Finite-volume complex surfaces without cuspidal Einstein metrics

We derive an obstruction to the existence of cuspidal Einstein metrics on finite-volume complex surfaces. This generalizes a theorem of LeBrun for compact complex surfaces. As in the compact case, such a result relies on a scalar curvature estimate. Finally, the obstruction is made explicit on some examples.     

Determination of the Chemical Structure of Poly-β (-)-pinene by NMR Spectroscopy

This paper is dedicated to the memory of our friend and colleague Annalaura Segre.

The chemical structure of a series of β (-)-pinene polymers (PBP) obtained by radiation-induced polymerization, free radical initiation, cationic polymerization over a Friedel-Craft catalyst and by coordinative polymerization over a Ziegler-Natta catalyst has been fully elucidated by ¹H and ¹³C-NMR spectroscopy. 2D NMR techniques have been applied in order to assign all the NMR resonances to the structures of the PBP investigated. The NMR spectra show that the most regular PBP structure is obtained by radiation-induced polymerization followed by the free radical initiated polymerization. The most defective structure has been observed in the case of PBP prepared by cationic mechanism over a Friedel-Crafts catalyst. The discussion accounts for different types of defects and cross-links present in the PBPs investigated whose fundamental structure is based on the p-menthene repeating unit.

NMR self-diffusion measurements have been performed to evaluate the molecular weight of all the PBP investigated. The highest molecular weight (2600 Dalton) was found in the case of PBP prepared by Ziegler-Natta catalyst, while the lowest molecular weight was found in the case of PBP prepared by radiation-induced polymerization (about 1000 Dalton).     

Molecular Recognition of Carbonyl Compounds by Uranyl-salophen Based Neutral Receptors Driven by Van Der Waals Forces

The complexation of the salophen-uranyl metallocleft 2 and of its half-cleft analogue 3 with enones and other carbonyl compounds was assessed in chloroform by UV-Vis titration and, occasionally, by FT-IR measurements. Complexes with receptors 2 and 3 are in all cases more stable than those with the control unsubstituted uranyl-salophen 1 , showing that in addition to the primary binding force provided by coordination of the carbonyl oxygen to the uranium, a significant driving force for complexation, typically in the range of 2-3 kcal/mol, results from van der Waals interactions of the guest with the aromatic walls. Replacement of the phenyl group in 3 with larger aromatic residues to give 4 and 5 , led to enhanced complex stabilities, due to more extended contact surfaces between host and guest.     

Stereoconvergent Generation of a Contrasteric syn‐Bicyclopropylidene (=syn‐Cyclopropylidenecyclopropane) by Stille‐Like Coupling

Stereoisomerically pure endo‐ and exo‐7‐halo‐7‐(trimethylstannyl)benzonorcar‐3‐enes (=endo‐ and exo‐(1‐halo‐1a,2,7,7a‐tetrahydro‐1H‐cyclopropa[b]naphthalen‐1‐yl)trimethylstannane) 4 and 6 were selectively obtained by lithium? tin or magnesium? tin transmetalation in good yields (Scheme 2 and 3). The reaction of these compounds with copper(I) thiophene‐2‐carboxylate (CuTC) produced in both cases the corresponding C_S‐symmetric bicyclopropylidene (=cyclopropylidenecyclopropane) syn‐ 1 , a single diastereoisomer (Schemes 5 and 6). The structure of syn‐ 1 was undoubtedly elucidated by X‐ray single crystal diffraction. The coupling mechanism of the carbenoid cyclopropane is discussed (Scheme 7).     

Acetic Anhydride/Et3N/DMAP: An Effective Acetylating System for Hemiacetals

The selective and efficient acetylation of the hemiacetal hydroxyl in the equilibrium mixture between RCl₂C(OAll)OH and AllOH/RCl₂CHO was achieved using the acylating system Ac₂O/Et₃N/dimethylaminopyridine (DMAP).

Combined use of three forms of chiroptical spectroscopies in the study of the absolute configuration and conformational properties of 3-phenylcyclopentanone, 3-phenylcyclohexanone,and 3-phenylcycloheptanone

Three forms of chiroptical spectroscopies, electronic circular dichroism (ECD), vibrational circular dichroism (VCD), and optical rotatory dispersion (ORD) have been employed to study the configuration and conformational properties of the three molecules: (S)-3-phenylcyclopentanone, (S)-3-phenylcyclohexanone, and (S)-3-phenylcycloheptanone (including (S)-3-phenylcyclopentanone-2,2,5,5-d₄ and (S)-3-phenylcyclohexanone-2,2,6,6-d₄). ECD and VCD spectra in the mid-IR for the three molecular systems are marginally dependent on fine conformational details, as interpreted in terms of standard DFT computational methods, with common spectroscopic features to the three systems clearly identified. Accounting for vibronic coupling mechanisms reproduces the structuring of ECD n→π^∗ band. The ORD curves are quite similar for the three types of molecules, but their interpretation highlights a crucial role played by conformations of the cycloalkanone ring in the case of (S)-3-phenylcycloheptanone. The same conclusions are reached by considering the VCD spectra in the CH-stretching region.     

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this “Multi-Map” variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich–Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.