A Variational Finite Element Discretization of Compressible Flow

Foundations of Computational Mathematics - We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure-preserving way,...     

Black and white local invariants of mappings from surfaces into three-space

Goryunov proved that the space of local invariants of Vassiliev type for generic maps from surfaces to three-space is three-dimensional. The basic invariants were the number of pinch points, the number of triple points and one linked to a Rokhlin type invariant. In this paper we show that, by colouring the complement of the image of the map with a chess board pattern, we can produce a six-dimensional space of local invariants. These are essentially black and white versions of the above. Simple examples show how these are more effective. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bouquet and join theorems for disentanglements

The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre. The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ ⁿ to ℂ ^{n +1} it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given. Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001     

Adhesion between graphite and modified polyester surfaces: a theoretical study

This study examines the adhesion of graphite to functionalized polyester surfaces using a range of qualitative and quantitative measures of theoretical adhesion. Modifications to the polyester surfaces include the addition of hydroxyl, carboxyl, or fluorine substituents with coverages of 0.4 and 0.9 groups per nm(2). In each case, the introduction of substituents to the surface of the polyester was calculated to lead to reduced adhesion to graphite. Effects of surface relaxation on adhesion are studied by employing different simulation protocols. The theoretical results suggest one mechanism to reduce adhesion to carbonaceous solids is to increase atomic roughness using strongly hydrophilic or alternatively strongly hydrophobic substituents.     

Fast 3D shape screening of large chemical databases through alignment-recycling

Background  

Large chemical databases require fast, efficient, and simple ways of looking for similar structures. Although such tasks are now fairly well resolved for graph-based similarity queries, they remain an issue for 3D approaches, particularly for those based on 3D shape overlays. Inspired by a recent technique developed to compare molecular shapes, we designed a hybrid methodology, alignment-recycling, that enables efficient retrieval and alignment of structures with similar 3D shapes.     

BonDNet: a graph neural network for the prediction of bond dissociation energies for charged molecules

A broad collection of technologies, including e.g. drug metabolism, biofuel combustion, photochemical decontamination of water, and interfacial passivation in energy production/storage systems rely on chemical processes that involve bond-breaking molecular reactions. In this context, a fundamental thermodynamic property of interest is the bond dissociation energy (BDE) which measures the strength of a chemical bond. Fast and accurate prediction of BDEs for arbitrary molecules would lay the groundwork for data-driven projections of complex reaction cascades and hence a deeper understanding of these critical chemical processes and, ultimately, how to reverse design them. In this paper, we propose a chemically inspired graph neural network machine learning model, BonDNet, for the rapid and accurate prediction of BDEs. BonDNet maps the difference between the molecular representations of the reactants and products to the reaction BDE. Because of the use of this difference representation and the introduction of global features, including molecular charge, it is the first machine learning model capable of predicting both homolytic and heterolytic BDEs for molecules of any charge. To test the model, we have constructed a dataset of both homolytic and heterolytic BDEs for neutral and charged (−1 and +1) molecules. BonDNet achieves a mean absolute error (MAE) of 0.022 eV for unseen test data, significantly below chemical accuracy (0.043 eV). Besides the ability to handle complex bond dissociation reactions that no previous model could consider, BonDNet distinguishes itself even in only predicting homolytic BDEs for neutral molecules; it achieves an MAE of 0.020 eV on the PubChem BDE dataset, a 20% improvement over the previous best performing model. We gain additional insight into the model''s predictions by analyzing the patterns in the features representing the molecules and the bond dissociation reactions, which are qualitatively consistent with chemical rules and intuition. BonDNet is just one application of our general approach to representing and learning chemical reactivity, and it could be easily extended to the prediction of other reaction properties in the future.

Prediction of bond dissociation energies for charged molecules with a graph neural network enabled by global molecular features and reaction difference features between products and reactants.     

