of 1-dimensional submanifolds is presented. The correspondence with the variational theory of parameter-invariant problems on manifolds is discussed in terms of the theory of jets (slit tangent bundles) and contact elements. In particular, the Helmholtz expressions for parameter-invariant variational problems, measuring local variationality of differential forms and differential equations, are given in the canonical and adapted coordinates. The methods can easily be extended to higher order variational problems.