Effect on Ring Current of the Kekulé Vibration in Aromatic and Antiaromatic Rings

Derivative current–density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic “antiring-current”, leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained <i>D</i>_4<i>h</i> COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and <i>D</i>_4<i>h</i> COT reduce aromaticity and increase antiaromaticity, respectively

Simulating the Pyrolysis of Polyazides: a Mechanistic Case Study of the [P(N₃)₆]⁻ Anion

Pyrolysis of the homoleptic azido complex [P­(N₃)₆]⁻ was simulated using density functional theory based molecular dynamics and analyzed further using electronic-structure calculations in atom-centered basis sets to calculate the geometries and electronic structures. Simulations at 600 and 1200 K predict a thermally induced and, on the simulation time scale, irreversible dissociation of an azido anion. The ligand loss is accompanied by a barrierless (free-energy) transition of the geometry of the complex coordination sphere from octahedral to trigonal bipyramidal. [P­(N₃)₅] is fluxional and engages in pseudorotation via a Berry mechanism

Effect of Ring Size and Migratory Groups on [1,<i>n</i>] Suprafacial Shift Reactions. Confirmation of Aromatic and Antiaromatic Transition-State Character by Ring-Current Analysis

Suprafacial sigmatropic shift reactions of 5-substituted cyclopentadienes, 3-substituted cyclopropenes, and 7-substituted cycloheptatrienes have been studied computationally at the MP2/6-31+G* level for structures and energetics and with the ipsocentric method at the CHF/6-31G** level to calculate current–density maps. The hydrogen shifts in cyclopentadienes have a diatropic ring current indicating aromatic, cyclopentadienide anion character. This result stands in contrast to the fluorine shift in 5-fluorocyclopentadiene which requires much more energy and has a paratropic ring current in the TS pointing to antiaromatic, cyclopentadienyl cation character. [1,3] hydrogen shifts in cyclopropenes are very difficult, passing through transition states that have an extended C–C bond. For 3-fluorocyclopropene, the [1,3] fluorine shift is much easier than the hydrogen shift. For 7-fluorocycloheptatriene, the [1,7] hydrogen shift is predicted but requires very high energy and has a paratropic ring current and antiaromatic character. The [1,7] suprafacial fluorine shift is relatively easy, having a TS with cycloheptatrienyl cation character. Patterns of currents, and the reversal for H and F migration, are rationalized by orbital analysis based on the ipsocentric method. Calculated charges and structural features for reactants and transition states support these conclusions

Concurrence between Current Density, Nucleus-Independent Chemical Shifts, and Aromatic Stabilization Energy: The Case of Isomeric [4]- and [5]Phenylenes

The 17 isomers of the [4]- and [5]­phenylenes have been studied with three different computational levels of current-density analysis (CDA) and by calculation of the out-of-plane contribution to nucleus-independent chemical shifts (NICS_πzz). Current-density maps for these isomeric phenylenes are typically dominated by strong paratropic ring currents in four-membered rings. The relative energies of the isomers, which differ only through the effects of differential strain and aromaticity, were computed at the B3LYP/6-311G* computational level. It was found that the three levels of CDA correlate well among themselves and with NICS_πzz. The latter correlation is improved when the ring sum ∑NICS_πzz for each isomer is correlated to the ring-current sum ∑<i>J</i> extracted from CDA. The strain-corrected relative energies of the isomers correlate linearly with ∑NICS_πzz. In particular, the compatibility of different summed quantities with easily computed Hückel–London ring currents suggests a simply calculated measure for dealing with global aromaticity of polycyclic systems

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Accurately measuring carbon flows is a challenge for understanding processes such as diverse intracellular metabolic pathways and predator-prey interactions. Combined with stable isotope probing (SIP), single-cell Raman spectroscopy was demonstrated for the first time to link the food chain from carbon substrate to bacterial prey up to predators at the single-cell level in a quantitative and nondestructive manner. <i>Escherichia coli</i> OP50 with different ¹³C content, which were grown in a mixture of ¹²C- and fully carbon-labeled ¹³C-glucose (99%) as a sole carbon source, were fed to the nematode. The ¹³C signal in <i>Caenorhabditis elegans</i> was proportional to the ¹³C content in <i>E. coli</i>. Two Raman spectral biomarkers (Raman bands for phenylalanine at 1001 cm^–1 and thymine at 747 cm^–1 Raman bands), were used to quantify the ¹³C content in <i>E. coli</i> and <i>C. elegans</i> over a range of 1.1–99%. The phenylalanine Raman band was a suitable biomarker for prokaryotic cells and thymine Raman band for eukaryotic cells. A biochemical mechanism accounting for the Raman red shifts of phenylalanine and thymine in response to ¹³C-labeling is proposed in this study and is supported by quantum chemical calculation. This study offers new insights of carbon flow via the food chain and provides a research tool for microbial ecology and investigation of biochemical pathways

Stable Isotope Probing and Raman Spectroscopy for Monitoring Carbon Flow in a Food Chain and Revealing Metabolic Pathway

