Ring Currents in the Clar Goblet Calculated Using Configurational State Averaging.

The closed-shell Hückel-London-Pople-McWeeny formalism for ring currents is extended to Aufbau configurations with open shells calculated as configurational averages. The method is applied to the non-Kekulean benzenoid known as the Clar goblet, recently synthesized on the Au(111) surface. Multiplicity of the ground state is a complication: for the Clar goblet, Hund's rule of maximum multiplicity implies a triplet whereas Ovchinnikov's rule implies a singlet.

Tuning (Anti)Aromaticity: Variations on the [8]-Circulene Framework.

Optoelectronic properties of organic molecules are underpinned by delocalisation and delocalisability of π-electrons. These properties are sensitive to small changes in electron count, whether achieved by heteroatom substitution or redox chemistry. One measure of the delocalisability of π-electrons is the current induced by an external magnetic field, which is diagnostic of (anti)aromaticity.

iodoannulenes: A Generalized Annulene-within-an-Annulene Paradigm for Combined σ and π Ring Currents.

iodoannulene molecules and ions CI in planar geometry offer examples of systems with the potential for outer σ and inner π ring-current double aromaticity, given a sufficient overlap of tangential p-orbital manifolds on the large atoms of the outer cycle. Previous theoretical work indicated concentric diatropic currents in the dication CI. Ab initio ipsocentric calculations support an account in terms of frontier-orbital selection rules for current contributions in CI (and radical CI, implicated in recent experimental work on the oxidation of iodobenzene).

A Correlated Source-Sink-Potential Model Consistent with the Meir-Wingreen Formula.

We model a molecular device as a molecule attached to a set of leads treated at the tight-binding level, with the central molecule described to any desired level of electronic structure theory. Within this model, in the absence of electron-phonon interactions, the Landauer-Büttiker part of the Meir-Wingreen formula is shown to be sufficient to describe the transmission factor of the correlated device. The key to this demonstration is to ensure that the correlation self-energy has the same functional form as the exact correlation self-energy.

Modelling aromatisation of (BN)H azabora-annulenes.

Despite a long tradition of descriptions of borazine as an 'inorganic benzene', this molecule is a non-aromatic species according to the magnetic (ring-current) criterion. Borazine, borazocine, and the larger neutral (BN)nH2n azabora-annulene heterocycles in planar conformations, although π-isoelectronic with [2n]annulenes, support only localized induced currents in perpendicular magnetic fields. The π-current maps of these systems comprise superpositions of separate 'lone-pair' circulations on all nitrogen centres.

Ring-Current Maps for Benzenoids: Comparisons, Contradictions, and a Versatile Combinatorial Model.

As a key diagnostic property of benzenoids and other polycyclic hydrocarbons, induced ring current has inspired diverse approaches for calculation, modeling, and interpretation. Grid-based methods include the ipsocentric calculation of current maps, and its surrogate, the pseudo-π model. Graph-based models include a family of conjugated-circuit (CC) models and the molecular-orbital Hückel-London (HL) model.

Design of annulene-within-an-annulene systems by the altanisation approach. A study of altan-[n]annulenes.

The altanisation strategy, devised to design molecules with large and paratropic perimeter circulations, is applied to the family of [n]annulenes to give, altan-[n]annulenes, i.e. [n,5]coronenes.

Molecular graphs and molecular conduction: the d-omni-conductors.

Ernzerhof's source-and-sink-potential (SSP) model for ballistic conduction in conjugated π systems predicts transmission of electrons through a two-wire device in terms of characteristic polynomials of the molecular graph and subgraphs based on the pattern of connections. We present here a complete classification of conduction properties of all molecular graphs within the SSP model. An omni-conductor/omni-insulator is a molecular graph that conducts/insulates at the Fermi level (zero of energy) for all connection patterns.

In search of Coulson's lost theorem.

In Hückel theory, the bond number is the sum of the orders of the π bonds incident on a given carbon center. From the work of Coulson and his school, it has been believed for over 70 years that the bond number has a maximum of 3 and that this bound is realized by exactly one conjugated framework, that of the trimethylenemethane radical. Search of published literature and archived correspondence failed to find any formal proof of these two statements.

