Absolute continuity of the law for the two dimensional stochastic Navier–Stokes equations

We consider the two dimensional Navier–Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and colored in space. First, we prove existence and uniqueness of a weak (in the Walsh sense) solution process $\xi$ and we show that, if the initial vorticity ${\xi }_0$ is continuous in space, then there exists a space–time continuous version of the solution. In addition we show that the solution $\xi (t,x)$ (evaluated at fixed points in time and space) is locally differentiable in the Malliavin calculus sense and that its image law is absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$.     

How solvent controls electronic energy transfer and light harvesting: toward a quantum-mechanical description of reaction field and screening effects

This paper presents a quantum-mechanical study of electronic energy transfer (EET) coupling on over 100 pairs of chromophores taken from photosynthetic light-harvesting antenna proteins. Solvation effects due to the protein, intrinsic waters, and surrounding medium are analyzed in terms of screening and reaction field contributions using a model developed recently that combines a linear response approach with the polarizable continuum model (PCM). We find that the screening of EET interactions is quite insensitive to the quantum-mechanical treatment adopted. In contrast, it is greatly dependent on the geometrical details (distance, shape, and orientation) of the chromophore pair considered. We demonstrate that implicit (reaction field) as well as screening effects are dictated mainly by the optical dielectric properties of the host medium, while the effect of the static properties is substantially less important. The empirical distance-dependent screening function we proposed in a recent letter (Scholes, G. D.; Curutchet, C.; Mennucci, B.; Cammi, R.; Tomasi, J. J. Phys. Chem. B 2007, 111, 6978-6982) is analyzed and compared to other commonly used screening factors. In addition, we show that implicit medium effects on the coupling, resulting from changes in the transition densities upon solvation, are strongly dependent on the particular system considered, thus preventing the possibility of defining a general empirical expression for such an effect.     

Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model

In this paper we present the theory and implementation of analytic derivatives of time-dependent density functional theory (TDDFT) excited states energies, both in vacuo and including solvent effects by means of the polarizable continuum model. The method is applied to two case studies: p-nitroaniline and 4-(dimethyl)aminobenzonitrile. For both molecules PCM-TDDFT is shown to be successful in supporting the analysis of experimental data with useful insights for a better understanding of photophysical and photochemical pathways in solution.     

Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data

We obtain existence results for some strongly nonlinear Cauchy problems posed in and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone operator of Leray-Lions type acting on , they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results.     

Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition

For the positive solutions of the Gross–Pitaevskii system we prove that L^∞‐boundedness implies C^0,α‐boundedness for every α ? (0,1), uniformly as β → +∞. Moreover, we prove that the limiting profile as β → +∞ is Lipschitz‐continuous. The proof relies upon the blowup technique and the monotonicity formulae by Almgren and Alt, Caffarelli, and Friedman. This system arises in the Hartree‐Fock approximation theory for binary mixtures of Bose–Einstein condensates in different hyperfine states. Extensions to systems with k > 2 densities are given. © 2009 Wiley Periodicals, Inc.     

Theoretical investigation of the mechanism and dynamics of intramolecular coherent resonance energy transfer in soft molecules: a case study of dithia-anthracenophane

A computational study is conducted on dithia-anthracenophane (DTA), for which there is experimental evidence for coherent resonance energy transfer dynamics, and on dimethylanthracene (DMA), a molecule representing the energy donor and the acceptor in DTA. Electronic excitation energies are calculated by configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) methods and are compared to experimental ones. Electronic coupling constants are calculated between two DMAs embedded into the ground-state structure of DTA employing methods based on transition densities. The resulting values of electronic coupling provide a more consistent interpretation of experiments than those based on one-half the level spacing of DTA excitation energies. Solvation effects are studied based on the polarizable continuum model (PCM). Solvent-induced polarization and screening effects are shown to make opposite contributions, and the net electronic coupling is little different from the value in a vacuum. The likelihood of coherent population transfer is assessed on the basis of a recently developed theory of coherent resonance energy transfer. The time scale of bath is shown to have an important role in sustaining the quantum coherence. The combination of quantum chemical and dynamical data suggests that the electronic coupling in DTA is in the range of 50-100 cm(-1). The presence of oscillatory excitation population dynamics can be understood from the picture of polaronic excitation moderately dressed with dispersive vibrational modes. The effect of torsional modulation on the excitation energies of DTA and electronic coupling is examined on the basis of optimized structures with the torsional angle constrained. The result suggests that inelastic effect due to torsional motion cannot be disregarded in DTA.     