Accurately measuring carbon flows is a challenge for understanding processes such as diverse intracellular metabolic pathways and predator-prey interactions. Combined with stable isotope probing (SIP), single-cell Raman spectroscopy was demonstrated for the first time to link the food chain from carbon substrate to bacterial prey up to predators at the single-cell level in a quantitative and nondestructive manner. <i>Escherichia coli</i> OP50 with different ¹³C content, which were grown in a mixture of ¹²C- and fully carbon-labeled ¹³C-glucose (99%) as a sole carbon source, were fed to the nematode. The ¹³C signal in <i>Caenorhabditis elegans</i> was proportional to the ¹³C content in <i>E. coli</i>. Two Raman spectral biomarkers (Raman bands for phenylalanine at 1001 cm^–1 and thymine at 747 cm^–1 Raman bands), were used to quantify the ¹³C content in <i>E. coli</i> and <i>C. elegans</i> over a range of 1.1–99%. The phenylalanine Raman band was a suitable biomarker for prokaryotic cells and thymine Raman band for eukaryotic cells. A biochemical mechanism accounting for the Raman red shifts of phenylalanine and thymine in response to ¹³C-labeling is proposed in this study and is supported by quantum chemical calculation. This study offers new insights of carbon flow via the food chain and provides a research tool for microbial ecology and investigation of biochemical pathways

Visible Mie Scattering from Hollow Silica Particles with Particulate Shells

A series of colloidal nanocomposite dispersions are synthesized by alcoholic dispersion polymerization of styrene in the presence of an ultrafine silica sol. The original core/shell polystyrene/silica nanocomposite particles have mean diameters ranging from 321 to 471 nm, as determined by dynamic light scattering. Upon calcination of the polystyrene cores, some shrinkage occurs but intact hollow silica shells are observed by transmission electron microscopy. On visual inspection, these silica residues display remarkable colors that vary depending on the particle diameter. When examined in transmittance mode (i.e., with an illuminated background) the silica powders appear yellow to red in color, but when viewed in reflectance (i.e., with a dark background) relatively intense blue/green colors are observed. The latter phenomenon has been analyzed by visible reflectance spectroscopy and the reflectance maximum depends on the dimensions of the silica shell, which are in turn dictated by the initial nanocomposite particle diameter. Small-angle X-ray scattering is used to determine the packing density of the silica nanoparticles, both in the original polystyrene/silica nanocomposite particles and in the calcined silica shells. Combined with geometrical considerations, this allows the equivalent <i>uniform</i> silica shell thickness to be calculated for a <i>particulate</i> silica shell and this parameter is then related to the theoretical predictions made by Retsch et al. for hollow particles comprising uniform silica shells (see Retsch, M.; Schmelzeisen, M.; Butt, H. J.; Thomas, E. L. <i>Nano Lett.</i>, <b>2011</b>, <i>11</i>, 1389)

Correcting for a Density Distribution: Particle Size Analysis of Core–Shell Nanocomposite Particles Using Disk Centrifuge Photosedimentometry

Many types of colloidal particles possess a core–shell morphology. In this Article, we show that, if the core and shell densities differ, this morphology leads to an inherent density distribution for particles of finite polydispersity. If the shell is denser than the core, this density distribution implies an artificial narrowing of the particle size distribution as determined by disk centrifuge photosedimentometry (DCP). In the specific case of polystyrene/silica nanocomposite particles, which consist of a polystyrene core coated with a monolayer shell of silica nanoparticles, we demonstrate that the particle density distribution can be determined by analytical ultracentrifugation and introduce a mathematical method to account for this density distribution by reanalyzing the raw DCP data. Using the mean silica packing density calculated from small-angle X-ray scattering, the real particle density can be calculated for each data point. The corrected DCP particle size distribution is both broader and more consistent with particle size distributions reported for the same polystyrene/silica nanocomposite sample using other sizing techniques, such as electron microscopy, laser light diffraction, and dynamic light scattering. Artifactual narrowing of the size distribution is also likely to occur for many other polymer/inorganic nanocomposite particles comprising a low-density core of variable dimensions coated with a high-density shell of constant thickness, or for core–shell latexes where the shell is continuous rather than particulate in nature

Base-Catalyzed Dehydration of 3‑Substituted Benzene <i>cis</i>-1,2-Dihydrodiols: Stabilization of a Cyclohexadienide Anion Intermediate by Negative Aromatic Hyperconjugation

Evidence that a 1,2-dihydroxycyclohexadienide anion is stabilized by aromatic “negative hyperconjugation” is described. It complements an earlier inference of “positive” hyperconjugative aromaticity for the cyclohexadienyl cation. The anion is a reactive intermediate in the dehydration of benzene <i>cis</i>-1,2-dihydrodiol to phenol. Rate constants for 3-substituted benzene <i>cis</i>-dihydrodiols are correlated by σ^– values with ρ = 3.2. Solvent isotope effects for the reactions are <i>k</i>_H₂O/<i>k</i>_D₂O = 1.2–1.8. These measurements are consistent with reaction via a carbanion intermediate or a concerted reaction with a “carbanion-like” transition state. These and other experimental results confirm that the reaction proceeds by a stepwise mechanism, with a change in rate-determining step from proton transfer to the loss of hydroxide ion from the intermediate. Hydrogen isotope exchange accompanying dehydration of the parent benzene <i>cis</i>-1,2-dihydrodiol was not found, and thus, the proton transfer step is subject to internal return. A rate constant of ∼10¹¹ s^–1, corresponding to rotational relaxation of the aqueous solvent, is assigned to loss of hydroxide ion from the intermediate. The rate constant for internal return therefore falls in the range 10¹¹–10¹² s^–1. From these limiting values and the measured rate constant for hydroxide-catalyzed dehydration, a p<i>K</i>_a of 30.8 ± 0.5 was determined for formation of the anion. Although loss of hydroxide ion is hugely exothermic, a concerted reaction is not enforced by the instability of the intermediate. Stabilization by negative hyperconjugation is proposed for 1,2-dihydroxycyclohexadienide and similar anions, and this proposal is supported by additional experimental evidence and by computational results, including evidence for a diatropic (“aromatic”) ring current in 3,3-difluorocyclohexadienyl anion