Can percolation theory explain the gelation behavior of diblock copolymer worms?

It is well known that polymerization-induced self-assembly (PISA) offers an efficient synthetic route for the production of highly anisotropic diblock copolymer worms. When prepared in aqueous media, such worms form thermoresponsive free-standing hydrogels that are (i) readily sterilizable, (ii) can act as a 3D matrix for the culture of normal mammalian cells and (iii) can induce stasis in human stem cell colonies. Herein we critically examine the gelation behavior of two types of diblock copolymer worms in terms of recent advances in percolation theory for rigid rods, which explicitly account for the effect of rod length polydispersity.

Raman Deuterium Isotope Probing Reveals Microbial Metabolism at the Single-Cell Level.

We illustrate that single-cell Raman microspectroscopy, coupled with deuterium isotope probing (Raman-DIP), provides a culture-independent and nondestructive approach to probe metabolic pathways of carbon substrates at the single-cell level. We found a distinguishable C-D vibration band at 2070-2300 cm in single-cell Raman spectra (SCRS) when Escherichia coli used deuterated glucose and Pseudomonas sp. used deuterated naphthalene as sole carbon sources.

Near omni-conductors and insulators: Alternant hydrocarbons in the SSP model of ballistic conduction.

Within the source-and-sink-potential model, a complete characterisation is obtained for the conduction behaviour of alternant π-conjugated hydrocarbons (conjugated hydrocarbons without odd cycles). In this model, an omni-conductor has a molecular graph that conducts at the Fermi level irrespective of the choice of connection vertices. Likewise, an omni-insulator is a molecular graph that fails to conduct for any choice of connections.

Bespoke Diblock Copolymer Nanoparticles Enable the Production of Relatively Stable Oil-in-Water Pickering Nanoemulsions.

Sterically stabilized diblock copolymer nanoparticles with an intensity-average diameter of 25 nm are prepared in the form of a concentrated aqueous dispersion using polymerization-induced self-assembly (PISA). The addition of n-dodecane followed by high-shear homogenization produces n-dodecane-in-water Pickering macroemulsions of 22-46 μm diameter. If the nanoparticles are present in sufficient excess, then subsequent processing using a high-pressure microfluidizer leads to the formation of Pickering nanoemulsions with a mean oil droplet diameter below 200 nm.

A Hückel source-sink-potential theory of Pauli spin blockade in molecular electronic devices.

This paper shows how to include Pauli (exclusion principle) effects within a treatment of ballistic molecular conduction that uses the tight-binding Hückel Hamiltonian and the source-sink-potential (SSP) method. We take into account the many-electron ground-state of the molecule and show that we can discuss ballistic conduction for a specific molecular device in terms of four structural polynomials. In the standard one-electron picture, these are characteristic polynomials of vertex-deleted graphs, with spectral representations in terms of molecular-orbital eigenvectors and eigenvalues.

An atlas of endohedral ScS cluster fullerenes.

Structural identification is a difficult task in the study of metallofullerenes, but understanding of the mechanism of formation of these structures is a pre-requisite for new high-yield synthetic methods. Here, systematic density functional theory calculations demonstrate that metal sulfide fullerenes ScS@C have similar cage geometries from C to C and form a close-knit family of structures related by Endo-Kroto insertion/extrusion of C units and Stone-Wales isomerization transformations. The stabilities predicted for favoured isomers by DFT calculations are in good agreement with available experimental observations, have implications for the formation of metallofullerenes, and will aid structural identification from within the combinatorially vast pool of conceivable isomers.

From C(58) to C(62) and back: Stability, structural similarity, and ring current.

An increasing number of observations show that non-classical isomers may play an important role in the formation of fullerenes and their exo- and endo-derivatives. A quantum-mechanical study of all classical isomers of C , C , and C , and all non-classical isomers with at most one square or heptagonal face, was carried out. Calculations at the B3LYP/6-31G* level show that the favored isomers of C , C , and C have closely related structures and suggest plausible inter-conversion and growth pathways among low-energy isomers.

Effect of Ring Size and Migratory Groups on [1,n] 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.

