Chip-Firing Games on Directed Graphs

We consider the following (solitary) game: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. We extend to directed graphs several results on the undirected version obtained earlier by the authors, P. Shor, and G. Tardos, and we discuss some new topics such as periodicity, reachability, and probabilistic aspects.Among the new results specifically concerning digraphs, we relate the length of the shortest period of an infinite game to the length of the longest terminating game, and also to the access time of random walks on the same graph. These questions involve a study of the Laplace operator for directed graphs. We show that for many graphs, in particular for undirected graphs, the problem whether a given position of the chips can be reached from the initial position is polynomial time solvable.Finally, we show how the basic properties of the probabilistic abacus can be derived from our results.     

Regiochemical Control and Suppression of Double Bond Isomerization in the Heck Arylation of 1-(Methoxycarbonyl)-2,5-dihydropyrrole

Arylation of 1-(methoxycarbonyl)-2,5-dihydropyrrole under standard Heck reaction conditions produces a mixture of compounds. The olefin undergoes two types of palladium-catalyzed reactions: (a) arylation to provide C-3 arylated derivatives and (b) competing double bond isomerization. Addition of silver carbonate and thallium acetate fully suppressed the isomerization, and good yields of C-3 substituted compounds were achieved after arylation with aryl halides. With regard to aryl triflates as arylating agents, addition of lithium chloride was necessary to promote the Heck reaction. This additive excluded the use of silver and thallium salts, but high regioselectivity and good yields could be obtained by employing tri-2-furylphosphine as ligand. Arylation was rendered both regioselective and enantioselective (58% ee) with 1-naphthyl triflate as substrate utilizing a (R)-BINAP/thallium acetate combination. The C-3 arylated enamides were converted further into the corresponding 3-arylpyrrolidines.     

Investigation of a cylindrical chemosorptive denuder for sampling and phase separation of toluene diisocyanate aerosols

A cylindrical chemosorptive denuder in series with a glass fibre filter has been evaluated for sampling toluene diisocyanate (TDI) aerosols. The sampler is designed for measuring personal exposure to diisocyanates. Several denuder coatings and derivatising reagents were investigated. Dimethylpolysiloxane (SE-30) and 5% phenyl dimethylpolysiloxane (SE-54) with either dibutylamine (DBA) or dipentylamine (DPeA) as derivatising reagents yielded the lowest vapour breakthrough (the amount (%) of the vapour that passes through the denuder), close to values predicted by theory. Immobilisation of the SE-30 denuder coating by in-situ cross-linking yielded comparable results. With an SE-30/DBA-coated denuder operating within an airflow range of 100–500 mL min^–1, the phase separation was shown to be consistent with theoretical predictions derived by use of the Gormley–Kennedy equation. This provides a means of calculating the vapour breakthrough and correcting experimentally obtained values with regard to vapour–particulate phase distribution, suggesting that the denuder can provide accurate phase-distribution measurements. The SE-30/DBA denuder can be used over a concentration range spanning nearly six orders of magnitude. Its capacity is sufficient to perform 15-min exposure measurements of a TDI aerosol with air concentrations as high as 1,700 g m^–3, 40 times higher than the Swedish occupational exposure limit (OEL). At the other end of the range, the estimated limit of detection (LOD) was less than 2 ng m^–3 for both the vapour and the aerosol phases when LC–ESI–MS–MS was used for chemical analysis.Electronic Supplementary Material Supplementary material for this article is available at     

A neutron powder diffraction study of the κ phase in the FeWC system

The crystal structure of the κ-carbide in the FeWC system has been refined from neutron powder diffraction data using the Rietveld profile analysis method. κ-(FeWC) is isostructural with κ-(CoWC); space group $\text{P6}{}_3\text{mmc}$; unit cell dimensions a = 7.7982(2)Å, c = 7.8298(4) Å. The structure refinement indicates $\text{Fe}\text{W}$ substitution at two of the tungsten sites, and 46% vacancies at one of the carbon sites. The composition corresponds to the formula Fe_3+xW_10?xC_4?y, with x = 0.57(3) and y = 0.46(1).     

