Tailoring the Structure of Two‐Dimensional Self‐Assembled Nanoarchitectures Based on NiII–Salen Building Blocks

The synthesis of a series of Ni^II–salen‐based complexes with the general formula of [Ni(H₂L)] (H₄L=R²‐N,N′‐bis[R¹‐5‐(4′‐benzoic acid)salicylidene]; H₄L1: R²=2,3‐diamino‐2,3‐dimethylbutane and R¹=H; H₄L2: R²=1,2‐diaminoethane and R¹=tert‐butyl and H₄L3: R²=1,2‐diaminobenzene and R¹=tert‐butyl) is presented. Their electronic structure and self‐assembly was studied. The organic ligands of the salen complexes are functionalized with peripheral carboxylic groups for driving molecular self‐assembly through hydrogen bonding. In addition, other substituents, that is, tert‐butyl and diamine bridges (2,3‐diamino‐2,3‐dimethylbutane, 1,2‐diaminobenzene or 1,2‐diaminoethane), were used to tune the two‐dimensional (2D) packing of these building blocks. Density functional theory (DFT) calculations reveal that the spatial distribution of the LUMOs is affected by these substituents, in contrast with the HOMOs, which remain unchanged. Scanning tunneling microscopy (STM) shows that the three complexes self‐assemble into three different 2D nanoarchitectures at the solid–liquid interface on graphite. Two structures are porous and one is close‐packed. These structures are stabilized by hydrogen bonds in one dimension, while the 2D interaction is governed by van der Waals forces and is tuned by the nature of the substituents, as confirmed by theoretical calculations. As expected, the total dipolar moment is minimized     

Cyclodimerization versus Polymerization of Methyl Methacrylate Induced by N‐Heterocyclic Carbenes: A Combined Experimental and Theoretical Study

The activation behavior of two N‐heterocyclic carbenes (NHCs), namely, 1,3‐bis(isopropyl)imidazol‐2‐ylidene(NHCiPr) and 1,3‐bis(tert‐butyl) imidazol‐2‐ylidene (NHCtBu), as organic nucleophiles in the reaction with methyl methacrylate (MMA) is described. NHCtBu allows the polymerization of MMA in DMF at room temperature and in toluene at 50 °C, whereas NHCiPr reacts with two molecules of MMA, forming an unprecedented imidazolium–enolate cyclodimer (NHCiPr/MMA=1:2). It is proposed that the reaction mechanism occurs by initial 1,4‐nucleophilic addition of NHCiPr to MMA, generating a zwitterionic enolate 2 , followed by addition of 2 to a second MMA molecule, forming a linear imidazolium–enolate 3 (NHCiPr/MMA=1:2). Proton transfer, generating intermediate 5 , followed by cyclization and release of methanol yielded the aforementioned zwitterionic cyclodimer 1:2 adduct 7 , the molecular structure of which has been established by NMR spectroscopy, X‐ray diffraction, and mass spectrometry. This unexpected difference between NHCtBu and NHCiPr in the reaction with MMA (polymerization and cyclodimerization, respectively) can be rationalized by using DFT calculations. In particular, the nature of the NHC strongly influences the cyclodimerization pathway, the cyclization of 5 and the release of methanol are the discriminating step and limiting step, respectively. In the case of NHCtBu, both steps are strongly disfavoured compared with that of NHCiPr (energetic difference of around 14 and 9 kcal mol^?1, respectively), preventing the cyclization mechanism from a kinetic viewpoint. Moreover, addition of a third molecule of MMA in the polymerization pathway results in a lower activation barrier than that of the limiting step in the cyclodimerization pathway (difference of around 14 kcal mol^?1), in agreement with the formation of polymethyl methacrylate (PMMA) by using NHCtBu as nucleophile.     

From the N‐Heterocyclic Carbene‐Catalyzed Conjugate Addition of Alcohols to the Controlled Polymerization of (Meth)acrylates

Among various N‐heterocyclic carbenes (NHCs) tested, only 1,3‐bis(tert‐butyl)imidazol‐2‐ylidene (NHC^tBu) proved to selectively promote the catalytic conjugate addition of alcohols onto (meth)acrylate substrates. This rather rare example of NHC‐catalyzed 1,4‐addition of alcohols was investigated as a simple means to trigger the polymerization of both methyl methacrylate and methyl acrylate (MMA and MA, respectively). Well‐defined α‐alkoxy poly(methyl (meth)acrylate) (PM(M)A) chains, the molar masses of which could be controlled by the initial [(meth)acrylate]₀/[ROH]₀ molar ratio, were ultimately obtained in N,N‐dimethylformamide at 25 °C. A hydroxyl‐terminated poly(ethylene oxide) (PEO‐OH) macro‐initiator was also employed to directly access PEO‐b‐PMMA amphiphilic block copolymers. Investigations into the reaction mechanism by DFT calculations revealed the occurrence of two competitive concerted pathways, involving either the activation of the alcohol or that of the monomer by NHC^tBu.     

Recasting wave functions into valence bond structures: A simple projection method to describe excited states

A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap‐based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low‐lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V‐state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V‐state of ethene. © 2015 Wiley Periodicals, Inc.     

ESTIMATION OF PARAMETERS IN A CLOSED PYGMY POPULATION IN CAMEROON

Inspired by Kouakep [16], we consider in this note a wellposed model with differential susceptibility and infectivity adding continuous age structure to an ODE model for a "Baka" pygmy group in the East of Cameroon(Africa).Assuming a very low contribution of carriers to infection compared to acute infection, we estimate a probability p(a)(to develop symptomatic Hepatitis B state at age a) and acute carriers' transmission rate. The value R_0= 2:67 1 of the basic reproduction number estimated from data in the east of Cameroon confirms that HBV is endemic in the Baka pygmy group.     

Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions

We present theorems which provide the existence of invariant whiskered tori in finite-dimensional exact symplectic maps and flows. The method is based on the study of a functional equation expressing that there is an invariant torus.We show that, given an approximate solution of the invariance equation which satisfies some non-degeneracy conditions, there is a true solution nearby. We call this an a posteriori approach.The proof of the main theorems is based on an iterative method to solve the functional equation.The theorems do not assume that the system is close to integrable nor that it is written in action-angle variables (hence we can deal in a unified way with primary and secondary tori). It also does not assume that the hyperbolic bundles are trivial and much less that the hyperbolic motion can be reduced to constant linear map.The a posteriori formulation allows us to justify approximate solutions produced by many non-rigorous methods (e.g. formal series expansions, numerical methods). The iterative method is not based on transformation theory, but rather on successive corrections. This makes it possible to adapt the method almost verbatim to several infinite-dimensional situations, which we will discuss in a forthcoming paper. We also note that the method leads to fast and efficient algorithms. We plan to develop these improvements in forthcoming papers.