Computing a molecule in its environment: A mathematical viewpoint

This article is the sequel of a previous survey where we presented the mathematical results rigorously known on the models used in quantum chemistry to simulate an isolated molecular system. The emphasis here is on the models that take into account the environment of the molecule, namely, the models of the condensed phase and the models of interaction with electromagnetic fields. Some related issues are also dealt with. A bibliography of more than 150 references are provided. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 227–250, 1999     

Tandem diazonium salt electroreduction and click chemistry as a novel, efficient route for grafting macromolecules to gold surface

Bis-alkynylated oligoethyleneglycol (OEG) and a monopropargyl-functionalized perfluorinated ethylene glycol (FEG) were clicked to azide-functionalized gold surface (Au–N₃) at room temperature via the well known 1,3 cycloaddition click chemical reaction. The Au–N₃ substrate was obtained by nucleophilic attack of NaN₃ on gold substrates modified by the electrochemical reduction of the , ⁺N₂–C₆H₄–CH₂Br diazonium salt. This electrochemical process yields aryl layer-modified gold of the type Au–C₆H₄–CH₂Br (hereafter Au–Br). The untreated and modified gold plates were examined by XPS, PMIRRAS and contact angle measurements. XPS brought evidence for electrografting aryl layers by the detection of Br3d; azide functionalization by the increase of the N/Br atomic ratio; and click reaction of OEG with Au–N₃ by the increase of O/N ratio. In addition, the perfluorinated plate (Au-FEG) exhibited F1s and characteristic C1s peaks from -(CF₂)₇- chain and terminal CF₃. Infra red spectroscopy (PMIRRAS) evidenced (i) grafting N₃ to Au–Br; (ii) characteristic stretching bands, from ethylene glycol units, C–O–C (1100–1300 cm⁻¹); CF₂ (1000–1100 cm⁻¹) and CF₃ (1100–1350 cm⁻¹) from FEG grafts; and (iii) suppression of alkynyl bands from OEG and FEG after surface click chemistry. More importantly, PMIRRAS results support an important bridging of the bispropargyl oligoethylene glycol at the gold surface. Water drop contact angles were found to be 48.7° and 83.0° for Au-OEG and Au-FEG, respectively, therefore highlighting the control over the hydrophilic/hydrophobic character of the clicked substrate.This work shows that clicking macromolecules to grafted, diazonium salt-derived aryl layers is a novel, simple and valuable approach for designing robust, functional surface organic coatings.     

Ultraviolet Radiation in the Rhône River Lenses of Low Salinity and in Marine Waters of the Northwestern Mediterranean Sea: Attenuation and Effects on Bacterial Activities and Net Community Production

The high content in nutrients of freshwater outflows induces highly productive and buoyant plumes spreading over marine waters (MW). As a consequence, the growth of organisms developing in these low‐salinity waters (LSW) might be potentially affected by UV‐R (280–400 nm). This study investigated the penetration of UV‐R and its impact on net community production (NCP) and bacterial protein (B_PROTS) and DNA (B_DNAS) synthesis in mesotrophic‐LSW formed from the Rhône River and in oligotrophic MW of the Northwestern Mediterranean Sea (Gulf of Lions) in May 2006. High concentrations of chlorophyll a (up to 8 μg L^?1) measured in the LSW (<37.8 psu, 0–10 m) were the main factor influencing the diffuse attenuation coefficients (K_d) of both UV‐R and photosynthetically active radiation (PAR). The mean ratio of the K_d measured between the LSW and the MW increased with wavelength from 2.4 at 305 nm to 2.9 at 380 nm and 3.1 for PAR indicating more similarity in the UV region. NCP was severely inhibited by UV‐R at the surface of the LSW, whereas no effect was measured in the surrounding MW. In contrast, B_PROTS and B_DNAS were affected deeper by UV‐R in the MW (up to 8 m depth) compared to the LSW where inhibition was only observed at the surface. Differences in response of bacteria in LSW and MW are largely explained by differences in UV‐R transparency; however, transplant experiments indicate that bacterial assemblages from the MW were also more sensitive to UV‐R than those present in the LSW. We also observed that higher activity of bacteria after nutrient additions increased their sensitivity to UV‐R during the day, but favored their recovery during the night incubation period for both LSW and MW. Results suggest that riverine and nutrient inputs may alter the effects of UV‐R on microbial activity by attenuating the UV‐R penetration and by modifying the physiology of bacteria.     

Diaqua(oxydiacetato‐κ3O,O′,O′′)(pyridine‐3‐carboxamide‐κN1)copper(II)

In the mononuclear title compound, [Cu(C₄H₄O₅)(C₆H₆N₂O)(H₂O)₂], the Cu^II centre is bound to a chelating oxydiacetate ligand, a monodentate pyridine‐3‐carboxamide unit and two water molecules, defining an octahedral coordination where the first two ligands form the equatorial plane and the last two occupy the apical sites. The planar oxydiacetate ligand is slightly disordered at its central ether O atom. The availability of efficient donors and acceptors for hydrogen bonding results in a complex interaction scheme where each monomer links to six similar units to define a well connected three‐dimensional structure. A comparison is made with related structures in the literature, and the reasons for their differences are discussed.     

