Parrondo?s game using a discrete-time quantum walk

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A (B) to have a winning probability more than player B (A). Significance of the game strategy in information theory and physical applications are also discussed.     

NMR investigations of self-aggregation characteristics of SDS in a model assembled tri-block copolymer solution

The present work was undertaken with a view to understand the influence of a model non-ionic tri-block copolymer PEO-PPO-PEO (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)) with molecular weight 5800 i.e., P123 [(EO)(20)-(PO)(70)-(EO)(20)] on the self-aggregation characteristics of the anionic surfactant sodium dodecylsulfate (SDS) in aqueous solution (D(2)O) using NMR chemical shift, self-diffusion and nuclear spin-relaxation as suitable experimental probes. In addition, polymer diffusion has been monitored as a function of SDS concentration. The concentration-dependent chemical shift, diffusion data and relaxation data indicated the significant interaction of polymeric micelles with SDS monomers and micelles at lower and intermediate concentrations of SDS, whereas the weak interaction of the polymer with SDS micelles at higher concentrations of SDS. It has been observed that SDS starts aggregating on the polymer at a lower concentration i.e., critical aggregation concentration (cac=1.94 mM) compared to polymer-free situation, and the onset of secondary micelle concentration (C(2)=27.16 mM) points out the saturation of the 0.2 wt% polymer or free SDS monomers/micelles at higher concentrations of SDS. It has also been observed that the parameter cac is almost independent in the polymer concentrations of study. The TMS (tetramethylsilane) has been used as a solubilizate to measure the bound diffusion coefficient of SDS-polymer mixed system. The self-diffusion data were analyzed using two-site exchange model and the obtained information on aggregation dynamics was commensurate with that inferred from chemical shift and relaxation data. The information on slow motions of polymer-SDS system was also extracted using spin-spin and spin-lattice relaxation rate measurements. The relaxation data points out the disintegration of polymer network at higher concentrations of SDS. The present NMR investigations have been well corroborated by surface tension and conductivity measurements.     

Modified corroles with one meso-free carbon: synthesis and characterization

[reaction: see text] Synthesis of mono meso-free modified corroles by a [3+1] methodology is reported.     

Core-modified hexaphyrins; characterization of two- and four-ring inverted 26 pi aromatic macrocycles

[reaction: see text] Synthesis and structural characterization of aromatic core-modified 26 pi hexaphyrin analogues are reported.     

Inverted porphyrins and expanded porphyrins: An overview

Porphyrins and metallopophyrins have attracted the attention of chemists for the past 100 years or more owing to their widespread involvement in biology. More recently, synthetic porphyrins and porphyrin-like macrocycles have attracted the attention of researchers due to their diverse applications as sensitizers for photodynamic therapy, MRI contrasting agents, and complexing agents for larger metal ions and also for their anion binding abilities. The number of π-electrons in the porphyrin ring can be increased either by increasing the numberof conjugated double bonds between the pyrrole rings or by increasing the number of heterocyclic rings. Thus, 22π sapphyrins, 26π rubyrins, 30π heptaphyrins, 34π octaphyrins and higher cyclic polypyrrole analogues containing 40π, 48π, 64π, 80π and 96π systems have recently been reported in the literature. These macrocycles show rich structural diversity where normal and different kinds of inverted structures have been identified. In this review, an attempt has been made to collect the literature of the inverted porphyrins and expanded porphyrins reported until December 2001. Since themeso aryl expanded porphyrins have tendency to form both inverted and non-inverted structures more emphasis has been given tomeso aryl expanded porphyrins.     

Spectral and electrochemical properties of deformed short-chain basket-handle iron (III) porphyrins

The spectral and electrochemical properties of series of deformed iron(III) derivatives of short-chain basket-handle porphyrins are reported. 1HNMR and optical studies demonstrated that deformation arises because of the bridging of opposite phenyl groups by short chains. Axial ligation studies indicate that the straps present over both sides of the porphyrin ring do not prevent the entry of small ligands. Electrochemistry in four different solvents suggests the stabilisation of Fe(II) and Fe(I) over Fe(III) in strong coordinating solvents.     

