A Kekulé structure basis for phenylenes

By means of Kekulé structures and, in particular, their count K, many properties of benzenoid molecules can be rationalized. The analogous properties of non-benzenoid polycyclic conjugated molecules require the consideration of some, but not all, Kekulé structures, whose number is the precisely defined and long time known ‘algebraic structure count’ ASC. In the general case it is not known how to construct a Kekulé structure basis for non-benzenoid molecules, consisting of ASC Kekulé structures, ASC≤K. We now offer a solution of this problem for phenylenes and point out some applications.     

Balancing the Pauling bond orders in Kekuléan benzenoid hydrocarbons

We consider a cutting of the molecular graph B of a Kekuléan benzenoid molecule into two disconnected subgraphs, S and the other, by deleting from B certain edges. It is required that both subgraphs remain Kekuléan. The edges involved in this cutting are classified as starred and unstarred. A starred edge is incident to a starred carbon site of the subgraph S, whereas an unstarred edge to an unstarred carbon site of S. The following regularity is established: for any above-described cutting of any Kekuléan benzenoid system, the sum of the Pauling bond orders of the starred edges is equal to that for the unstarred edges.     

On the generalized approach to the structure count

A generalized approach to the structure count of n-radical-m-cation systems based on the properties of the acyclic polynomial is presented. The mathematical proof for the expression relating the structure count to the coefficients of the acyclic polynomial is given. The connection between the structure count of biradical structures and the number of Dewar structures is discussed and tested on some examples.     

Incorporating two different chromophores onto a silicon atom: the crystal structure and photophysical properties of 9‐{4‐[(9,9‐dimethyl‐9H‐fluoren‐2‐yl)dimethylsilyl]phenyl}‐9H‐carbazole

The crystal structure of the title bifunctional silicon‐bridged compound, C₃₅H₃₁NSi, (I), has been determined. The compound crystallizes in the centrosymmetric space group P2₁/c. In the crystal structure, the pairs of aryl rings in the two different chromophores, i.e. 9‐phenyl‐9H‐carbazole and 9,9‐dimethyl‐9H‐fluorene, are positioned orthogonally. In the crystal packing, no classical hydrogen bonding is observed. UV–Vis absorption and fluorescence emission spectra show that the central Si atom successfully breaks the electronic conjugation between the two different chromophores, and this was further analysed by density functional theory (DFT) calculations.     

Unprecedented μ3-O face-capping ligand in a [Mo6Br6L2Br6] (L = 0.5 O + 0.5 Br) molybdenum cluster unit: crystal structure of the Cs3Mo6Br13O oxybromide

The new Cs₃Mo₆Br₁₃O oxybromide, synthesized by solid-state chemistry, crystallizes in the trigonal system (Rc space group; a = 15.5784(2) Å, c = 19.5103(5) Å, V = 4100.5(1) Å³ and Z = 6). It is based on a [Mo₆L₁₄] unit that contains an unprecedented μ₃ face-capping oxygen. The crystal structure determined by single crystal X-ray diffraction is built up from discrete face-capped [Mo₆Brⁱ₆Lⁱ₂Br^a₆]^3– (L = 0.5 O + 0.5 Br) anionic units in which two inner positions are randomly occupied by one bromine and one oxygen whereas the other ligand positions are fully occupied by bromine. The cesium cations randomly occupy two close crystallographic positions generated by the A-B-C-A′-B′-C′ close-packed stacking of the units. The cesium site occupancy is related to the random distribution of oxygen and bromine on the Lⁱ inner positions. To cite this article: K. Kirakci et al., C. R. Chimie 8 (2005).     

Use of heat capacities for the estimation of cubic equation-of-state parameters—application to the prediction of very low vapor pressures of heavy hydrocarbons

Improvement in the prediction of very low vapor pressures is checked by introducing heat capacity data into the estimation of cubic equation-of-state (EOS) parameters. As the key parameter is the temperature-dependent parameter a, several expressions (mainly of exponential form) were investigated. All of them were chosen in order to show a consistent behavior for the two considered properties (vapor pressures and heat capacities). The cubic EOS used as an illustration is of the Peng–Robinson type applied to heavy hydrocarbons. No satisfactory refinement in the prediction of the very low vapor pressures was observed in comparison with the results obtained by extrapolating the EOS from medium to very low pressures. This work has, however, the following benefits: (1) to point out the changes that should be made to improve these predictions; (2) to inform on the accuracy that may be obtained if vapor pressures of heavy organic compounds are predicted from heat capacity data as the sole alternative for estimating the temperature-dependent parameter a of a cubic EOS; (3) to confirm the reliability of the cubic group-contribution (GC)-based EOS proposed by Coniglio et al. [Ind. Eng. Chem. Res. 39 (2000) 5037] when extrapolated for modeling crude oils or gas condensates encountered in the petroleum industry.     

DFT calculations for the structure and properties of polychlorodibenzo-<Emphasis Type="Italic">para</Emphasis>-dioxine anion-radicals

Calculations for molecules and anion-radicals (ARs) of polychlorodibenzo-para-dioxines (PCDDs) in gas phase have been performed by Becke-Lee-Yang-Parr (B3LYP) hybrid method. The peculiarity of PCDD AR structure consists in the fact that one of C-Cl bonds is approximately by 0.75 Å longer than the other C-Cl bonds and is about 2.6 Å. A symmetric structure of 2,3,7,8-tetrachlorodibenzo-para-dioxine (TCDD) AR is the local minimum on the potential energy surface, which is higher than the absolute minimum by 2.76 kcal/mol. The electron affinity values were computed. PCDDs with one or two chlorine atoms have negative values of the electron affinity, while those with three or more chlorine atoms have positive ones.     

High-pressure preparation, crystal structure, and properties of the new rare-earth oxoborate β-Dy2B4O9

In this work we report about a new rare-earth oxoborate β-Dy₂B₄O₉ synthesized under high-pressure/high-temperature conditions from Dy₂O₃ and boron oxide B₂O₃ in a B₂O₃/Na₂O₂ flux with a walker-type multianvil apparatus at 8 GPa and 1000°C. Single crystal X-ray structure determination of β-Dy₂B₄O₉ revealed: , a=616.2(1) pm, b=642.8(1) pm, c=748.5(1) pm, α=102.54(1)°, β=97.08(1)°, γ=102.45(1)°, Z=2, R1=0.0151, wR₂=0.0475 (all data). The compound exhibits a new structure type which is built up from bands of linked BO₃- (Δ) and tetrahedral BO₄-groups (□). The Dy³⁺-cations are positioned in the voids between the bands. According to the conception of fundamental building blocks β-Dy₂B₄O₉ can be classified with the notation 2Δ6□:Δ3□=4□=3□Δ. Furthermore we report about temperature-resolved in situ powder diffraction measurements and IR-spectroscopic investigations on β-Dy₂B₄O₉.