Constitutive equations for an electroactive polymer

Ionic electroactive polymers can be used as sensors or actuators. For this purpose, a thin film of polyelectrolyte is saturated with a solvent and sandwiched between two platinum electrodes. The solvent causes a complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip and vice versa. The material is modeled by a two-phase continuous medium. The solid phase, constituted by the polymer backbone inlaid with anions, is depicted as a deformable porous media. The liquid phase is composed of the free cations and the solvent (usually water). We used a coarse grain model. The conservation laws of this system have been established in a previous work. The entropy balance law and the thermodynamic relations are first written for each phase and then for the complete material using a statistical average technique and the material derivative concept. One deduces the entropy production. Identifying generalized forces and fluxes provides the constitutive equations of the whole system: the stress–strain relations which satisfy a Kelvin–Voigt model, generalized Fourier’s and Darcy’s laws and the Nernst–Planck equation.     

The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is {1+\sqrt{2}}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is ${\mu=\sqrt{2+\sqrt{2}}}$ . A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with ${n\in [-2,2]}$ (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface fugacity y associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov’s identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be ${y_{\rm c}=1+2/\sqrt{2-n}}$ . This value plays a crucial role in our generalized identity, just as the value of the growth constant did in Smirnov’s identity. For the case n = 0, corresponding to self-avoiding walks interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height T, taken at its critical point 1/μ, tends to 0 as T increases, as predicted from SLE theory.     

Benzo[1,2‐d:4,5‐d′]bisimidazoles as a Convenient Platform Towards Dyes that are Capable of Excited‐State Intramolecular Proton Transfer and of Two‐Photon Absorption

New, strongly fluorescent benzo[1,2‐d:4,5‐d′]bisimidazoles have been prepared by the reaction of Bandrowski′s base with various aldehydes. Their structures were carefully designed to achieve efficient excited‐state intramolecular proton transfer and good two‐photon‐absorption (2PA) cross‐sections. Functional dyes that possessed both high fluorescence quantum yields and large Stokes shifts were prepared. A π‐expanded D‐A‐D derivative that possessed Φ_fl=50 % and σ₂=230 GM in the spectroscopic area of interest for biological imaging is an excellent candidate as a fluorescent probe. Thanks to the presence of two reactive amino groups, such compounds can be easily transformed into probes for bioconjugation. All of these benzo[1,2‐d:4,5‐d′]bisimidazoles were also strongly fluorescent in the solid state.     

Octupolar Derivatives Functionalized with Superacceptor Peripheral Groups: Synthesis and Evaluation of the Electron‐Withdrawing Ability of Potent Unusual Groups

Novel tripodal derivatives with a triphenylamine core and that bear “superacidifiers” (i.e., fluorinated sulfoximinyl blocks) or novel sulfiliminyl moieties as peripheral groups were synthesized. These new chromophores show strong absorption in the near‐UV region and emission in the visible region. The fluorinated sulfoximinyl moieties were found to behave as potent auxochromic and electron‐withdrawing (EW) groups, thus leading to redshifted absorption and emission. These moieties promote a core‐to‐periphery intramolecular charge transfer (ctp‐ICT) transition, the energy of which was found to be correlated to their EW strength. In this study, we provide evidence of a linear correlation between the Hammett constant (σ_p) values and the electronic gap between the ground and first excited state of the three‐branched derivatives. This in turn was used to derive σ_p values of fluorinated sulfoximinyl moieties. These EWGs show unprecedentedly high σ_p values, up to 1.45 relative to 0.8 for NO₂. Also, by using this method, the sulfiliminyl moiety was shown to exhibit similar EW strength as NO₂, while promoting improved transparency and solubility. Finally, the superior EW strength of the fluorinated sulfoximine peripheral moieties was shown to induce significant enhancement of the two‐photon absorption responses in the red near‐IR region of the three‐branched derivatives relative to similar octupoles that bear more usual strong EW groups. These characteristics (improved nonlinear responses or transparency) open new routes for the design of nonlinear optical (NLO) chromophores for optical limiting or electro‐optical modulation. Such building blocks could also be of interest for optoelectronic applications, including the development of solar cells.     

Triaquatris(μ‐oxydiacetato)dipraseodymium(III) pentahydrate and hexaaquatris(μ‐oxydiacetato)dineodymium(III) oxydiacetic acid solvate dihydrate

Two new complexes of the Ln₂(oda)₃·nH₂O (oda =–O₂CCH₂OCH₂CO₂–) series are reported, i.e. {[Pr₂(C₄H₄O₅)₃(H₂O)₃]·5H₂O}_n and {[Nd₂(C₄H₄O₅)₃(H₂O)₆]·C₄H₆O₅·‐2H₂O}_n. The former is isostructural with the reported La analogue, while the latter is a new structural variety within the series. Each compound exhibits two independent nine‐coordinated Ln centres showing a variety of coordination geometries.     

Morse theory for some lower-C 2 functions in finite dimension

Using inf-regularization methods, we prove that Morse inequalities hold for some lower-C ² functions. For this purpose, we first recall some properties of the class of lower-C ² functions and of their Moreau-Yosida approximations. Then, we establish, under some qualification conditions on the critical points, that it is possible to define a Morse index for a lower-C ² functionf. This index is preserved by the Moreau-Yosida approximation process. We prove in particular that the Moreau-Yosida approximations are twice continuolusly differentiable around such a critical point which is shown to be a strict local minimum of the restriction off and of its approximations to some affine space. In a last step, Morse inequalities are written for Moreau-Yosida approximations and with the aid of deformation retractions we prove that these inequalities also hold for some lower-C ² functions.