Injective metrizability and the duality theory of cubings

Following his discovery that finite metric spaces have injective envelopes naturally admitting a polyhedral structure, Isbell, in his pioneering work on injective metric spaces, attempted a characterization of cellular complexes admitting the structure of an injective metric space. A bit later, Mai and Tang confirmed Isbell’s conjecture that a simplicial complex is injectively metrizable if and only if it is collapsible. Considerable advances in the understanding, classification and applications of injective envelopes have since been made by Dress, Huber, Sturmfels and collaborators, and most recently by Lang. Unfortunately a combination theory for injective polyhedra is still unavailable.Here we expose a connection to the duality theory of cubings –simply connected non-positively curved cubical complexes –which provides a more principled and accessible approach to Mai and Tang’s result, providing one with a powerful tool for systematic construction of locally-compact injective metric spaces:Main Theorem. Any complete pointed Gromov–Hausdorff limit of locally-finite piecewise-${?}_{\infty }$ cubings is injective. □This result may be construed as a combination theorem for the simplest injective polytopes, ${?}_{\infty }$-parallelopipeds, where the condition for retaining injectivity is the combinatorial non-positive curvature condition on the complex. Thus it represents a first step towards a more comprehensive combination theory for injective spaces.In addition to setting the earlier work on injectively metrizable complexes within its proper context of non-positively curved geometry, this paper is meant to provide the reader with a systematic review of the results – otherwise scattered throughout the geometric group theory literature – on the duality theory and the geometry of cubings, which make this connection possible.     

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

Integrating proton coupled electron transfer (PCET) and excited states

In many of the chemical steps in photosynthesis and artificial photosynthesis, proton coupled electron transfer (PCET) plays an essential role. An important issue is how excited state reactivity can be integrated with PCET to carry out solar fuel reactions such as water splitting into hydrogen and oxygen or water reduction of CO₂ to methanol or hydrocarbons. The principles behind PCET and concerted electron–proton transfer (EPT) pathways are reasonably well understood. In Photosystem II antenna light absorption is followed by sensitization of chlorophyll P₆₈₀ and electron transfer quenching to give P₆₈₀⁺. The oxidized chlorophyll activates the oxygen evolving complex (OEC), a CaMn₄ cluster, through an intervening tyrosine–histidine pair, Y_Z. EPT plays a major role in a series of four activation steps that ultimately result in loss of 4e^?/4H⁺ from the OEC with oxygen evolution. The key elements in photosynthesis and artificial photosynthesis – light absorption, excited state energy and electron transfer, electron transfer activation of multiple-electron, multiple-proton catalysis – can also be assembled in dye sensitized photoelectrochemical synthesis cells (DS-PEC). In this approach, molecular or nanoscale assemblies are incorporated at separate electrodes for coupled, light driven oxidation and reduction. Separate excited state electron transfer followed by proton transfer can be combined in single semi-concerted steps (photo-EPT) by photolysis of organic charge transfer excited states with H-bonded bases or in metal-to-ligand charge transfer (MLCT) excited states in pre-associated assemblies with H-bonded electron transfer donors or acceptors. In these assemblies, photochemically induced electron and proton transfer occur in a single, semi-concerted event to give high-energy, redox active intermediates.     

Synthesis and Biological Activity of Argiotoxin 636 and Analogues: Selective Antagonists for Ionotropic Glutamate Receptors

More discerning than the parent : Analogues of the polyamine toxin argiotoxin 636 (shown docked in the ion channel of an ionotropic glutamate (iGlu) receptor; N blue, O red) distinguish subtypes of iGlu receptors. Depending on which of the two internal amine groups is replaced with a methylene group, the analogue inhibits one or other of two receptor subtypes as potently as the natural compound, which itself inhibits both subtypes nonselectively.

     

Dynamic solvation in imidazolium-based ionic liquids on short time scales

Steady-state and time-resolved Stokes shift data for the probe coumarin 153 in two imidazoles, six imidazolium-based ionic liquids, and several other solvents are presented. These results are consistent with our original suggestion (J. Phys. Chem. B 2004, 108, 10245-10255) that initial solvation is dominated by the organic moiety of the ionic liquid, and they show that for the imidazole-based liquids initial solvation is in all cases very rapid. Solvation by methylimidazole and butylimidazole is complete in 100 ps, and all of the imidazolium ionic liquids demonstrate similarly rapid initial solvation. Owing to the importance of determining the amount of initial solvation that is missed in a given experiment with finite time resolution, we discuss a method of estimating the intramolecular contribution to the reorganization energy. This method yields 2068 cm(-1) and is compared with an alternative method.     

Determination of solute partition behavior with room-temperature ionic liquid based micellar gas-liquid chromatography stationary phases using the pseudophase model

The use of micelles in ionic liquid based gas-chromatography stationary phases was evaluated using equations derived for a "three-phase" model. This model allows the determination of all three partition coefficients involved in the system, and elucidates the micellar contribution to retention and selectivity. Four types of micellar-ionic liquid columns were examined in this study: 1-butyl-3-methylimidazolium chloride with sodium dodecylsulfate or dioctyl sulfosuccinate, and 1-butyl-3-methylimidazolium hexafluorophosphate with polyoxyethylene-100-stearyl ether or polyoxyethylene-23-lauryl ether. The partition coefficients were measured for a wide range of probe molecules capable of a variety of types and magnitudes of interactions. In general, most probe molecules preferentially partitioned to the micellar pseudophase over the bulk ionic liquid component of the stationary phase. Therefore, addition of surfactant to the stationary phase usually resulted in greater solute retention. It is also shown that the selectivity of the stationary phase is significantly altered by the presence of micelles, either by enhancing or lessening the separation. The effects of surfactant on the interaction parameters of the stationary phase are determined using the Abraham solvation parameter model. The addition of sodium dodecylsulfate and dioctyl sulfosuccinate to 1-butyl-3-methylimidazolium chloride stationary phases generally increased the phase's hydrogen bond basicity and increased the level of dispersion interaction. Polyoxyethylene-100-stearyl ether and polyoxyethylene-23-lauryl ether surfactants, however, enhanced the pi-pi/n-pi, polarizability/dipolarity, and hydrogen bond basicity interactions of 1-butyl-3-methylimidazolium hexafluorophosphate to a greater degree than the ionic surfactants with 1-butyl-3-methylimidazolium chloride. However, these nonionic surfactants appeared to hinder the ability of the stationary phase to interact with solutes via dispersion forces. Therefore, it is possible to effectively predict which analytes will be most highly retained by these micellar-ionic liquid stationary phases.     

Sequential hydrocarbon functionalization: allylic C-H oxidation/vinylic C-H arylation

A Pd(II)/sulfoxide-catalyzed sequential allylic C-H oxidation/vinylic C-H arylation of alpha-olefins to furnish E-arylated allylic esters in high regio- and E:Z selectivities (>20:1) is reported. The broad scope of this method with respect to the alpha-olefin, carboxylic acid, and aryl boronic acid enables the rapid assembly of densely functionalized fragments for complex molecule synthesis from cheap, abundant hydrocarbon starting materials. The Pd(II)/sulfoxide-catalyzed vinylic C-H arylation of electronically unbiased olefins with aryl boronic acids proceeds under oxidative, acidic conditions and mild temperatures (room temperature to 45 degrees C).