Expanded Pyridiniums: Bis‐cyclization of Branched Pyridiniums into Their Fused Polycyclic and Positively Charged Derivatives—Assessing the Impact of Pericondensation on Structural,Electrochemical, Electronic,and Photophysical Features

This study evaluates the impact of the extension of the π‐conjugated system of pyridiniums on their various properties. The molecular scaffold of aryl‐substituted expanded pyridiniums (referred to as branched species) can be photochemically bis‐cyclized into the corresponding fused polycyclic derivatives (referred to as pericondensed species). The representative 1,2,4,6‐tetraphenylpyridinium ( 1^H ) and 1,2,3,5,6‐pentaphenyl‐4‐(p‐tolyl)pyridinium ( 2^Me ) tetra‐ and hexa‐branched pyridiniums are herein compared with their corresponding pericondensed derivatives, the fully fused 9‐phenylbenzo[1,2]quinolizino[3,4,5,6‐def]phenanthridinium ( 1^H f ) and the hitherto unknown hemifused 9‐methyl‐1,2,3‐triphenylbenzo[h]phenanthro[9,10,1‐def]isoquinolinium ( 2^Me f ). Combined solid‐state X‐ray crystallography and solution NMR experiments showed that stacking interactions are barely efficient when the pericondensed pyridiniums are not appropriately substituted. The electrochemical study revealed that the first reduction process of all the expanded pyridiniums occurs at around ?1 V vs. SCE, which indicates that the lowest unoccupied molecular orbital (LUMO) remains essentially localized on the pyridinium core regardless of pericondensation. In contrast, the electronic and photophysical properties are significantly affected on going from branched to pericondensed pyridiniums. Typically, the number of absorption bands increases with extended activity towards the visible region (down to ca. 450 nm in MeCN), whereas emission quantum yields are increased by three orders of magnitude (at ca. 0.25 on average). A relationship is established between the observed differential impact of the pericondensation and the importance of the localized LUMO on the properties considered: predominant for the first reduction process compared with secondary for the optical and photophysical properties.     

On a question of Vaisman concerning complex surfaces

The last years have seen striking improvements on Vaisman’s question about existence of locally conformally Kähler (lcK) metrics on compact complex surfaces. The aim of this paper is twofold. We review results of different authors which, for all known examples of compact complex surfaces, give a complete answer to the Vaisman’s question. We also point out a relation between lcK surfaces and generalized Kähler geometry in four-dimension and prove a new result concerning hyperbolic Inoue surfaces. We conclude with a simple observation on a question of Brunella.     

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash–Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients.     

High-order moments conservation in thermostatted kinetic models

Recently the thermostatted kinetic framework has been proposed as mathematical model for studying nonequilibrium complex systems constrained to keep constant the total energy. The time evolution of the distribution function of the system is described by a nonlinear partial integro-differential equation with quadratic type nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with further developments of this thermostatted framework. Specifically the term related to the Gaussian thermostat is adjusted in order to ensure the conservation of even high-order moments of the distribution function. The derived framework that constitutes a new paradigm for the derivation of specific models in the applied sciences, is analytically investigated. The global in time existence and uniqueness of the solution to the relative Cauchy problem is proved. Existence and moments conservation of stationary solutions are also performed. Suitable applications and research perspectives are outlined in the last section of the paper.     

Modeling triplet flavin-indole electron transfer and interradical dipolar interaction: a perturbative approach

A benchmark biochemical reaction is here theoretically investigated by means of a perturbative approach in order to model each reaction step. The reaction is the flavin-indole electron transfer, involving also a spin-state relaxation of the ionic complex. The whole reaction path is modeled and the kinetics of the process is studied. The dipolar interaction between the two radicals is explicitly considered during the dynamic evolution of the system in order to investigate the proper conditions for the triplet-to-singlet transition to occur.     

Stochastic quantum molecular dynamics for finite and extended systems

We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel, M. Di Ventra, Phys. Rev. B 80 (2009) 212303] to describe coupled electron-ion dynamics in open quantum systems. As example applications of the method we consider both finite systems with and without ionic motion, as well as describe its applicability to extended systems in the limit of classical ions. The latter formulation allows the study of important phenomena such as decoherence and energy relaxation in bulk systems and surfaces in the presence of time-dependent fields.     

A ‘waterproof’ catalyst for the oxidation of secondary amines to nitrones with alkyl hydroperoxides

Catalytic oxidation of secondary amines to nitrones using alkyl hydroperoxides as primary oxidant has been demonstrated for the first time. The titanium alkoxide catalyst is protected from co-product water by the combined use of a tightly binding trialkanolamine ligand and molecular sieves. Nitrones can be obtained in high yield (up to 98%) under homogeneous, anhydrous conditions and even in the absence of solvent. The reactions are fast (2-7 h) and good selectivity can be achieved with as little as 1% catalyst.     

Stochastic time-dependent current-density-functional theory

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state |Psi0> and the particle-bath interaction operator, two external vector potentials A(r,t) and A'(r,t) that produce the same ensemble-averaged current density, j(r,t), must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.