Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

BIT Numerical Mathematics - In uncertainty quantification, it is commonly required to solve a forward model consisting of a partial differential equation (PDE) with a spatially varying uncertain...     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance-dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short-range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O⋅⋅⋅C=O interactions.     

A Mechanistically and Operationally Simple Route to Metal–N-Heterocyclic Carbene (NHC) Complexes

We have been puzzled by the involvement of weak organic and inorganic bases in the synthesis of metal–N-heterocyclic carbene (NHC) complexes. Such bases are insufficiently strong to permit the presumed required deprotonation of the azolium salt (the carbene precursor) prior to metal binding. Experimental and computational studies provide support for a base-assisted concerted process that does not require free NHC formation. The synthetic protocol was found applicable to a number of transition-metal- and main-group-centered NHC compounds and could become the synthetic route of choice to form M–NHC bonds.     

An Aluminum Telluride with a Terminal Al=Te Bond and its Conversion to an Aluminum Tellurocarbonate by CO2 Reduction

Facile access to dimeric heavier aluminum chalcogenides [(NHC)Al(Tipp)-μ-Ch]₂ (NHC=IiPr (1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene, IMe₄ (1,3,4,5-tetramethylimidazol-2-ylidene); Tipp=2,4,6-iPr₃C₆H₂; Ch=Se, Te) by treatment of NHC-stabilized aluminum dihydrides with elemental Se and Te is reported. The higher affinity of IMe₄ in comparison with IiPr toward the Al center in [(NHC)Al(Tipp)-μ-Ch]₂ can be used for ligand exchange. Additionally, the presence of excess IMe₄ allows for cleavage of the dimers to form a rare example of a neutral multiply bonded heavier aluminum chalcogenide in the form of a tetracoordinate aluminum complex, (IMe₄)₂(Tipp)Al=Te. This species reacts with three equivalents of CO₂ across two Al−C^NHC and the Al=Te bond affording a pentacoordinate aluminum complex containing a dianionic tellurocarbonate ligand [CO₂Te]²⁻, which is the first example of tellurium analogue of a carbonate [CO₃]²⁻.     

Partitioning Solvophobic and Dispersion Forces in Alkyl and Perfluoroalkyl Cohesion

Fluorocarbons often have distinct miscibility properties compared to their nonfluorinated analogues. These differences may be attributed to van der Waals dispersion forces or solvophobic effects, but their contributions are notoriously difficult to separate in molecular recognition processes. Here, molecular torsion balances were used to compare cohesive alkyl and perfluoroalkyl interactions in a range of solvents. A simple linear regression enabled the energetic partitioning of solvophobic and van der Waals forces in the self‐association of apolar chains. The contributions of dispersion interactions in apolar cohesion were found to be strongly attenuated in solution compared to the gas phase, but still play a major role in fluorous and organic solvents. In contrast, solvophobic effects were found to be dominant in driving the association of apolar chains in aqueous solution. The results are expected to assist the computational modelling of van der Waals forces in solution.     

Electrogenerated Chemiluminescence of Cationic Triangulene Dyes: Crucial Influence of the Core Heteroatoms

Trianguleniums are fascinating conjugated hexacyclic cations that exhibit interesting electronic and optical properties. Herein, the electrogenerated chemiluminescence (ECL) emission of this family of fluorescent dyes is reported for the first time. Redox behavior and fluorescence properties of eight cationic triangulene luminophores with different heteroatom patterns in the core structure and various pending substituents were examined to rationalize the ECL. Clearly, the more electron‐rich the carbocation, the more efficient the corresponding ECL; two very distinct classes of triangulenes can be drawn from these studies by using an ECL wall sufficiency formalism.