Analytical first derivatives of molecular surfaces with respect to nuclear coordinates

We present analytical expressions for the first derivatives of area and other geometrical quantities of polygonal tesserae defined on molecular surfaces. This is a necessary step in the calculation of free energy derivatives with respect to nuclear coordinates for molecular solutes, in the framework of the polarizable continuum method. An application to solute-solvent dispersion energy derivatives is presented. © 1996 by John Wiley & Sons, Inc.     

Effect of the introduction of an alcohol-soluble conjugated polyelectrolyte as cathode interlayer in solution-processed organic light-emitting diodes and photovoltaic devices

Interfacial engineering provides an important tool for optimizing the performances of optoelectronic devices. We show that poly[(2,7-(9,9′-dioctyl)fluorene)-alt-(2,7-(9,9′-bis(5″-trimethylammonium bromide)pentyl)fluorene)])], an alcohol-soluble π-conjugated polymer based on polyfluorene backbone and ammonium groups on the alkyl side chains, is capable of modifying the interface between the organic layer and the metal cathode in both organic solar cells and light-emitting diodes based on commercial materials and conventional architectures, improving their performances. The introduction of the cathode interlayer enhances the efficiency of a red-emitting phosphorescent OLED by 15% and decreases its turn-on voltage. The same polymer improves the power conversion efficiency of a PTB7/PC₇₁BM solar cell by 55% and shows a beneficial effect in terms of device stability.     

Theoretical study of the SN2 reaction of Cl−(H2O)+CH3Cl using our own N-layered integrated molecular orbital and molecular mechanics polarizable continuum model method (ONIOM, PCM)

The effects of solvation in the S_N2 reaction Cl^–(H₂O)+CH₃Cl were investigated using our own N-layered integrated molecular orbital and molecular mechanics (ONIOM) polarizable continuum model (PCM) method [Vreven T, Mennucci B, da Silva CO, Morokuma K, Tomasi J (2001) J Chem Phys 115:62–72], which surrounds the microsolvated ONIOM system with a polarizable continuum. The microsolvating water molecule tends to stay in the vicinity of the original chloride ion. In the ONIOM calculations, Cl^–+CH₃Cl was considered as the model system and was handled with the high-level method, while the explicit water molecule in the microsolvated complex was treated at the low-level. The molecular orbital (MO) and ONIOM(MO:MO) calculations allow us to assess the errors introduced by the ONIOM extrapolation, as well as the effects of microsolvation on the potential-energy surfaces. We find that ONIOM[B3LYP/6-31+G(d,p):HF/6-31+G(d,p)] and ONIOM[B3LYP/6-31+G(d,p):HF/6-31+G(d,p)]-PCM methods are good approximations to the target B3LYP/6-31+G(d,p) and B3LYP/6-31+G(d,p)-PCM methods. In addition, several approximate (computationally less expensive) schemes in the ONIOM-PCM method have been compared to the exact scheme, and all are shown to perform well.Contribution to the Jacopo Tomasi Honorary Issue     

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 $\mathbb{R}$.     

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.