Cycloaddition reactions of 2,3-didehydrothiophene generated by flow vacuum thermolysis of thiophene-2,3-dicarboxylic anhydride

Flow vacuum thermolysis (FVT) of thiophene-2,3-dicarboxylic anhydride ($\text{2}$) in the presence of 2,3-dimethylbutadiene ($\text{6}$) gives, in addition to 5,6-dimethylthianaphthene ($\text{9}$). small quantities of a dihydrodimethylthianaphthene ($\text{12}$) and another dimethylthianaphthene ($\text{13}$) which is probably also formed by dehydrogenation of $\text{12}$ with chloranil. The partial structures of these minor products are consistent with their being formed by a [2+2]-cycloaddition between $\text{6}$ and an intermediate aryne, 2,3-didehydrothiophene ($\text{1}$), followed by a rearrangement of the resulting adduct $\text{11}$ and dehydrogenation. FVT of $\text{2}$ in the presence of 2,5- ($\text{17b}$) or 3,4-dimethylthiophene ($\text{17c}$) also gave a mixture of the dimethylthianaphthenes ($\text{18}$$\text{22}$, $\text{23}$) which can be rationalized as arising by a [4+2]- and two [2+2]-cycloadditions of the aryne $\text{1}$ to the thiophenes $\text{17}$ with subsequent desulfurization. The lack of equilibration of the products $\text{18}$, $\text{22}$ and $\text{23}$, was demonstrated and their origin as a function of the structure and reactivity of the aryne $\text{1}$ discussed.     

Excited-state dynamics of fac-[ReI(L)(CO)3(phen)]+ and fac-[ReI(L)(CO)3(5-NO2-phen)]+ (L = imidazole, 4-ethylpyridine; phen = 1,10-phenanthroline) complexes

The nature and dynamics of the lowest excited states of fac-[Re(I)(L)(CO)(3)(phen)](+) and fac-[Re(I)(L)(CO)(3)(5-NO(2)-phen)](+) [L = Cl(-), 4-ethyl-pyridine (4-Etpy), imidazole (imH); phen = 1,10-phenanthroline] have been investigated by picosecond visible and IR transient absorption spectroscopy in aqueous (L = imH), acetonitrile (L = 4-Etpy, imH), and MeOH (L = imH) solutions. The phen complexes have long-lived Re(I) --> phen (3)MLCT excited states, characterized by CO stretching frequencies that are upshifted relative to their ground-state values and by widely split IR bands due to the out-of-phase A'(2) and A"nu(CO) vibrations. The lowest excited states of the 5-NO(2)-phen complexes also have (3)MLCT character; the larger upward nu(CO) shifts accord with much more extensive charge transfer from the Re(I)(CO)(3) unit to 5-NO(2)-phen in these states. Transient visible absorption spectra indicate that the excited electron is delocalized over the 5-NO(2)-phen ligand, which acquires radical anionic character. Similarly, involvement of the -NO(2) group in the Franck-Condon MLCT transition is manifested by the presence of an enhanced nu(NO(2)) band in the preresonance Raman spectrum of [Re(I)(4-Etpy)(CO)(3)(5-NO(2)-phen)](+). The Re(I) --> 5-NO(2)-phen (3)MLCT excited states are very short-lived: 7.6, 170, and 43 ps for L = Cl(-), 4-Etpy, and imH, respectively, in CH(3)CN solutions. The (3)MLCT excited state of [Re(I)(imH)(CO)(3)(5-NO(2)-phen)](+) is even shorter-lived in MeOH (15 ps) and H(2)O (1.3 ps). In addition to (3)MLCT, excitation of [Re(I)(imH)(CO)(3)(5-NO(2)-phen)](+) populates a (3)LLCT (imH --> 5-NO(2)-phen) excited state. Most of the (3)LLCT population decays to the ground state (time constants of 19 (H(2)O), 50 (MeOH), and 72 ps (CH(3)CN)); in a small fraction, however, deprotonation of the imH.+ ligand occurs, producing a long-lived species, [Re(I)(im.)(CO)(3)(5-NO(2)-phen).-]+.     

A convenient synthesis of phenols

Abstract

Anilines are rapidly, often within 60?minutes, converted into the corresponding phenols in up to 87% isolated yield. The presented experimentally simple protocol display broad compatibility with a variety of functional groups, and in particular, well suited for the preparation of methyl-substituted phenols. Such phenols are not easily available by other synthetic approaches. The formation of phenolic radical coupling products was not observed even for activated anilines using this open flask method.