Polar Symplectic Representations

We study polar representations in the sense of Dadok and Kac which are symplectic. We show that such representations are coisotropic and use this fact to give a classification. We also study their moment maps and prove that they separate closed orbits. Our work can also be seen as a specialization of some of the results of Knop on multiplicity free symplectic representations to the polar case.     

Excited-state intramolecular proton transfer in hydroxyoxime-based chemical sensors

The electronic structure of a series of β-hydroxy-oximes, with different aromatic cores (naphthalene, pyrene, coumarin, pyridine) between the oxime and the hydroxyl groups, has been investigated by time-dependent density functional theory (TDDFT) and of the naphthalene-based oxime, in addition, by resolution-of-identity second-order perturbative coupled cluster (RICC2) calculations with basis sets up to augmented triple-ζ quality. The particular systems have been proposed as fluorescent sensors of organophosphorus (OP) nerve agents, with enhancement of fluorescence accompanying the sensing of OP agents. It is found that the experimentally observed fluorescence quenching of the oxime sensors in their initial form can be attributed to intramolecular proton transfer upon excitation from the β-hydroxyl group to the nitrogen atom, thus forming a weakly emitting hydroxylaminoquinoid.     

Theoretical study of hydrogen bonding in homodimers and heterodimers of amide, boronic acid, and carboxylic acid, free and in encapsulation complexes

The homodimers and the heterodimers of two amides, two boronic acids, and two carboxylic acids have been calculated in the gas phase and in N,N-dimethylformamide (DMF) and CCl(4) solvents using the DFT (M06-2X and M06-L) and the MP2 methods in conjunction with the 6-31G(d,p) and 6-311+G(d,p) basis sets. Furthermore, their pairwise coencapsulation was studied to examine its effect on the calculated properties of the hydrogen bonds at the ONIOM[M06-2X/6-31G(d,p);PM6], ONIOM[MP2/6-31G(d,p); PM6], and M06-2X/6-31G(d,p) levels of theory. The present work is directed toward the theoretical rationalization and interpretation of recent experimental results on hydrogen bonding in encaptulation complexes [D. Ajami et al. J. Am. Chem. Soc. 2011, 133, 9689-9691]. The calculated dimerization energy (ΔE) values range from 0.74 to 0.35 eV for the different dimers in the gas phase, with the ordering carboxylic homodimers > amide-carboxylic dimers > amide homodimers > boronic-carboxylic dimers > amide-boronic dimers > boronic homodimers. In solvents, generally smaller ΔE values are calculated with only small variations in the ordering. In the capsule, the ΔE values range between 0.67 and 0.33 eV with practically the same ordering as in the gas phase. The calculated % distributions of the encapsulated dimers, taking into account statistical factors, are in agreement with the experimental distribution, where the occurrence of boronic homodimer dominates, even though it is calculated to have the smallest ΔE.     

Conformations and fluorescence of encapsulated stilbene

Absorption and emission spectra of free and encapsulated stilbene in two different capsules were calculated using the DFT and the TDDFT methodology at the B3LYP, CAM-B3LYP, M06-2X, PBE0, and ωB97X-D/6-31G(d,p) levels of theory. The present work is directed toward the theoretical interpretation of recent experimental results on control of stilbene conformation and fluorescence in capsules [Ams, M. R.; et al. Beilstein J. Org. Chem. 2009, 5, 79]. The results of the calculations are in agreement with experiment and show that fluorescence of trans-stilbene persists in the large cage while it is quenched in the small one. It is found that the geometry of trans-stilbene in the ground as well as in the first excited singlet state is unaffected by encapsulation in the large cage, and consequently the absorption and emission spectra are similarly unaffected. In the small cage, the ground state of encapsulated trans-stilbene is distorted, with the two phenyl groups twisted, while the geometry of the excited state, after relaxation, lies at the conical intersection with the ground state. Consequently, there is no emission similar to that of free trans-stilbene, and the state decays nonradiatively to the ground state.     

Single-layer graphdiyne-covered Pt(111) surface: improved catalysis confined under two-dimensional overlayer

In recent years, two-dimensional confined catalysis, i.e., the enhanced catalytic reactions in confined space between metal surface and two-dimensional overlayer, makes a hit and opens up a new way to enhance the performance of catalysts. In this work, graphdiyne overlayer was proposed as a more excellent material than graphene or hexagonal boron nitride for two-dimensional confined catalysis on Pt(111) surface. Density functional theory calculations revealed the superiority of graphdiyne overlayer originates from the steric hindrance effect which increases the catalytic ability and lowers the reaction barriers. Moreover, with the big triangle holes as natural gas tunnels, graphdiyne possesses higher efficiency for the transit of gaseous reactants and products than graphene or hexagonal boron nitride. The results in this work would benefit future development of two-dimensional confined catalysis.

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Polynomials in operator space theory: matrix ordering and algebraic aspects

We extend the \(\lambda \)-theory of operator spaces given in Defant and Wiesner (J. Funct. Anal. 266(9): 5493–5525, 2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach \(*\)-algebras. Given matrix regular operator spaces and operator systems, we introduce cones related to \(\lambda \) for the algebraic operator space tensor product that respect the matricial structure of matrix regular operator spaces and operator systems, respectively. The ideal structure of \(\lambda \)-tensor product of \(C^*\)-algebras has also been discussed.     

Theoretical investigation of the complexation of crown ethers and crown ethers of fulleropyrrolidine with (CH3)(x)NH+(4-x), x = 0-4

The electronic and geometric structures of dibenzo-12-crown-4, dibenzo-18-crown-6, and dibenzo-24-crown-8 ethers, and dibenzo-18-crown-6 ether of fullero-N-methylpyrrolidine and their complexes with (CH(3))(x)NH+(4-x), x = 0-4 were investigated by employing density functional theory (B3LYP, M05-2X, M06-2X, MPWBIK and B2PLYP-D) in conjunction with three basis sets. Different energetic minima have been identified for all of the above molecules and complexes in the gas phase as well as in CHCl(3) solvent. We report geometries, complexation energies and some thermochemical data. For increasing values of x, the complexation energies, corrected for the basis set superposition error range from 3.29 to 0.73 eV in the gas phase and from 1.56 to 0.13 eV in the CHCl(3) solvent. In the case of the largest crown ethers, the 24-crown-8 ethers are folded around the ammonium cation so as to maximize the number of hydrogen bonds formed and present the largest complexation energies. Finally, the presence of fullero-N-methylpyrrolidine, attached to the crown ethers, does not change the complexation energies substantially.     

Social Isomers of Picolines in a Small Space

Encapsulation complexes permit the observation of molecules under conditions of limited motion. Inside capsules, molecular encounters are prolonged, prearranged, and protected from the medium, in contrast to the short‐lived and random encounters that occur in bulk solution. Herein, the interaction of α‐, β‐, and γ‐picolines in a cylindrical capsule is described. Two picolines were taken up, and NMR spectra indicated dynamic combinations of various social isomers. The stabilities of the complexes are interpreted through computational methods. The shape of the space in the capsule allowed the alignment of molecules and revealed delicate, atom‐to‐atom interactions and attractive forces that elude observation in dilute solution. These weak forces were amplified in the isolated small space of the capsule.