Solvation of N3- at the water surface: the polarizable continuum model approach

We present a new quantum mechanical model to introduce Pauli repulsion interaction between a molecular solute and the surrounding solvent in the framework of the Polarizable Continuum Model. The new expression is derived in a way to allow naturally for a position-dependent solvent density. This development makes it possible to employ the derived expression for the calculation of molecular properties at the interface between two different dielectrics. The new formulation has been tested on the azide anion (N3-) for which we have calculated the solvation energy, the dipole moment, and the static polarizability at the interface as a function of the ion position. The calculations have been carried out for different ion-surface orientations, and the results have also been compared with the parallel electrostatic-only solvation model.     

Radiative and nonradiative decay rates of a molecule close to a metal particle of complex shape

We present a model to evaluate the radiative and nonradiative lifetimes of electronic excited states of a molecule close to a metal particle of complex shape and, possibly, in the presence of a solvent. The molecule is treated quantum mechanically at Hartree-Fock (HF) or density-functional theory (DFT) level. The metal/solvent is considered as a continuous body, characterized by its frequency dependent local dielectric constant. For simple metal shapes (planar infinite surface and spherical particle) a version of the polarizable continuum model based on the integral equation formalism has been used, while an alternative methodology has been implemented to treat metal particles of arbitrary shape. In both cases, equations have been numerically solved using a boundary element method. Excitation energies and nonradiative decay rates due to the energy transfer from the molecule to the metal are evaluated exploiting the linear response theory (TDHF or TDDFT where TD--time dependent). The radiative decay rate of the whole system (molecule + metal/solvent) is calculated, still using a continuum model, in terms of the response of the surrounding to the molecular transition. The model presented has been applied to the study of the radiative and nonradiative lifetimes of a lissamine molecule in solution (water) and close to gold spherical nanoparticles of different radius. In addition, the influence of the metal shape has been analyzed by performing calculations on a system composed by a coumarin-type molecule close to silver aggregates of complex shape.     

Activating intramolecular singlet exciton fission by altering π-bridge flexibility in perylene diimide trimers for organic solar cells

In this study, two analogous perylene diimide (PDI) trimers, whose structures show rotatable single bond π-bridge connection (twisted) vs. rigid/fused π-bridge connection (planar), were synthesized and investigated. We show via time resolved spectroscopic measurements how the π-bridge connections in A–π–D–π–A–π–D–π–A multichromophoric PDI systems strongly affect the triplet yield and triplet formation rate. In the planar compound, with stronger intramolecular charge transfer (ICT) character, triplet formation occurs via conventional intersystem crossing. However, clear evidence of efficient and fast intramolecular singlet exciton fission (iSEF) is observed in the twisted trimer compound with weaker ICT character. Multiexciton triplet generation and separation occur in the twisted (flexible-bridged) PDI trimer, where weak coupling among the units is observed as a result of the degenerate double triplet and quintet states, obtained by quantum chemical calculations. The high triplet yield and fast iSEF observed in the twisted compound are due not only to enthalpic viability but also to the significant entropic gain allowed by its trimeric structure. Our results represent a significant step forward in structure–property understanding, and may direct the design of new efficient iSEF materials.

We show via time resolved spectroscopy that triplet formation proceeds via intersystem crossing in a rigid-bridged perylene diimide trimer and via efficient and fast intramolecular singlet exciton fission in the analogous flexible-bridged trimer.     

Synthesis of Functionalized Six-Membered-Ring Azahelicenes

Functionalization, namely the introduction of side groups onto the molecular scaffold of a helicene, may have either the purpose of modifying the electronic properties of the parent helicene, e.g., by adding electron-withdrawing or electron-donating groups, or the scope of providing the helicene with a “handle”, which can be reacted to bind the molecule to another molecule or to a solid structure, such as a carbon or metal surface, or again to allow for complexation of the helicene with metal ions. The possible approaches are two-fold: the synthesis of the helicene can be performed using starting materials that already contain a side group, or the side group can be introduced after the synthesis of the parent helicene. As azahelicenes are helicenes bearing one or more nitrogen atom(s) in the molecular framework, parent azahelicenes can be functionalized on carbon atoms by exploiting the presence of the electron-withdrawing nitrogen atom. Moreover, they can be transformed into quaternary salts, whose properties are quite different from those of the parent azahelicenes in terms of the solubility and electronic properties. This review aims to provide a survey of the different synthetic methods available to attain this fascinating class of compounds.