Oxasmaragdyrin-ferrocene and oxacorrole-ferrocene conjugates: synthesis, structure, and nonlinear optical properties

Ferrocenyl macrocyclic conjugates involving 22 pi oxasmaragdyrins and 18 pi oxacorroles have been synthesized and characterized. The direct covalent linkage of the ferrocenyl moiety to the meso position of the macrocycle is achieved by simple oxidative coupling of appropriate precursors with trifluoroacetic acid as catalyst. The electronic coupling between the ferrocenyl moiety and the macrocyclic pi system is apparent from: a) the red shifts (293-718 cm(-1)) of the Soret and Q-bands in the electronic absorption spectra of ferrocenyl conjugates; b) the shift of oxidation potentials (50-130 mV) of both the ferrocene and the corrole rings to the positive potentials; and c) considerable shortening of the C-C bond which connects the ferrocene and the meso-carbon atom of the macrocycle. The single-crystal X-ray structure of oxasmaragdyrin-ferrocene conjugate 9 reveals the planarity of the 22 pi skeleton with very small deviations of the meso-carbon atoms. The meso-ferrocenyl substituent has a small dihedral angle of 38 degrees, making way for mixing of the molecular orbitals of the ferrocene and the macrocycle. However, the other two meso substituents are almost perpendicular to the mean plane, defined by the three meso carbon atoms. Classical C-H...O and nonclassical C-H...pi interactions lead to a two-dimensional supramolecular network. Ferrocene-smaragdyrin conjugate 9 bonds to a chloride ion in the protonated form and a rhodium(i) ion in the free base form. Nonlinear optical measurements reveal a larger nonlinear refractive index (-5.83 x 10(-8)cm(2)W(-1)) and figure of merit (2.28 x 10(-8)cm(3)W(-1)) for the rhodium smaragdyrin-ferrocene conjugate 19 than for the others, suggesting its possible application in optical devices.     

Synthesis of trisubstituted alkenes by reductive dehydroxylation of Baylis-Hillman adducts using polymethylhydrosiloxane (PMHS) and catalytic B(C6F5)3

B(C₆F₅)₃ as a catalyst and polymethylhydrosiloxane as a hydride source have been employed for the reductive dehydroxylation of Baylis-Hillman adducts wherein the hydride adds in an S_N2′ manner onto the unactivated allyl alcohol moiety with concomitant elimination of the hydroxy group along with double bond migration. The products formed were found to be E in the case of ester adducts and Z in the case of nitrile adducts.     

30pi aromatic meso-substituted heptaphyrin isomers: syntheses,characterization, and spectroscopic studies

The syntheses of new aromatic 30pi heptaphyrins either through a [5 + 2] or a [4 + 3] acid-catalyzed condensation and oxidative coupling reactions of easily available and air-stable precursors are reported. The methodology followed is not only simple and efficient but also allows synthesis of a range of heptaphyrins with different heteroatoms in the core. The oxidative coupling reactions of modified tripyrranes 11 and tetrapyrranes 12 were found to be dependent on the acid concentration used and as well as the substituents present on the meso position. The change of meso aryl substituents in 11 and 12 to meso mesityl substituents gave a new heptaphyrin 18. The structural characterization has been done with extensive 1H and 2D NMR studies. The heptaphyrins reported here show rich structural diversity when the connections of the heterocyclic rings are altered, and accordingly, one ring and two ring inversions have been observed. By a judicious choice of the precursors it has been possible to control the site of ring inversion either in the bithiophene unit or in the tripyrrane unit. Theoretical calculations performed on three different heptaphyrins, 4, 5, and 17, also reveal that the inverted structures are approximately 35-40 kJ lower in energy relative to the corresponding noninverted structures. Furthermore, one of the heptaphyrins 10c shows the presence of two conformers in solution in the ratio 1:2 and no interconversion between the conformers have been observed in the temperature range of 343-228 K. On protonation, the aromaticity and the ring inversions are retained and the deltadelta values vary in the range 10.07-20.59 ppm. The energies of the Soret maxima and the HOMO-LUMO gap vary linearly with the increase in pi electrons further justifying the aromatic nature of the heptaphyrins.     

Core-modified expanded porphyrins with large third-order nonlinear optical response

The third-order nonlinear optical response through measurement of two-photon absorption cross-sections (TPACS) for aromatic core-modified expanded porphyrin analogues by a femtosecond open aperture Z-scan method is reported. The values reported here are among the largest known so far in the literature for any organic molecules.