Weakly o-minimal structures and real closed fields

A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field is real closed. We also develop a substantial theory of definable sets in weakly o-minimal structures, patterned, as much as possible, after that for o-minimal structures.

     

High-efficiency energy transfer from carotenoids to a phthalocyanine in an artificial photosynthetic antenna

Two carotenoid pigments have been linked as axial ligands to the central silicon atom of a phthalocyanine derivative, forming molecular triad 1. Laser flash studies on the femtosecond and picosecond time scales show that both the carotenoid S1 and S2 excited states act as donor states in 1, resulting in highly efficient singlet energy transfer from the carotenoids to the phthalocyanine. Triplet energy transfer in the opposite direction was also observed. In polar solvents efficient electron transfer from a carotenoid to the phthalocyanine excited singlet state yields a charge-separated state that recombines to the ground state of 1.     

Discrete dinuclear cyano-bridged complexes

The cyano-bridged complexes [L14CoIIINCFeII(CN)5]-, [L14CoIIINCFeIII(CN)5], [L15CoIIINCFeII(CN)5]-, and [L15CoIIINCFeIII(CN)5] (L14 = 6-methyl-1,4,8,11-tetraazacyclotetradecan-6- amine, L15 = 10-methyl-1,4,8,12-tetraazacyclopentadecan-10-amine) are prepared and characterized both structurally and spectroscopically. In each complex, the pendant amine is trans to the bridging CN ligand, as determined by spectroscopy and X-ray crystallography: Na(trans-[L14CoIIINCFeII(CN)5]).8H2O, monoclinic space group P2(1)/c, a = 15.58(1) A, b = 19.797(4) A, c = 19.830(6) A, beta = 91.62(4) degrees, Z = 8; trans-[L14CoIIINCFeIII(CN)5].4H2O, monoclinic space group P2(1)/m, a = 9.9690(9) A, b = 13.316(1) A, c = 10.1180(8) A, beta = 90.720(6) degrees, Z = 2; [L15CoIIINCFeIII(CN)5].4H2O, triclinic space group P1, a = 9.454(1) A, b = 9.778(1) A, c = 9.865(2) A, alpha = 60.37(1) degrees, beta = 62.60(1) degrees, gamma = 65.82(1) degrees, Z = 1. A precursor to the 14-membered macrocyclic complexes is prepared for the first time, and its crystal structure is also reported: trans-I [CoL14Cl](ClO4)2, orthorhombic space group Pbca, a = 11.833(3) A, b = 13.363(2) A, c = 26.015(2) A, Z = 8. These compounds form part of a novel series of discrete CN-bridged dinuclear compounds. The mixed-valent CoIII-FeII compounds exhibit metal-to-metal charge-transfer (MMCT) transitions in the region 510-530 nm.     

Tuning the metal-to-metal charge transfer energy of cyano-bridged dinuclear complexes

The metal-to-metal charge transfer (MMCT) transitions of a series of Class II mixed valence dinuclear complexes bearing cyano bridging ligands may be varied systematically by variations to either the hexacyanometallate(II) donor or Co(III) acceptor moieties. Specifically, the new dinuclear species trans-[L(14S)CoNCFe(CN)(5)](-)(L(14S)= 6-methyl-1,11-diaza-4,8-dithia-cyclotetradecane-6-amine) and trans-[L(14)CoNCRu(CN)(5)](-)(L(14)= 6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine) have been prepared and their spectroscopic and electrochemical properties are compared with the relative trans-[L(14)CoNCFe(CN)(5)](-). The crystal structures of Na(trans-[L(14S)CoNCFe(CN)(5)]).51/2H(2)O.1/2EtOH, Na(trans-[L(14)CoNCRu(CN)(5)]).3H(2)O and Na(trans-[L(14)CoNCRu(CN)(5)]).8H(2)O are also reported. The ensuing changes to the MMCT energy have been examined within the framework of Hush theory, and it was found that the free energy change between the redox isomers was the dominant effect in altering the energy of the MMCT transition.     

