Conformational variability in a new terpenoid-like bischalcone: Structure and theoretical studies

A new terpenoid-like bischalcone (1E,4E)-1-(4-nitrophenyl)-5-(2,6,6-trimethylcyclohex-1-enyl)-penta-1,4-dien-3-one was synthesized from a β-ionone and 4-nitrobenzaldehyde by Claisen-Schmidt condensation reaction and its structure was determined by single crystal X-ray diffraction analysis. Additionally, this compound was featured by powder X-ray diffraction, ¹H, ¹³C NMR and IR spectroscopy techniques. The molecule in the asymmetric unit showed disordered occupancy sites over two positions for the trimethylcyclohexene atoms. These two conformations were related by a rotation of about 180° around the axis of the C-C bond linking the six-membered ring and the olefin carbons. Single-molecule calculations using the DFT method have strengthened this structural finding, since our theoretical approaches also suggest two well-defined conformations of similar energies which resemble the molecular geometries determined by X-ray diffraction. Furthermore, the inspection of the crystal packing revealed that the hydrogen bonding patterns are different for each conformation of the compound reported here.     

On Buchsbaum bundles on quadric hypersurfaces

Let E be an indecomposable rank two vector bundle on the projective space ℙ ⁿ , n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q _n ⊂ ℙ ⁿ⁺¹, n ≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q ₃, k ≥ 2, we prove two boundedness results.     

Lewis Superacidic Divalent Bis(m-terphenyl)element Cations [(2,6-Mes2C6H3)2E]+ of Group 13 Revisited and Extended (E=B,Al, Ga,In, Tl)

In a combined experimental and computational study, the molecular and electronic structures of the divalent bis(m-terphenyl)element cations [(2,6-Mes₂C₆H₃)₂E]⁺ of group 13 ( 1 , E=B; 2 , E=Al; 3 , E=Ga; 4 , E=In; 5 , E=Tl) were investigated. The preparation and characterization of 2 , 3 and 5 were previously reported by Wehmschulte's (Organometallics 2004 , 23, 1965–1967; J. Am. Chem. Soc. 2003 , 125, 1470–1471) and our groups (Organometallics 2009 , 28, 6893–6901). The indinium ion 4 was prepared and fully characterized for the first time. Attempts to prepare the borinium ion 1 by fluoride or hydride abstraction were unsuccessful. The electronic structures of 1 – 5 and the stabilization by the bulky m-terphenyl substituents were analyzed using quantum chemical calculations and compared to the divalent bis(m-terphenyl)pnictogenium ions [(2,6-Mes₂C₆H₃)₂E]⁺ of group 15 ( 6 , E=P; 7 , E=As; 8 , E=Sb; 9 , E=Bi) previously investigated by our group (Angew. Chem. Int. Ed. 2018 , 57, 10080–10084). The calculated fluoride ion affinities (FIA) of 1–9 are higher than that of SbF₅, which classifies them as Lewis superacids.     

Cohomological property of vector bundles on biprojective spaces

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

     

Spatial arrangements of particles with different mobility tendencies in a model glass-former

The use of the isoconfigurational method has enabled one to determine the existence of particles with high and low dynamic propensity (tendency to be mobile) and particles with preferred directionality for motion (directional particles) in supercooled liquids. On the other hand, dynamical studies have shown that the relaxation of such systems evolves by means of rapid crossings between metabasins of the potential energy surface (a metabasin being a group of mutually similar, closely related structures which differ markedly from the ones belonging to other metabasins), as collectively relaxing units (d-clusters) take place. Here we determine the spatial arrangements of such particles in a model three dimensional glass-forming system. We show that both the highest and the lowest propensity particles form compact clusters, which are separated from each other by the high directionality particles. The particles of this interfacial region seem to behave as to help make room for the enhanced (expansion) movement of the high propensity cluster and to keep the local density constant. Finally, we also find that only the high propensity particles (but not the directional ones) exhibit a great tendency to take part in d-cluster events.     

Gevrey local solvability in locally integrable structures

We consider a locally integrable real-analytic structure, and we investigate the local solvability in the category of Gevrey functions and ultradistributions of the complex \(\mathrm{d}^{\prime }\) naturally induced by the de Rham complex. We prove that the so-called condition \(Y(q)\) on the signature of the Levi form, for local solvability of \(\mathrm{d}^{\prime }u=f\) , is still necessary even if we take \(f\) in the classes of Gevrey functions and look for solutions \(u\) in the corresponding spaces of ultradistributions.     

Ab initio study of the isomeric equilibrium of the HCN...H2O and H2O...HCN hydrogen-bonded clusters

An ab initio study of the stability, spectroscopic properties, and isomeric equilibrium of the hydrogen-bonded HCN...H2O and H2O...HCN isomers is presented. Density functional theory and perturbative second-order MP2 and coupled-cluster CCSD(T) calculations were carried out and binding energies obtained with correlation-consistent basis sets including extrapolation to the infinity basis set level. At the best theoretical level, CCSD(T), the H2O...HCN complex is more stable than the HCN...H2O complex by ca. 6.3 kJ mol(-1). Rotational and vibrational spectra, including anharmonic corrections, are calculated. These calculated spectroscopic data are used to obtain thermochemical contributions to the thermodynamic functions and hence the Gibbs free energy. The relative free energies are used to estimate the equilibrium constant for isomerism. We find that under typical conditions of supersonic expansion experiments (T < 150 K) H2O...HCN is essentially the only isomer present. Furthermore, our calculations indicate that the hydrogen-bonded cluster becomes favorable over the separated moieties at temperatures below 200 K.     

Atomistic Simulations of COSAN: Amphiphiles without a Head-and-Tail Design Display “Head and Tail” Surfactant Behavior

Cobaltabisdicarbollide (COSAN) anions have an unexpectedly rich self-assembly behavior, which can lead to vesicles and micelles without having a classical surfactant molecular architecture. This was rationalized by the introduction of new terminology and novel driving forces. A key aspect in the interpretation of COSAN behavior is the assumption that the most stable form of these ions is the transoid rotamer, which lacks a “hydrophilic head” and a “hydrophobic tail”. Using implicit solvent DFT calculations and MD simulations we show that in water, 1) the cisoid rotamer is the most stable form of COSAN and 2) this cisoid rotamer has a well-defined hydrophilic polar region (“head”) and a hydrophobic apolar region (“tail”). In addition, our simulations show that the properties of this rotamer in water (interfacial affinity, micellization) match those expected for a classical surfactant. Therefore, we conclude that the experimental results for the COSAN ions can now be understood in terms of its amphiphilic molecular architecture.     

Monads and rank 3 vector bundles on quadrics

In this paper we give the classification of rank 3 vector bundles without “inner” cohomology on a quadric hypersurface (n > 3) by studying the associated monads.      

Eigenmode structure in solar-wind Langmuir waves

We show that observed spatial- and frequency-domain signatures of intense solar-wind Langmuir waves can be described as eigenmodes trapped in a parabolic density well. Measured solar-wind electric field spectra and waveforms are compared with 1D linear solutions and, in many cases, can be represented by 1-3 low-order eigenstates. To our knowledge, this report is the first observational confirmation of Langmuir eigenmodes in space. These results suggest that linear eigenmodes may be the starting point of the nonlinear evolution, critical for producing solar type II and type III radio bursts.