Some problems in metric fixed point theory

Three papers, published coincidentally and independently by Felix Browder, Dietrich G?hde, and W. A. Kirk in 1965, triggered a branch of mathematical research now called metric fixed point theory. This is a survey of some of the highlights of that theory, with a special emphasis on some of the problems that remain open. Dedicated to Felix Browder on the occasion of his 80th birthday     

Cation effect on anion separations by aza-crown ligands in liquid membranes

New carriers have been prepared based on the aza-18-crown-6 structure to facilitate membrane transport of ions. One of these incorporates four aza-18-crown-6 molecules bonded to a resorcinarene ring. The other, aza-18-crown-6 bonded to an undecyl chain, was studied as a monomeric analog. These carriers have been included in dichloromethane bulk liquid membranes (BLMs) to assess cation influence on competitive transport among anions (ReO₄⁻, NO₃⁻, ClO₄⁻). ReO₄⁻ was investigated as a non-radioactive analog of the pertechnetate anion, which is of interest in nuclear waste separations. The permeability values and selectivity for ReO₄⁻ and ClO₄⁻ were the greatest when neutral source and receiving phases were used with K⁺ as the co-transported cation. The carriers also showed selectivity for ReO₄⁻ and ClO₄⁻ over NO₃⁻ with K⁺ and Na⁺ as the co-transported cations using neutral and basic aqueous phase solutions. It was also found that some cations inhibit anion transport.     

Improving the effectiveness of interfacial trapping in removing single-walled carbon nanotube bundles

Single-walled carbon nanotube (SWNT) bundles are selectively removed from an aqueous dispersion containing individually suspended carbon nanotubes coated with gum Arabic via interfacial trapping. The suspensions are characterized with absorbance, fluorescence, and Raman spectroscopy as well as atomic force microscopy (AFM) and rheology. The resulting aqueous suspensions have better dispersion quality after interfacial trapping and can be further improved by altering the processing conditions. A two-step extraction process offers a simple and fast approach to preparing high-quality dispersions of individual SWNTs comparable to ultracentrifugation. Partitioning of SWNTs to the liquid-liquid interface is described by free energy changes. SWNT bundles prefer to reside at the interface over individually suspended SWNTs because of greater free energy changes.     

Photophysics of diplatinum polyynediyl oligomers: chain length dependence of the triplet state in sp carbon chains

The series of polyynes with the structure trans, trans-[Ar-Pt(P 2)-(C[triple bond]C) n -Pt(P 2)-Ar], where P = tri( p-tolyl)phosphine, Ar = p-tolyl, and n = 3, 4, 5, 6 (6, 8, 10, 12 sp carbon atoms), has been subjected to a comprehensive photophysical investigation. At low temperature ( T < 140 K) in a 2-methyltetrahydrofuran (MTHF) glass, the complexes exhibit moderately efficient phosphorescence appearing as a series of narrow (fwhm < 200 cm (-1)) vibronic bands separated by ca. 2100 cm (-1). The emission is assigned to a (3)pi,pi* triplet state that is concentrated on the sp carbon chain, and the vibronic progression arises from coupling of the excitation to the -C[triple bond]C- stretch. The 0-0 energy of the phosphorescence decreases with increasing sp carbon chain length, spanning a range of over 6000 cm (-1) across the series. Transient absorption spectroscopy carried out at ambient temperature confirms that the (3)pi,pi* triplet is produced efficiently, and it displays a strongly allowed triplet-triplet absorption. In the MTHF solvent glass ( T < 140 K), the emission lifetimes increase with emission energy. Analysis of the triplet nonradiative decay rates reveals a quantitative energy gap law correlation. The nonradiative decay rates can be calculated by using parameters recovered from a single-mode Franck-Condon fit of the emission spectra.     

Energy-consistent relativistic pseudopotentials for the 4d elements: atomic and molecular applications