Enhanced visible photoluminescence in ultrathin poly(3-hexylthiophene) films by incorporation of Au nanoparticles

Incorporation of non-luminescent dodecanethiolate-protected gold clusters into regioregular poly(3-hexylthiophene) films results in a 6-fold increase in the visible photoluminescence (PL) of the polymer, which arises predominantly from NP-induced structural changes in the composite films.     

Interpretable Groups, Stably Embedded Sets, and Vaughtian Pairs

The paper concerns sufficiently saturated structures M overa countable language with a unary predicate P. It is shown thatif P(M)is stably embedded and there are no Vaughtian pairs withrespect to P, then an infinite group is interpretable over M(in an infinitary sense of ‘interpretable’). Also,it is shown that if M is -categorical, f:DP is a 0-definablemap with finite fibres, and P(M) is stably embedded but D isnot, then some infinite group is first-order interpretable overM.     

Orbit-equivalent infinite permutation groups

Let G,H be closed permutation groups on an infinite set X, with H a subgroup of G. It is shown that if G and H are orbit-equivalent, that is, have the same orbits on the collection of finite subsets of X, and G is primitive but not 2-transitive, then G=H.     

Iron(III) complex of a crown ether-porphyrin conjugate and reversible binding of superoxide to its Iron(II) form

The synthesis and characterization of the Fe(III) complex of a novel crown ether-porphyrin conjugate, 52-N-(4-aza-18-crown-6)methyl-54,104,154,204-tetra-tert-butyl-56-methyl-5,10,15,20-tetraphenylporphyrin (H2Porph), as well as the corresponding hydroxo, dimeric, Fe(II), and peroxo species are reported. The crystal structure of [FeIII(Porph)Cl].H3O+.FeCl4-.C6H6.EtOH is also reported. [FeIII(Porph)(DMSO)2]+ and K[FeIII(Porph)(O22-)] are high-spin species (M?ssbauer data: delta = 0.38 mm s(-1), DeltaEq = 0.83 mm s(-1) and delta = 0.41 mm s(-1), DeltaEq = 0.51 mm s(-1), respectively), whereas in a solution of reduced [FeIII(Porph)(DMSO)2]+ complex the low-spin [FeII(Porph)(DMSO)2] (delta = 0.44 mm s(-1), DeltaEq = 1.32 mm s(-1)) and high-spin [FeII(Porph)(DMSO)] (delta = 1.27 mm s(-1), DeltaEq = 3.13 mm s(-1)) iron(II) species are observed. The reaction of [FeIII(Porph)(DMSO)2]+ with KO2 in DMSO has been investigated. The first reaction step, involving reduction to [FeII(Porph)(DMSO)2], was not investigated in detail because of parallel formation of an Fe(III)-hydroxo species. The kinetics and thermodynamics of the second reaction step, reversible binding of superoxide to the Fe(II) complex and formation of an Fe(III)-peroxo species, were studied in detail (by stopped-flow time-resolved UV/vis measurements in DMSO at 25 degrees C), resulting in kon = 36 500 +/- 500 M(-1) s(-1), koff = 0.21 +/- 0.01 s(-1) (direct measurements using an acid as a superoxide scavenger), and KO2- = (1.7 +/- 0.2) x 10(5) (superoxide binding constant kinetically obtained as kon/koff), (1.4 +/- 0.1) x 10(5), and (9.0 +/- 0.1) x 10(4) M(-1) (thermodynamically obtained in the absence and in the presence of 0.1 M NBu4PF6, respectively). Temperature-dependent kinetic measurements for kon (-40 to 25 degrees C in 3:7 DMSO/CH3CN mixture) yielded the activation parameters DeltaH = 61.2 +/- 0.9 kJ mol(-1) and DeltaS = +48 +/- 3 J K(-1) mol(-1). The observed reversible binding of superoxide to the metal center and the obtained kinetic and thermodynamic parameters are unique. The finding that fine-tuning of the proton concentration can cause the Fe(III)-peroxo species to release O2- and form an Fe(II) species is of biological interest, since this process might occur under very specific physiological conditions.