Conditions for the relativistic virial theorem for one electron

Conditions for the usual form of one-electron relativistic virial theorem to be satisfied are derived and illustrated. These can be applied to generate quality basic spinors for solving a one-electron Dirac equation.     

Rigidity of Interfaces in the Falicov–Kimball Model

We analyze the thermodynamic properties of interfaces in the three-dimensional Falicov–Kimball model, which can be viewed as a primitive quantum lattice model of crystalline matter. In the strong coupling limit, the ionic subsystem of this model is governed by the Hamiltonian of an effective classical spin model whose leading part is the Ising Hamiltonian. We prove that the 100 interface in this model, at half-filling, is rigid, as in the three-dimensional Ising model. However, despite the above similarities with the Ising model, the thermodynamic properties of its 111 interface are very different. We prove that even though this interface is expected to be unstable for the Ising model, it is stable for the Falicov–Kimball model at sufficiently low temperatures. This rigidity results from a phenomenon of ground-state selection and is a consequence of the Fermi statistics of the electrons in the model.     

Analysis of a Chiral Dielectric Supported Broadband Helix Slow-Wave Structure for Millimeter-Wave TWTs

A novel technique of broadbanding a helical slow-wave structure through negative dispersion shaping is proposed. The model considers a simple continuous chiral dielectric support for the helix inside a metallic barrel, unlike conventional helix slow-wave structures with three discrete dielectric supports at 120⁰ apart. The dispersion relation of the slow-wave structure was derived following sheath-helix abstraction, suitably benchmarked for special cases, and was used for analyzing the dispersion behavior of a typical slow-wave structure. Chiral dielectric loading could easily provide negative dispersion characteristics (required for broadband operation) by merely controlling the chirality parameter alone. The scheme with its simple geometric configuration is expected to be useful for millimeter-wave devices providing better thermal management. The basic concept was presented as a conference abstract at the 27th IEEE International Conference on Infrared and Millimeter Waves, California, 22–26 September 2002, as: S. K. Datta, E. V. Jayashree, S. D. Veena, and Lalit Kumar, “Broadbanding of a Helical Slow-Wave Structure Using Chiral Dielectric Loading.”     

Synthesis and biological evaluation of 12-, 13-, 14-membered macrolides and open chain 2,6-trans-disubstituted dihydropyran analogues for aspergillides

Stereoselective synthesis of twenty (three 12-, five 13- and twelve 14-membered) macrolides and seventeen functionalized 2,6-trans-disubstituted dihydropyran derivatives have been achieved. The key reactions include an Achmatowicz rearrangement, Ferrier-type alkynylation, Yamaguchi macrolactonization and Lindlar’s hydrogenation. Biological screening of the synthesised compounds showed moderate activity against human cancer cell-lines.     

Synthesis of star-shaped pyrrole-based C3-symmetric molecules via ring-closing metathesis,Buchwald–Hartwig cross-coupling and Clauson–Kaas pyrrole synthesis as key steps

We have demonstrated three contrasting synthetic strategies to assemble pyrrole-based C₃-symmetric molecule. Here, ring-closing metathesis (RCM), Buchwald–Hartwig cross-coupling and Clauson–Kaas pyrrole synthesis have been used as key steps. Interestingly, readily available starting materials such as 4-aminoacetophenone, 4-bromo acetophenone and 4-nitro acetophenone have been used as starting materials. Grubbs’ first generation catalyst (G-I) is useful for one-pot RCM and aromatization sequence without the involvement of additional reagents. We also report photophysical properties of these star-shaped molecules.     

Dithiobissuccinimidyl propionate self assembled monolayer based cholesterol biosensor

A dithiobissuccinimidyl propionate (DTSP) self-assembled monolayer (SAM) prepared onto a gold (Au) surface has been utilized for covalent immobilization of cholesterol oxidase (ChOx) and cholesterol esterase (ChEt). These ChOx-ChEt/DTSP/Au bio-electrodes have been characterized using electrochemical impedance and cyclic voltammetric (CV) techniques, respectively. Differential pulse voltammetry (DPV) has been used for enzymatic assay of immobilized ChOx and ChEt onto the DTSP modified gold surface as a function of cholesterol oleate concentration. The response measurement conducted on ChOx-ChEt/DTSP/Au bio-electrode reveal the value of Michaelis-Menten constant (Km) as 0.95 mM suggesting enhanced affinity of enzymes (ChOx and ChEt). The ChOx-ChEt/DTSP/Au bio-electrodes show linearity in range of 50 to 400 mg dl(-1) of cholesterol oleate and the shelf-life of more than 50 days when stored at 4 degrees C. This biosensing electrode shows correlation coefficient of 0.9973 and standard deviation of regression as 0.859 microA.     