General approach for the synthesis of chiral perylenequinones via catalytic enantioselective oxidative biaryl coupling

By using oxygen as the terminal oxidant, copper complexes derived from chiral 1,5-diaza-cis-decalin catalyze the enantioselective oxidative biaryl coupling of highly functionalized naphthols to provide octa- and decasubstituted binaphthalenes with high selectivity (86-90% ee). Products containing very electron-rich naphthalenes were prone to epimerization under the reaction conditions. This epimerization could be suppressed by employing naphthol starting materials with phenol protecting groups that attenuated the electron-rich nature of the naphthalenes. Direct oxidation of the resultant chiral 1,1'-binaphthol framework completed the first asymmetric synthesis of a perylenequinone containing only an axial chirality element.     

Photochemical and Acid-Catalyzed Rearrangements of 4-Carbomethoxy-4-methyl-3-(trimethylsilyl)-2,5-cyclohexadien-1-one

The synthesis of 4-carbomethoxy-4-methyl-3-(trimethylsilyl)-2,5-cyclohexadien-1-one (1) in 60% overall yield from benzaldehyde is described. Irradiation (366 nm) of 1 in benzene solution gave products of type A photorearrangement; e.g., diastereomers of the 4-(trimethylsilyl)- and 5-(trimethylsilyl)bicyclo[3.1.0]hex-3-en-2-ones 8 and 9. Bicyclohexenones 9a and 9b could not be isolated, but underwent acid-catalyzed protiodesilylative rearrangements on attempted chromatography (silica gel) to give a 1:1 mixture of (E)- and (Z)-4-(carbomethoxymethylmethylene)cyclopent-2-en-1-ones 12 and 13. Irradiation (366 nm) of either 12 or 13 resulted in photoisomerization to a photostationary state that was also a 1:1 mixture. Irradiation of 8a or 8b gave equivalent mixtures of phenols 14 and 15 by way of the type B oxyallyl zwitterion 17. The available experimental evidence suggests that both 9a and 9b undergo regiospecific photorearrangement to phenol 16 with no trace of 3-methyl-4-carbomethoxyphenol (19), the product of ipso substitution of the Me(3)Si group at C(4). Phenol 15 was isolated in 65% yield from the photoreaction of 1 in benzene with 20 equiv of CF(3)CO(2)H. The acid-catalyzed rearrangement of 1 to 3-carbomethoxy-4-methylphenol (21) occurs in 91% yield by way of CO(2)Me group rearrangement to C(3) to give the Me(3)Si-stabilized carbocation 23.     

A chemically consistent graph architecture for massive reaction networks applied to solid-electrolyte interphase formation

Modeling reactivity with chemical reaction networks could yield fundamental mechanistic understanding that would expedite the development of processes and technologies for energy storage, medicine, catalysis, and more. Thus far, reaction networks have been limited in size by chemically inconsistent graph representations of multi-reactant reactions (e.g. A + B → C) that cannot enforce stoichiometric constraints, precluding the use of optimized shortest-path algorithms. Here, we report a chemically consistent graph architecture that overcomes these limitations using a novel multi-reactant representation and iterative cost-solving procedure. Our approach enables the identification of all low-cost pathways to desired products in massive reaction networks containing reactions of any stoichiometry, allowing for the investigation of vastly more complex systems than previously possible. Leveraging our architecture, we construct the first ever electrochemical reaction network from first-principles thermodynamic calculations to describe the formation of the Li-ion solid electrolyte interphase (SEI), which is critical for passivation of the negative electrode. Using this network comprised of nearly 6000 species and 4.5 million reactions, we interrogate the formation of a key SEI component, lithium ethylene dicarbonate. We automatically identify previously proposed mechanisms as well as multiple novel pathways containing counter-intuitive reactions that have not, to our knowledge, been reported in the literature. We envision that our framework and data-driven methodology will facilitate efforts to engineer the composition-related properties of the SEI – or of any complex chemical process – through selective control of reactivity.

A chemically consistent graph architecture enables autonomous identification of novel solid-electrolyte interphase formation pathways from a massive reaction network.