Determining the Effective Density and Stabilizer Layer Thickness of Sterically Stabilized Nanoparticles.

A series of model sterically stabilized diblock copolymer nanoparticles has been designed to aid the development of analytical protocols in order to determine two key parameters: the effective particle density and the steric stabilizer layer thickness. The former parameter is essential for high resolution particle size analysis based on analytical (ultra)centrifugation techniques (e.g.

Structural interconnections and the role of heptagonal rings in endohedral trimetallic nitride template fullerenes.

Recent experiments indicate that fullerene isomers outside the classical definition can also encapsulate metallic atoms or clusters to form endohedral metallofullerenes. Our systematic study using DFT calculations, suggests that many heptagon-including nonclassical trimetallic nitride template fullerenes are similar in stability to their classical counterparts, and that conversion between low-energy nonclassical and classical parent cages via Endo-Kroto insertion/extrusion of C2 units and Stone-Wales isomerization may facilitate the formation of endohedral trimetallic nitride fullerenes. Close structural connections are found between favored isomers of trimetallic nitride template fullerenes from C78 to C82 .

Perimeter ring currents in benzenoids from Pauling bond orders.

It is shown that the ring currents in perimeter hexagonal rings of Kekulean benzenoids, as estimated within the Randić conjugated-circuit model, can be calculated directly without tedious pairwise comparison of Kekulé structures or Kekulé counting for cycle-deleted subgraphs. Required are only the Pauling bond orders of perimeter bonds and the number of Kekulé structures of the benzenoid, both readily available from the adjacency matrix of the carbon skeleton. This approach provides easy calculation of complete current maps for benzenoids in which every face has at least one bond on the perimeter (as in the example of cata-condensed benzenoids), and allows qualitative evaluation of the main ring-current contributions to (1)H chemical shifts in general benzenoids.

A new approach to the method of source-sink potentials for molecular conduction.

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells.

Distributed curvature and stability of fullerenes.

Energies of non-planar conjugated π systems are typically described qualitatively in terms of the balance of π stabilisation and the steric strain associated with geometric curvature. Curvature also has a purely graph-theoretical description: combinatorial curvature at a vertex of a polyhedral graph is defined as one minus half the vertex degree plus the sum of reciprocal sizes of the faces meeting at that vertex. Prisms and antiprisms have positive combinatorial vertex curvature at every vertex.

Determination of Effective Particle Density for Sterically Stabilized Carbon Black Particles: Effect of Diblock Copolymer Stabilizer Composition.

Two poly(styrene-b-hydrogenated isoprene) (PS-PEP) copolymers and a poly(styrene-b-hydrogenated butadiene) (PS-PB) diblock copolymer of differing polystyrene content (20, 28 or 35 mol %) and molecular weight (117-183 kg mol(-1)) are examined. These copolymers form star-like micelles in n-dodecane, as judged by TEM, DLS, and SAXS studies. At ambient temperature, such micelles are known to adsorb intact onto a model colloidal substrate such as carbon black, conferring a high degree of dispersion (Growney, D.

Tracking heavy water (D2O) incorporation for identifying and sorting active microbial cells.

Microbial communities are essential to the function of virtually all ecosystems and eukaryotes, including humans. However, it is still a major challenge to identify microbial cells active under natural conditions in complex systems. In this study, we developed a new method to identify and sort active microbes on the single-cell level in complex samples using stable isotope probing with heavy water (D2O) combined with Raman microspectroscopy.

Planar homotropenylium cation: a transition state with reversed aromaticity.

In contrast to the equilibrium structure of the homoaromatic C(s) homotropenylium cation, C8H9(+) (1), which supports a pinched diatropic ring current, the C(2v) transition state (2) for inversion of the methylene bridge of 1 is antiaromatic and supports a two-lobe paratropic π current, as detected by plotting B3LYP/6-31G** ipsocentric current maps. Participation of the bridge CH bonds is crucial for the change in global character of the current in the transition state, as shown by the quenching of its paratropicity on substitution of H by F. Orbital-based arguments allow rationalization of this transition between homoaromaticity and hyper(conjugative) antiaromaticity.