Diversity of new structural types in polynuclear iron chemistry with a tridentate N,N,O ligand

The syntheses, crystal structures, and magnetochemical characterization of four new iron clusters [Fe7O4(O2CPh)11(dmem)2] (1), [Fe7O4(O2CMe)11(dmem)2] (2), [Fe6O2(OH)4(O2CBut)8(dmem)2] (3), and [Fe3O(O2CBut)2(N3)3(dmem)2] (4) (dmemH=Me2NCH2CH2N(Me)CH2CH2OH)=2-{[2-(dimethylamino)ethyl]methylamino}ethanol) are reported. The reaction of dmemH with [Fe3O(O2CR)6(H2O)3](NO3) (R=Ph (1), Me (2), and But (3)) gave 1, 2, and 3, respectively, whereas 4 was obtained from the reaction of 3 with sodium azide. The complexes all possess rare or novel core topologies. The core of 1 comprises two [Fe4(mu3-O)2]8+ butterfly units sharing a common body Fe atom. The core of 2 consists of a [Fe3O3] ring with each doubly bridging O2- ion becoming mu3 by also bridging to a third, external Fe atom; a seventh Fe atom is attached on the outside of this core via an additional mu3-O2- ion. The core of 3 consists of a [Fe4(mu3-O)2]8+ butterfly unit with an Fe atom attached above and below this by bridging O atoms. Finally, the core of 4 is an isosceles triangle bridged by a mu3-O2- ion with a rare T-shaped geometry and with the azide groups all bound terminally. Variable-temperature, solid-state dc, and ac magnetization studies were carried out on complexes 1-4 in the 5.0-300 K range. Fitting of the obtained magnetization (M) vs field (H) and temperature (T) data by matrix diagonalization and including only axial anisotropy (zero-field splitting) established that 1, 2, and 4 each possess an S=5/2 ground state spin, whereas 3 has an S=5 ground state. As is usually the case, good fits of the magnetization data could be obtained with both positive and negative D values. To obtain more accurate values and to determine the sign of D, high-frequency EPR studies were carried out on single crystals of representative complexes 1.4MeCN and 3.2MeCN, and these gave D=+0.62 cm-1 and |E|>or=0.067 cm-1 for 1.4MeCN and D=-0.25 cm-1 for 3.2MeCN. The magnetic susceptibility data for 4 were fit to the theoretical chiM vs T expression derived by the use of an isotropic Heisenberg spin Hamiltonian and the Van Vleck equation, and this revealed the pairwise exchange parameters to be antiferromagnetic with values of Ja=-3.6 cm-1 and Jb=-45.9 cm-1. The combined results demonstrate the ligating flexibility of dmem and its usefulness in the synthesis of a variety of Fex molecular species.     

Kinetic selectivity in the N-alkylation of 2-pyridyl porphyrins: a facile approach to the alphaalphabetabeta scaffold

meso-Tetrakis(2-pyridyl)-porphyrin (2-PyP) was tetra-N-alkylated with three different alpha-bromoacetamides to generate a series of water-soluble N-alkylpyridinium porphyrins (1-3). The product mixtures showed a marked preference for the formation of the alphaalphabetabeta atropisomer. With alpha-bromo-N-n-butylacetamide, the corresponding alphaalphabetabeta 2-tetrakis (N-n-butylacetamido)-pyridyl porphyrin (2-TnBuPyP, 3) was obtained in 69% isolated yield in a single step. Prolonged heating lead to equilibration of the rotational isomers for the less bulky alkyl groups, indicating that the observed preference is a kinetic effect. The intermediate products for the N-bornyl case were identified by LC/ESI-MS to deduce an explanation for the observed nonstatistical selectivity.     

Magneto-Coulomb effect in carbon nanotube quantum dots filled with magnetic nanoparticles

Electrical transport measurements of carbon nanotubes filled with magnetic iron nanoparticles are reported. Low-temperature (40 mK) magnetoresistance measurements showed conductance hysteresis with sharp jumps at the switching fields of the nanoparticles. Depending on the gate voltage, positive or negative hysteresis was observed. The results are explained in terms of a magneto-Coulomb effect: The spin flip of the iron island at a nonzero magnetic field causes a shift of the chemical potential induced by the change of Zeeman energy; i.e., an effective charge variation is detected by the nanotube quantum dot.     

Water as a source for oxygen incorporation into acceptor doped SrTiO3 single crystals

The possibility of the incorporation of oxygen and deuteron stemming from the dissociation of water into iron doped strontium titanate single crystals with two different iron concentrations (0.13 and 0.013 at.% Fe) has been investigated. Double labeled water (²H₂¹⁸O) was used for Isotope Exchange Depth Profiling. It acts as an incorporation source of ¹⁸O into Fe-doped SrTiO₃(100) single crystals. Total dissociation of the water takes place in the vicinity of the SrTiO₃ surface and both oxygen and deuteron incorporate into the SrTiO₃. The results of the diffusion profile evaluation confirm that oxygen and deuteron migrate independently in the bulk. Oxygen incorporates into the material at high incorporation rates, practically comparable with the ones resulting from an O₂ atmosphere. The interaction of H₂O with SrTiO₃(100) surfaces was further studied with Metastable Induced Electron Spectroscopy and Ultraviolet Photoelectron Spectroscopy. Neither partial dissociation of water molecules nor any significant formation of surface OD groups was observed.