Kekulé structure counts for some classes of all-benzenoid and all-coronoid hydrocarbons

Summary A general formula for the Kekulé structure count (K) is deduced for the class of catacondensed all-benzenoids with unbranched backbones. The formula is extended to thin pericondensed all-benzenoids, where allowance is made for pyrene units. In this treatment the fragmentation matrices are employed. A generalization of these matrices is furnished. Next some generalK formulas for classes of catacondensed and thin pericondensed all-coronoids are deduced. Again the fragmentation matrices are employed, but the problem is also studied in terms of certain polynomials.Dedicated to the memory of Professor Oskar E. Polansky, who died in January 1989. He was the one who coined the term all-benzenoid.     

Examination of the statistical method in the conjugated circuit theory

Summary The recently proposed statistical method for the calculation of resonance energies in the conjugated circuit theory is tested on the example of polyacenes. It is found that for the estimation of the resonance energy with a 10% average error, the method requires a sample consisting of about 20 (randomly chosen) Kekulé structures. Further increase of the sample size gives no significant gain in the accuracy of the method.

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Überprüfung der statistischen Methode in der Konjugierten-Ring-Theorie

Zusammenfassung Die unlängst vorgeschlagene statistische Methode in der Konjugierten-Ring-Theorie (conjugated circuit theory) wird am Beispiel der Polyacene getestet. Es wurde festgestellt, daß für die Abschätzung der Resonanzenergien bei einem mittleren Fehler von 10% für diese Methode ungefähr 20 (willkürlich gewählte) Kekulé-Strukturen nötig sind. Weitere Erhöhung dieser Anzahl bringt keine signifikante Verbesserung der Genauigkeit der Methode.

     

On a resonance energy model based on expansion in terms of acyclic moments: Exact results

Summary The new concept of the resonance energy in conjugated hydrocarbons introduced by Jiang Y, Zhang H (1989) Theor Chim Acta 75:279 is further developed. This model is based on expansion of the -electron energy in terms of moments which are also equal to numbers of closed walks in a molecular graph. The reference system is established by counting only acyclic walks, i.e. those tracing only on acyclic subgraphs. Because acyclic walks could be counted only up to some finite length, the energy of the reference system has been evaluated by truncating higher terms in the expansion. In this paper a finite expression for the energy of the same reference system is derived, thus allowing its exact evaluation. The exact values differ significantly from the truncated ones. This difference, as well as the discrepancy between exact results and chemical experience, are discussed.     

Time-resolved fluorescence analysis of the mobile flavin cofactor in p -hydroxybenzoate hydroxylase

Conformational heterogeneity of the FAD cofactor in p-hydroxybenzoate hydroxylase (PHBH) was investigated with time-resolved polarized flavin fluorescence. For binary enzyme/substrate (analogue) complexes of wild-type PHBH and Tyr222 mutants, crystallographic studies have revealed two distinct flavin conformations; the ‘in’ conformation with the isoalloxazine ring located in the active site, and the ‘out’ conformation with the isoalloxazine ring disposed towards the protein surface. Fluorescence-lifetime analysis of these complexes revealed similar lifetime distributions for the ‘in’ and ‘out’ conformations. The reason for this is twofold. First, the active site of PHBH contains various potential fluorescence-quenching sites close to the flavin. Fluorescence analysis of uncomplexed PHBH Y222V and Y222A showed that Tyr222 is responsible for picosecond fluorescence quenching free enzyme. In addition, other potential quenching sites, including a tryptophan and two tyrosines involved in substrate binding, are located nearby. Since the shortest distance between these quenching sites and the isoalloxazine ring differs only little on average, these aromatic residues are likely to contribute to fluorescence quenching. Second, the effect of flavin conformation on the fluorescence lifetime distribution is blurred by binding of the aromatic substrates: saturation with aromatic substrates induces highly efficient fluorescence quenching. The flavin conformation is therefore only reflected in the small relative contributions of the longer lifetimes.     

Monte-Carlo characterization of a miniature source of characteristic X rays based on an implantable needle

A new concept of an X-ray brachytherapy setup based on the use of fluorescence from a secondary target placed at the tip of an implantable needle is proposed. Spatial dose-rate distributions for four combinations of secondary target materials and shapes are calculated by the Monte-Carlo method.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Non‐symmetric bent‐core mesogens with one terminal vinyl group

Two series of non‐symmetric banana‐shaped compounds, both with one alkyl and one alkenyl terminal tail, have been synthesized and studied. Both series were compared with the corresponding series with two saturated terminal alkyl tails. All the compounds have a bent central 1,3‐phenylene bis(4‐benzoyloxy)benzoate core; their mesophases were characterized by polarizing optical microscopy, differential scanning calorimetry, X‐ray diffraction and switching current response experiments. In all four series one of the terminal tails is varied from OC₈H₁₇ to OC₁₆H₃₃. The other terminal tails are OC₁₁H₂₃, O(CH₂)₉CH?=?CH₂, OC₁₀H₂₁ and O(CH₂)₈CH?=?CH₂. The short‐tailed compounds show monotropic or enantiotropic B₁ phases and the long‐tailed compounds the B₂ phase. The introduction of one terminal vinyl group slightly lowers the transition temperatures. The introduction of a second terminal vinyl group further suppresses the liquid crystalline properties. All compounds with B₂ phases have layer spacings that suggest a tilt of ～45° of the bent molecules in the layers, and their switching behaviour is antiferroelectric.     

X-ray source based on a compact electron linear accelerator with a thin anode

An experiment confirming the possibility of extracting a narrow energy band from a wide spectrum produced by a compact electron linear accelerator with a thin transmission anode is described. A flat crystal of pyrolytic graphite was used as a monochromator.     

A note on medieval microfabrication: the visualization of a prayer nut by synchrotron‐based computer X‐ray tomography

One of the most fascinating objects in the Rijksmuseum (Amsterdam, The Netherlands) is an early 16th century prayer nut. This spherical wooden object measures 4 cm in diameter and consists of two hemispheres connected with a small hinge so that it can be opened. The interior of the nut holds wood carvings with scenes from the life of Christ. These miniature reliefs show an incredible degree of finish with carving details well beyond the millimetre scale. In the present paper it is shown how synchrotron‐based computer X‐ray tomography revealed the structure and fabrication method of the bead. The central part of the relief was cut from a single piece of wood, rather than assembled from multiple components, underlining the extraordinary manual dexterity of its maker. In addition, a piece of fibrous material contained in the inner structure of the bead is revealed. This may have served as a carrier for an odorous compound, which would be in line with the religious function of the prayer nut.