Recently reported energy-consistent relativistic pseudopotentials have been used with series of matching correlation consistent basis sets in benchmark calculations of various atomic and molecular properties. The basis set convergence of the 4d metal electron affinities and 5s2-->5s0 excitation energies are reported at the CCSD(T) level of theory, and the effects of valence and 4s4p correlation are investigated. In addition the impact of correlating the low-lying 3d electrons was also studied in all-electron Douglas-Kroll-Hess (DKH) calculations, which also included the ionization potentials and 5s2-->5s1 excitation energies. For all four atomic properties, higher order coupled cluster calculations through CCSDTQ are reported. The final calculated values are generally all within 1 kcal/mol of experiment. A notable exception is the ionization potential of Tc, the currently accepted experimental value of which is suggested to be too high by about 3 kcal/mol. Molecular calculations are also reported for the low-lying electronic states of ZrO and RuF, as well as the ground electronic state of Pd2. The effects of spin-orbit coupling are investigated for these cases in pseudopotential calculations. Wherever possible, the pseudopotential results have been calibrated against DKH calculations with correlation consistent basis sets of triple-zeta quality. In all cases the calculated data for these species are in very good agreement with experiment. In particular, the correct electronic ground state for the RuF molecule (4Phi92) was obtained, which was made possible by utilizing systematic sequences of correlation consistent basis sets.     

Substitution and derivatization reactions of a water soluble iron(II) complex containing a self-assembled tetradentate phosphine ligand

Facile substitution reactions of the two water ligands in the hydrophilic tetradentate phosphine complex cis-[Fe{(HOCH2)P{CH2N(CH2P(CH2OH)2)CH2}2P(CH2OH)}(H2O)2](SO4) (abbreviated to [Fe(L1)(H2O)2](SO4), 1) take place upon addition of Cl-, NCS-, N3(-), CO3(2-) and CO to give [Fe(L1)X2] (2, X = Cl; 4, X = NCS; 5, X=N3), [Fe(L1)(kappa2-O(2)CO)], 6 and [Fe(L1)(CO)2](SO4), 7. The unsymmetrical mono-substituted intermediates [Fe(L1)(H2O)(CO)](SO(4)) and [Fe(L(1))(CO)(kappa(1)-OSO(3))] (8/9) have been identified spectroscopically en-route to 7. Treatment of 1 with acetic anhydride affords the acylated derivative [Fe{(AcOCH2)P{CH2N(CH2P(CH2OAc)2)CH2}2P(CH2OAc)}(kappa2-O(2)SO2)] (abbreviated to [Fe(L2)(kappa2-O(2)SO2)], 10), which has increased solubility over 1 in both organic solvents and water. Treatment of 1 with glycine does not lead to functionalisation of L1, but substitution of the aqua ligands occurs to form [Fe(L(1))(NH(2)CH(2)CO(2)-kappa(2)N,O)](HSO(4)), 11. Compound 10 reacts with chloride to form [Fe(L(2))Cl(2)] 12, and 12 reacts with CO in the presence of NaBPh4 to form [Fe(L2)Cl(CO)](BPh4) 13b. Both of the chlorides in 12 are substituted on reaction with NCS- and N3(-) to form [Fe(L2)(NCS)2] 14 and [Fe(L2)(N3)2] 15, respectively. Complexes 2.H2O, 4.2H2O, 5.0.812H2O, 6.1.7H2O, 7.H2O, 10.1.3CH3C(O)CH3, 12 and 15.0.5H2O have all been crystallographically characterised.     

Donor-acceptor biradicals as ground state analogues of photoinduced charge separated states

A Valence Bond Configuration Interaction (VBCI) model is used to relate the intraligand magnetic exchange interaction (J) to the electronic coupling matrix element (HAB) in Tp(Cum,MeZn)(SQNN), a compound that possesses a Donor-Acceptor (D-A) SemiQuinone-NitronylNitroxide (SQNN) biradical ligand. Within this framework, an SQ --> NN charge transfer state mixes with the ground state and stabilizes the spin triplet (S = 1). This charge-transfer transition is observed spectroscopically and probed using resonance Raman spectroscopy. In addition, the temperature-dependent electronic absorption spectrum of the Ni(II) complex, Tp(Cum,MeNi)(SQNN), has been studied. Exchange coupling between the S = 1 Ni(II) ion and S = 1 SQNN provides a mechanism for observing the formally spin-forbidden, ligand-based 3GC --> 1CTC transition. This provides a means of determining U, the mean GC --> CTC energy, and a one-center exchange integral, K(0). The experimental determination of J, U, and K(0) permits facile calculation of HAB, and we show that this methodology can be extended to determine the electronic coupling matrix element in related SQ-Bridge-NN molecules. As magnetic susceptibility measurements are easily acquired in the solid state, H(AB) may be effectively determined for single molecules in a known geometry, provided a crystal structure exists for the biradical complex. Thus, SQ-Bridge-NN molecules possess considerable potential for probing both geometric and electronic structure contributions to the magnitude of the electronic coupling matrix element associated with a given bridge fragment.