Remarks on product

Well known results related to the compactness of Hankel operators of one complex variable are extended to little Hankel operators of two complex variables. Critical to these considerations is the result of Ferguson and Lacey (2002) characterizing the boundedness of the little Hankel operators in terms of the product BMO of S.-Y. Chang and R. Fefferman (1985), (1980).

     

Spontaneous transmission of chirality through multiple length scales

The hierarchical transfer of chirality in nature, from the nano‐, to meso‐, to macroscopic length scales, is very complex, and as of yet, not well understood. The advent of scanning probes has allowed chirality to be monitored at the single molecule or monolayer level and has opened up the possibility to track enantiospecific interactions and chiral self‐assembly with molecular‐scale detail. This paper describes the self‐assembly of a simple, model molecule (naphtho[2,3‐a]pyrene) that is achiral in the gas phase, but becomes chiral when adsorbed on a surface. This polyaromatic hydrocarbon forms a stable and reversibly ordered system on Cu(111) in which the transmission of chirality from single surface‐bound molecules to complex 2D chiral architectures can be monitored as a function of molecular packing density and surface temperature. In addition to the point chirality of the surface‐bound molecule, the unit cell of the molecular domains was also found to be chiral due to the incommensurate alignment of the molecular rows with respect to the underlying metal lattice. These molecular domains always aggregated in groups of three, all of the same chirality, but with different rotational orientations, forming homochiral “tri‐lobe” ensembles. At a larger length scale, these tri‐lobe ensembles associated with nearest‐neighbor tri‐lobe units of opposite chirality at lower packing densities before forming an extended array of homochiral tri‐lobe ensembles at higher converges. This system displayed chirality at a variety of size scales from the molecular (≈1 nm) and domain (≈5 nm) to the tri‐lobe ensemble (≈10 nm) and extended array (>25 nm) levels. The chirality of the tri‐lobe ensembles dictated how the overall surface packing occurred and both homo‐ and heterochiral arrays could be reproducibly and reversibly formed and interchanged as a function of surface coverage. Finally, these chirally templated surfaces displayed remarkable enantiospecificity for naphtho[2,3‐a]pyrene molecules adsorbed in the second layer. Given its simplicity, reversibility, and rich degree of order, this system represents an ideal test bed for the investigation of symmetry breaking and the hierarchical transmission of chirality through multiple length scales.     

Scope of the inverse electron demand Diels-Alder reactions of 1,2,3-triazine

An examination of the scope of the inverse electron demand Diels-Alder reactions of the parent unsubstituted 1,2,3-triazine is described including the first report of its unique capabilities for participating in previously unexplored [4 + 2] cycloaddition reactions with heterodienophiles.     

NCIPLOT: a program for plotting non-covalent interaction regions

Non-covalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these non-covalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define non-covalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their van der Waals radii. We recently developed an alternative perspective, derived from the electronic density: the Non-Covalent Interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of non-covalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical, as well as promolecular, densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm.     

Climate change and optimal energy technology R&D policy

Public policy response to global climate change presents a classic problem of decision making under uncertainty. Theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy, especially technology policy. However, theory also shows that the specific impacts of uncertainty are ambiguous. In this paper, we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development (R&D) policy in response to global climate change. We find that, given a budget constraint, the composition of the optimal R&D portfolio is highly diversified and robust to risk in climate damages. The overall optimal investment into technical change, however, does depend (in a non-monotonic way) on the risk in climate damages. Finally, we show that in order to properly value R&D, abatement must be included as a recourse decision.     

A novel pathway for maytansinoid release from thioether linked antibody-drug conjugates (ADCs) under oxidative conditions

A novel pathway for ex vivo maytansinoid release from thioether linked antibody maytansinoid conjugates (AMCs) upon incubation in human plasma has been identified. A thioether succinimide-linked AMC can undergo chemical oxidation followed by sulfoxide elimination under mild aqueous conditions (pH 5.5-7.5, 37 °C). Oxidized thioether-linked AMCs exhibit high, target-specific cytotoxicity toward cancer cells.     

Covalent ladder formation becomes kinetically trapped beyond four rungs

Scrambling experiments suggest that the self-assembly of 2D ladders via imine metathesis is kinetically trapped at four or more rungs. Consequently, ladders containing five or more rungs cannot be synthesized in high yield under the conditions used, as misaligned out-of-register byproducts cannot self-correct.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol⁻¹ per molecule for the X23 set and 0.19 kcal mol⁻¹ for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

A new implementation of the XDM dispersion model within FHI-aims allows efficient use of XDM-corrected hybrid functionals, found to be the most accurate DFT methods for molecular crystal lattice energies to date.     

Ladderane Natural Products: From the Ground Up

The ladderane family of natural products are well known for their linearly concatenated cyclobutane skeletal structure. Owing to their unique carbocyclic framework, several chemical syntheses have been reported since their discovery in 2002. The focus of this review is to showcase the novel tactics that have been used to generate the ladderane core and the challenges that are associated with the synthesis of these unusual and complex natural products.